Academic confidence and dyslexia at university

Outcomes

 

4.1 Overview

I - Objectives

 

The objectives of the analysis were to enable the research hypotheses (sub-section 1.4) to be addressed: firstly, by comparing ABC data from the research groups of dyslexic and non-dyslexic students; secondly, by comparing ABC data from the dyslexic students of the Control subgroup with data from the non-dyslexic students in the Base subgroup; finally, ABC data for the subgroup of quasi-dyslexic students of the Test subgroup were compared with those in the Control subgroup. Students were filtered into subgroups according to their levels of dyslexia-ness. This was determined by the output of the Dyslexia Index Profiler section of the self-report questionnaire that all participants in the study had completed (see sub-section 4.3(III) below). Through use of unique, continuous range input sliders, which displaced more conventional fixed anchor-point Likert-style scales, degrees of agreement with the questionnaire's scale-item dimension statements were converted into quantitative data. A text-input section of the questionnaire collected additional qualitative data, optionally provided.

II - Analysing quantitative data - rationales:

1. Internal consistency (reliability) - Cronbach's 'alpha' (ɑ)

 

Both the metrics in this study gauged the constructs of interest using linear scales. The existing, ABC Scale operationalized academic confidence, and the Dyslexia Index Profiler was developed especially for this study to assess participants' levels of dyslexia-ness. Each scale comprised multiple dimensions, collectively designed to assess their respective underlying construct. In order to have confidence that the data generated was meaningful it was important to assess the consistency (reliability) and validity of the scales (where validity is the precision of the scale). Typically used in social science research, notably in psychology, is the Cronbach's ɑ coefficient of internal reliability (Lund & Lund 2018). An ɑ value within the range 0.3 < α < 0.7 is considered as acceptable with preferred values being closest to the upper limit (Kline, 1986). On this basis, precedents have shown acceptable levels of internal reliability for the ABC Scale, determined by Cronbach's ɑ > 0.7, (Putwain & Sanders, 2016; Shaukat & Bashir, 2015; Nicholson et.al., 2013; Aguila Ochoa & Sander, 2012; Sander & Sanders, 2009; Sanders & Sander, 2007). Clearly, as the Dx Profiler has been developed for this current study, no prior measures of the scale's internal reliability or validity are available.

However, several issues emerge which indicate that an assessment of a scale's internal reliability using the ɑ coefficient should be considered tentatively. In the first instance, excessively high levels of ɑ (i.e. > 0.9) are suggested to indicate scale-item redundancy, that is, where some items (dimensions) are gauging very similar traits (Streiner, 2003; Panayides, 2013), although there is a lack of agreement about which level of ɑ should be chosen as the critical value for this interpretation with ɑ > 0.7 frequently considered as the popular 'rule of thumb' (e.g.: Morera & Stokes, 2016). This is despite (computational) evidence that a scale with more items, supposedly gauging the same underlying dimension, will naturally increase the value of ɑ (Cortina, 1993; Nunnally & Bernstein, 1994; Tavakol & Dennick, 2011). Secondly, it is important to note that Cronbach's ɑ tests the consistency of responses within a datapool as opposed to the reliability of the scale per se, and therefore is attributable to a specific use of the scale (Streiner, 2003; Boyle, 2015; Louangrath, 2018). Thirdly, and especially when used in conjunction with dimension reduction techniques, it is reasonable to suggests that the factors which emerge from such a reduction, that is, the sub-scales, should also be evalulted for their reliability, and these outcomes cited together with the ɑ value for the complete scale.

However, frameworks have been suggested for improved reporting and interpretation of internal consistency estimates to present a more comprehensive picture of the reliability of data collection procedures, particularly data elicited through self-report questionnaires. In particular, and consistent with the approach adopted in this current study for reporting effect size differences (see (2), below), reporting an estimate for a confidence interval for ɑ in addition to the single-point value, noting particularly the upper-tail limit is considered to be one improvement (Onwuegbuzie and Daniel, 2002). The idea of providing a confidence interval for Cronbach's α is attractive because the value of the coefficient is only a point estimate of the likely internal consistency of the scale (and hence the construct of interest). Interval estimates are stronger, not least as the point estimate value, α, is claimed by Cronbach in his original (1951) paper to be most likely a lower-bound estimate of score consistency. This implies that the traditionally calculated and reported single value of α is likely to be an under-estimate of the true internal consistency of the scale, were it possible to apply the process to the background population. Hence the upper-limit confidence interval can be reported in addition to the point-value of Cronbach's α because this is likely to be a more generalizable report about the internal consistency of the scale.

 

This principle is adopted in this current study, with confidence intervals calculated using Fisher's (1915) transformation which maps the Pearson Product-Moment Correlation Coefficient, r, (upon which Cronbach's alpha (α) is derived) onto a value, Z', which he showed to be approximately normally distributed and hence, confidence interval estimates could be constructed. Therefore it follows that Fisher's Z' can be used to transform Cronbach's alpha and subsequently create confidence interval estimates for of alpha. This process enabled a more complete reporting of the internal consistency of the ABC Scale, the Dx Profiler, and their respective sub-scales (identified through dimension reduction) for the datapool, and for each of the research groups, ND, DI (Table 12, sub-section 4.6).

2. Effect sizes

 

Effect size measures were used as the principal statistical evidence in this study. Effect size challenges the traditional convention that the p-value, an arbitrarily determined threshold derived from Null Hypothesis Significance Testing (NHST) (Vila et.al., 2016), is the most important data analysis outcome response to determine whether an observed effect is real or can be attributed to chance events (Maher et al., 2013). Effect size values are a measure of either the magnitude of associations or the magnitude of differences, depending on the nature of the data sets being analysed. Effect size is an absolute value measure, as opposed to the significance, of an observed effect (Cumming 2012), and provides a generally interpretable, quantitative statement about the magnitude of a difference in [or association between] observations (Fritz, et.al., 2012). When clearly defined in a study's methodology and reported together with their respective confidence intervals, effect sizes provide an improved way to interpret data (Ferguson, 2016). Effect size is easy to calculate, and when used to gauge the between-groups difference between means, is generally reported as Cohen's d (Cohen, 1988). If the groups being compared have dissimlar sample sizes (as is the case in this current study), the unbiased estimate of d can be used, alternatively referred to as Hedges' g, (Hedges, 1981)calculated using the weighted, pooled standard deviations of the datasets. Effect size is increasingly prevalent in quantitative analysis (Gliner, et.al., 2001; Sullivan & Feinn, 2012; Carson, 2012; Maher, et.al., 2013), and is particularly useful when observed measurements have no intrinsic meaning, such as with data formulated from Likert-style scales (Sullivan & Feinn, 2012). Guidance for researchers on the use and reporting of effect size is becoming more widely available (Ferguson, 2016; Lorah, 2018; Funder & Ozer, 2019), possibly due to some leading social science journals requiring effect size to be part of the data analysis in studies submitted for publication (Fritz, et.al., 2012; Funder & Ozer, 2019). The use of effect size as a method for reporting statistically important analysis outcomes is especially gaining traction in education, social science and psychology research (Kelley & Preacher, 2012; Rollins, et al., 2019), not least in studies about dyslexia, where it is claimed to be a vital statistic for quantifying intervention outcomes designed to assist struggling readers (ibid).

3. Null-hypothesis significance testing; ANOVA

 

Notwithstanding (2) above, the effect size data analyses were supported by measures of the statistical significance of the difference between independent sample means, determined through Student's t-test outcomes, to acknowledge the continued value of NHST in social science research. Thus, when taken together with effect sizes and their confidence intervals, comprehensive and pragmatic interpretation of the experimental outcomes can be discussed. One-tail t-tests were conducted in accordance with the alternative hypotheses stated (sub-section 1.4). Homogeneity of variances was established using Levene's Test, and according to the output, the appropriate p-value was taken, with the conventional 5% level being adopted as the significance boundary value. It is acknowledged that the application of ANOVA to this data may have been appropriate had dyslexia-ness been categorized into 'high', 'moderate', 'low', or other sub-gradations, that is, that the independent variable was categorical in nature (Moore & McCabe, 1999; Lund & Lund, 2016). The Student's t-test was considered as a better choice because it is easier to interpret, commonly used, and appropriate when the independent variable (in this case, Dyslexia Index), is continuous in nature (ibid).

4. Dimension reduction

 

Although these statistical processes (1,2, above) proved sufficient to address the research hypotheses, dimension reduction by principal components analysis (PCA) was applied later as a secondary process to determine whether meaningful factor structures could be established for both the ABC Scale and the Dyslexia Index metric. The objective was to explore the influences of groups of similar dimensions of dyslexia-ness (Dx factors) on academic confidence to search for more nuanced explanations for differences in ABC. The PCA process is said to be useful to explore whether a multi-item scale that is attempting to evaluate a construct can be reduced into a simpler structure with fewer components (Kline, 1994, Kanyongo, 2005), although there remains considerable debate about how to best identify the most appropriate number of factors to retain from those which emerge from dimension reduction (e.g.: Velicer, et.al, 2000). 

 

As a precedent, Sander and Sanders (2003) recognized that dimension reduction may be appropriate for their original, 24-item ABC Scale. The procedure generated a 6-factor structure, the components of which were designated as Grades, Studying, Verbalizing, Attendance, Understanding, and Requesting. By combining datasets from their earlier studies, a subsequent analysis found that the ABC Scale could be reduced to 17 items with 4 factors, designated as Grades, Verbalizing, Studying and Attendance (Sander & Sanders, 2009). The remaining dimensions of the reduced, 17-item ABC Scale were unamended. Hence, by retaining the the full, 24-item scale so that an independent, current-study PCA could be conducted, it was possible to calculate alternative 17-item overall mean ABC values simultaneously. The outcomes were examined for differences, which, although were found to be small and not significant (see Table ## below), nevertheless did indicate that the choice of scale may impact on the conclusions of a study were they based solely on NHST outcomes. Also shown, are the corresponding ABC values that emerged from the PCA on this current study's data, which suggested that a 3-factor, 21-dimension scale may be appropriate for this datapool.

 

Now just as Cronbach's ɑ can offer a measure of internal consistency to a local construct scale (and identify scale item redundancy), factor analysis is ascribable to the dataset onto which it is applied. It was considered therefore that the Sander and Sanders factor structures may not be entirely applicable universally, despite being widely used by other researchers in one form (ABC24-6) or the other (ABC17-4) (e.g.: de la Fuente et al., 2013; de la Fuente et al., 2014; Hilale & Alexander, 2009; Ochoa et al., 2012; Willis, 2010; Keinhuis et al., 2011; Lynch & Webber, 2011; Shaukat & Bashir, 2016). Indeed when reviewing the ABC Scale, Stankov et.al., (in Boyle et.al., 2015) implied that more work should be done to consolidate some aspects of the ABC Scale, not so much by levelling criticism at its construction or theoretical underpinnings, but more so to suggest that as a relatively new measure (> 2003) it would benefit from wider applications in the field, and subsequent scrutiny about how it is built and what it is attempting to measure. In the event, only one study was found (Corkery et.al., 2011) which appeared to share this cautious approach for adopting the ABC Scale per se, choosing instead to conduct a local factor analysis to determine the structure of the Scale according to their data, setting a single precendent for taking the same course of action in this current study. 

However, it also remains unclear from the Sander and Sanders original, and subsequent studies, whether the components analyses adopted for both the individual and the later, combined datasets, were compared with a factor structure that may have occurred by chance. Indeed, from the body of literature examined where the ABC Scale has been used either as the principal metric or as an additional aspect of the analysis processes, no studies' data analysis appear to suggest that any comparisons with a factor structure which may have occurred randomly were conducted. Common practice to determine the number of factors to retain in these, and in numerous other studies where component analysis has been applied use either a visual inspection of the scree plot of eigenvalues against components (Cattell, 1996; Horn & Engstrom, 1979) looking for the point where the slope changes markedly as a means to determine the number of components to declare; or otherwise choose components which present initial eigenvalues > 1 in the table of total variance explained, as those to be included in the final factor structure (Kaiser, 1960). Both processes are not without their difficulties: In the first instance, determining the the number of components to include from visual inspection of the scree plot relies on subjective judgement (e.g.: Zwick & Velicer, 1982), despite common convention; and when relying on eigenvalues > 1 in the table of total variance explained, when no clear distinction exists between two (or more) components that are very close to this critical value, it becomes difficult to decide which components to include and which to omit.

In this current study, early iterations of the process suggested that solutions of four, five, or six factors for both ABC and for Dx could be reasonably supported, using both the eigenvalues > 1, and visual interpretations of the scree plots criteria. In the event, five-factor solutions for both variables were initially adopted, based on realistically determining outcomes that could lead to a meaningful interpretation of the data generated. However, prompted by a Monte Carlo simulation to examine both a factor structure that may have occurred by chance (using Velicer's (1976) MAP test, and also a parallel analysis, both conducted in SPSS according to the guidance provided by O'Connor (2000)), and also the likelihood of assumption violations unduly influencing solutions for retaining factors (Hutchinson & Bandalos, 1997; Kanyongo, 2005), later re-analysis of the data suggested that a three-factor solution may be a better model (see sub-section 4.6 below). Guided by the dimensional themes that constituted the factors in each of the metrics, ABC Factors were designated as: Factor 1: Study Efficacy; Factor 2: Academic Engagement; Factor 3: Organization and Planning; and Dx Factors designated as: Factor 1: Language and Literacy; Factor 2: Thinking, Processing, and Memory; Factor 3: Organization and Time-management, which were closely aligned with the themes that emerged from a close interpretation of the BDA definition of dyslexia (see sub-section 3.3(III.2 Section 2(2/II)), above). Subsequently adopting these factor structures enabled the construction of a 3 x 3 cell comparison matrix of effect sizes and significance testing outcomes of Dx Factors versus ABC Factors to be established (see sub-section 4.6, below). Although considered as a useful aid for a deeper interpretation of the analysis outcomes, the conclusions reached on this basis remained tentative, not least due to the relatively small size of the datapool (n=166), especially when sifted into subgroups, and the untested viability of the Dx Profiler outside this current study.

5. Multiple Regression Analysis

Finally, a tentative multiple regression analysis was conducted to add a further dimension to the statistical evidence used to address the research hypotheses generated thus far, by examining differences between observed and expected ABC outcomes according to Dx inputs. Precedents suggest that multi-variable regression analysis can be valuable in dyslexia research (see sub-section 5.#) to add substance to the rationales which underpin the multi-factorial approaches to understanding dyslexia (see sub-section 2.1(II/6)). Hence regression analysis was considered to have value in this current study where the objective was to explore the predictive validity for indicating levels of ABC based on Dyslexia Index, given that the Dyslexia Index Profiler also uses a multivariable design. Whilst this proved interesting in itself, the greater value was to use the generated prediction equations to augment the evidence collected in this study so far, that students with quasi­-dyslexia, which may be unidentified dyslexia, return higher than expected levels of ABC than their dyslexia-identified peers.

III - Analysing qualitative data - rationales:

Qualitative data was not formally analysed, instead, elements of these data were used to elaborate the discussion element of the thesis where apposite (see Section 5). However, the principles for applying an Interpretative Phenomenological Analysis (IPA) to these data were considered, as IPA is typically used to explore, interpret and understand a phenomenon in people - dyslexia in students in this current study - from the perspectives of the lived-experiences of the individuals of interest (Reid et al., 2005). But an IPA approach was dismissed for three reasons: firstly, understanding how students with dyslexia make sense of their learning and study experiences at university and how they attach meaning to the life events that occur in this context (e.g.: Smith et al., 2009), was not the main focus of the research. Instead, the interest was quite specific, that is, trying to understand the ways that such students perceive how their dyslexia impacts on their academic confidence. Secondly, these (qualitative) data were only received from students in the dyslexic group. This was not by design, merely that no participants in the non-dyslexic group provided any data in this form. Hence it was considered that formal, qualitative analysis would have been skewed and not generalizable across the datapool. Lastly, although IPA attempts to uncover themes in qualitative data, it is conventionally conducted with small, purposive samples of typically fewer than ten participants (Hefferon & Gil-Rodriguez, 2011), with analysis being overly descriptive at times, rather than more deeply interpretative (ibid). In this study, the qualitative data was drawn from a moderately large dataset (n=68) rather than by selecting a small, representative sample.

Hence, although some elements of IPA are utilized, for example in identifying thematic narratives, these are used to support the quantitative outcomes of the data analysis, and the formal process was not adopted. That said, the data provided an extensive representation of the challenges and difficulties faced by dyslexic students at university, and hence may be used in a more focused study later.

4.2  Terminology

 

For ease of reference in this section, the meanings of labels, terms, acronyms and designations used in the reporting and discussion of the data, results and analysis which follows, is re-presented in Table 3.

 
 

Table 3:     Definitions and terminology (updated July 2020)

4.3  Results

I      Demographics

 

A total of n=183 questionnaire replies were received. Seventeen were discarded due to Dyslexia Index Profiler data less than 50% complete, and so to determine these individuals' Dyslexia Index was considered unrealistic.

 

The demographic distribution of the datapool according to dyslexia status, gender; home residency, and study level is shown in Table 4. The equivalent distributions for the Test and the Base subgroups, which were both subsets of the non-dyslexic students’ group; and for the Control subgroup, which was a subset of the dyslexic students’ group, are presented in Table 5.

 

I Distribution by gender

Overall, female participants (n=113, 67%) outnumbered male participants (n=55, 33%) by a factor of approximately 2 to 1. Amongst the dyslexic participants, females (n=53, 78%) outnumbered males (n=15, 22%) by more than 3 to 1. Of students recruited through the open invitation to all students and who subsequently formed research group ND (n=98), the distribution by gender, showed females (n=60) to substantially outnumber males (n=38) (39%). It is not known whether this is representative of the gender distribution of students more widely in the university as these data were not available.

 

II Distribution by domicile

Participants were asked to declare whether they were a 'home' or an 'international/overseas' student. Non-UK EU students were not identified as a distinct subgroup. National data for 2016/17 (HESA, 2018) demonstrated a broadly similar distribution although those data were for student enrolment for that academic year rather than a measure of the domicile distribution of all students studying at UK institutions at that time. It is reasonable to assume that the ratio of 'home' students to non-UK students would not be substantially different were an aggregated figure used (which was unavailable).

III Distribution by study level

Data about level of study was collected to determine whether the datapool represented a reasonable cross-sectional match to student communities attending UK universities more generally. Although a wide selection was available in the questionnaire for participants to choose the level of study which most closely matched their own, these data were grouped as either study at up to and including level 6 (equivalent to final-year undergraduate), or higher than level 6. Those participants who indicated study for professional or vocational qualifications were grouped with post-graduates, and that to be consistent with national levels, those studying at Foundation/Access level also includes those studying at pre-level 4 (pre-1st year undergraduate). National data for 2016/17 (HESA, 2018) showed that 54% of the UK student population were undergraduates, 12% were attending Foundation or Access courses, 31% were studying on post-graduate taught programmes and 3% were post-graduate researchers. Hence, where study at level 6 or lower accounted for 66% of the student population nationally, undergraduate respondents in this study (n=124, 75%) are slightly over-represented, and that the proportion studying at post-graduate level is somewhat under-represented (n=42, 25%).

 
 

Table 4: Demographic distribution of the datapool by dyslexia status, home domicile, gender, and study level

‡ Study level according to the Regulated Qualifications Framework for England and Wales (Ofqual, 2015) * +1 respondent study level not disclosed; ✟ +1 studying for Professional or Vocational qualification

Table 5: Demographic distribution of Test, Base and Control research subgroups by home domicile, gender and study level.

‡ Study level according to the Regulated Qualifications Framework for England and Wales (Ofqual, 2015)

 

 

 

II  How students with dyslexia learned of their dyslexia

 

The impact of a diagnosis of dyslexia on Academic Behavioural Confidence

 

This study's hypotheses were grounded on the premise that the dyslexia label may be one of the contributing factors to reduced ABC in students with dyslexia, and which may be especially likely when this label emerged from diagnosing dyslexia as a disability (see sub-ection 2.1(IV)). Thus, one aspect of the enquiry explored how dyslexic students were told about their dyslexia. A sub-hypothesis was constructed to test whether students whose dyslexia was diagnosed to them as a disability have substantially lower levels of academic confidence when compared with students who were told about their dyslexia, otherwise. Hence, a null sub-hypothesis was constructed to test against alternatives:

H0: the terminology used to tell dyslexic students of their dyslexia has no impact on their academic confidence;

AH1: students whose dyslexia is diagnosed to them as a disability (or as a difficulty (=AH2); or as a disability or a difficulty (=AH3)) show lower levels of academic confidence in comparison to those who are told about their dyslexia in other ways.

Participants in this current study who declared their dyslexia were invited to report how they learned about their dyslexia by selecting options to complete a simple statement (Figure 13).

 
Fig11.png

Figure 13:    Dyslexic students completed a verb-noun option sentence to indicate how they learned of their dyslexia

It was reasonable to assume that the 68 students who declared their dyslexia had participated in a formal dyslexia screening and/or assessment at university, or during their earlier years in education; 64/68 (94%) provided data (Table 6). 22/64 (34%) respondents said that their dyslexia was diagnosed to them as a disability; 40/64 (64%) respondents said that their dyslexia was diagnosed to them as a disability or a difficulty. 15/64 (23%) students learned of their dyslexia by one of the other alternatives offered, with 3/15 ( < 5% of the total) had their dyslexia described or identified as a difference. Of the 4 students with dyslexia who did not respond, it is not known whether this was due to a reluctance to disclose, or that an option that matched their recollection about how they learned of their dyslexia was not present.

Table 6: Summary of dyslexia self report statement: 'My dyslexia was ... to me as a learning ...

The 64 datasets were sorted into subgroups comprising: those whose dyslexia was diagnosed to them as a disability (subgroup DS); those whose dyslexia was diagnosed to them as a difficulty (subgroup DF); leaving the remainder to be aggregated into a third subgroup E.

 

The mean average ABC both overall and for each of the three ABC Factors (determined through PCA (see below, sub-section 4.4(II)) was calculated for each subgroup and also for subgroups DS and DF combined. Hedges 'g' effect size differences were calculated, supported by t-test outcomes. In accordance with the hypotheses, one-tail tests were applied at the 5% significance level. Levene's Test for homogeneity of variances was applied and where violated, the outcome for unequal populations variances is quoted. (Table 7).

 

Moderate to large effect size differences in mean ABC-overall values are indicated between subgroup E, and subgroups DF, DS, and DF+DS combined (g=0.704, 0.627, 0.639 respectively), supported by t-test outcomes indicating significant differences between mean values in all cases. Hence, students whose dyslexia was diagnosed as a disability or as a difficulty (or either), returned significantly lower overall ABC mean values when compared with students who were told of their dyslexia in any of the alternative ways. Thus the null hypothesis is rejected in favour of each of the alternatives, respectively.

At a more granular level, examining the outcomes for differences in ABC at a factorial level reveals a slightly more complex picture. Moderate, or moderate to large effect sizes were indicated between mean ABC factor values for each of the three subgroup comparisons, and although these were not universally supported by significant differences in means, most t-test outcomes were less than, (i.e. significant), or in the region of the 5% critical value (i.e., marginal). See Section 5 for an interpretation of these results.

 
 
 

Table 7:       Comparing ABC mean values of dyslexic students according to how they learned of their dyslexia

III    Dyslexia Index Profiler Data

 

I Internal reliability of the Dx Profiler

The Dx Profiler was at first, a 20-item scale, later found to have a 3-factor, sub-scale structure (see sub-section 4.5, below). However, given the relatively small sample of dyslexic students (n=68) upon which the sub-scale structure was determinined, it was considered wise to treat outcomes that relied on any of the three factors as tentative at best. In order to have greater confidence that the factor structure of the Dx Profiler is robust and stable, more data from a wider range of sources would be required. This could be the topic for a subsequent study. Nevertheless, and with these caveats in mind, the levels of internal reliability of the 20-item scale and of the sub-scales were assessed using the Cronbachs's ɑ criterion. According to the conventional interpretation of ɑ values (see 4.1(II/1) above), the Dx Profiler overall, together with each of the 3 sub-scales, presented acceptable levels of internal reliability (Table ##) for examining the datasets in this datapool.

However, the reliability analysis also suggested that some dimensions in the 20-item scale may be redundant by contributing minimally to the overall Dyslexia Index value for each respondent. By considering the matrix of correlation coefficients between dimensions to identify pairs of dimensions that showed a correlation of r > 0.7, eliminating each in turn and then re-running the reliability analysis, after several iterations the 20-item scale was reduced to a shorter, 16-item scale which demonstrated similar levels of reliability (Table ##). Dimension reduction was also later applied to this scale (sub-section 4.5) which also determined a three-factor structure. 

 

 

 

 

 

II Preliminary results

Table 8 presents an overview of the distributions of Dx values across the two main research groups, ND and DI, showing the groups’ sample sizes, the range of Dx values, the sample means and medians, and 95% confidence intervals for the population Dx means; together with outcomes for effect size difference between the sample means and the corresponding, supporting t-test.

Table ## Cronbach's ɑ reliability coefficients for the Dx Profiler

Table 8:     Dyslexia Index summary according to research group

Visual inspections of both distributions indicated them to be approximately normal by broadly exhibiting the characteristic bell-shaped outline (Figure 14), although the distribution for the non-dyslexic group does appear bimodal, which was unexpected. However, the Shapiro-Wilks test (p>0.05) provided confirmation of normality in both cases, further supported by interpretation of Q-Q plots (Figure 15) where the datapoints for each research group are all positioned approximately along the diagonal. There were no outliers in either distribution, determined by examination of the respective box-plots.

 

There are marked differences between Dx values for the two groups where both the sample mean Dx and median Dx are much lower for the non-dyslexic students. A very large effect size of g = 1.36 [95% CI: 1.01, 1.70] (Sullivan & Feinn, 2012) between the Dx sample means, was supported by an independent samples t-test, indicating a significantly lower mean Dx for students with dyslexia ( t(162) = 9.12, p<0.001; Levene’s test for homogeneity of variances was violated (F(164) = 7.65, p=0.006)). Hence, the Dyslexia Index Profiler is returning the expected, high Dx value for the majority of students who declared their dyslexia, and a much lower value for those who declared no dyslexic learning challenges. Thus, it was discriminating well between those two groups, with the Profiler exhibiting good sensitivity.

 
 
 
DxNormalDistributions.png

Figure 14:   Distributions of Dyslexia Index for the non-dyslexic (RG:ND) and the dyslexic groups (RG:DI).

Fig15.png

Figure 15:   Normal Q-Q plots for Dyslexia Index.

 

III Setting boundary values for Dx

 

1. Dx boundary value for the Test, and Control subgroups

 

Studies suggests that the proportion of known dyslexics studying at university is likely to be much lower than the true number of students with dyslexia or dyslexia-like study characteristics (e.g.: Richardson & Wydell, 2003; MacCullagh et al., 2016; Henderson, 2017). This current study was grounded on this (amongst other) research outcomes, and the core of the research design was to devise a robust mechanism to detect such quasi-dyslexic students so that their academic confidence could be compared to the other groups and subgroups which emerged from the datapool. Hence, to establish this Test subgroup of quasi-dyslexic students, it was necessary to define a boundary Dx value in the group of non-dyslexic students above which datasets would be filtered into the Test subgroup. At the design stage, setting a value of Dx = 600 as the filter was considered reasonable because this would correspond to a 60% agreement on average for the set of 20 dyslexia-ness dimensions that constituted the Dx Profiler. The Profiler was set so that higher percentage dimension-statement agreement was designed to be the marker for higher levels of dyslexia-ness.

 

Applying this boundary value to datasets in the non-dyslexic group generated a Test subgroup of n=17 quasi-dyslexic students - that is, individuals with no previously reported dyslexia but who appeared to be presenting similar levels of dyslexia-ness to students the dyslexic group. Although the size of this sample is small, this was expected, and considered large enough for some meaningful results to be derived later, although generalizability would be correspondingly tentative. Applying the same Dx filter value to datasets in the dyslexic group would establish the Control subgroup of students presenting similarly high levels of dyslexia-ness. In the event, approximately two-thirds of students with declared dyslexia returned a Dx value > 600.

However, in order for the academic confidence of the Test and Control subgroups to be justifiably compared later (through ABC Scale outcomes), it was important to establish that the defining, Dx parameters for each of these two subgroups were similar, that is, statistically not significantly different from each other. At the Dx = 600 filter boundary level, the mean Dx for the Test and Control subgroups were Dx = 690, 725 respectively. Conducting a one-tail t-test determined a non-significant difference between these means although the outcome was marginal (t(26) = 1.67; p = 0.053). Following several further iterations of this process based on selecting different boundary Dx values close to Dx = 600 (so that datasets were included or omitted into the respective subgroups accordingly), an outcome that was considered satisfactory was established at Dx = 592.5. This emerged from a t-test outcome of t(29) = 1.52, p = 0.070, being a less marginal result, hence providing more confidence that the sample means of the Test and Control subgroups (Dx = 685, 716, respectively) are not significantly different. These outcomes suggested that this adjustment of the boundary Dx criteria was unlikely to have a substantial impact on the composition of datasets in these subgroups. Indeed, the sample size of the Test subgroup increased from n=17 to n=18, and of the Control subgroup from n = 45 to n = 47 indicating only 3 additional datasets were now included as a consequence of this slightly lower boundary value. Hence the the filter boundary value of Dx = 592.5 was adopted.

 

2. Dx boundary value for the Base subgroup

Secondly, a lower boundary value was required to filter the additional comparator subgroup of students from research group ND who were presenting low levels of dyslexia-ness - the Base subgroup. It was considered reasonable to set this value at Dx = 400, representing a mean average agreement of 40% with the dyslexia-ness dimensions in the Profiler. This generated a Base subgroup of n=44, representing 45% of the non-dyslexic students, or 55% of the remaining students (in research group ND) after the Test subgroup had been filtered out. It is of note that a sizeable minority (n=36) of non-dyslexic students did present Dx levels between the two boundary values (400 < Dx < 592.5) with more than half of these (n=22) presenting levels of dyslexia-ness of 500 < Dx < 592.5), which accounts for the bimodal distribution of the complete group of non-dyslexic students (Figure ## above). By contrast, the Dx outputs of only 2 students with declared dyslexia (from research group DI) presented Dx values of Dx < 400 (respondent #16517091: Dx=340; respondent #90438618: Dx=376). However the analysis did not identify these as outliers to be removed, based on the exclusion criteria defined above. Hence, these remain anomalous results for other reasons, possibly that the conventional, dyslexia identifying processes that were likely to have been used with these individuals may have mis-identified them as dyslexic. No additional information about these students was available to confirm this or not. Figure 16 uses the Dyslexia Continuum to summarize these analyses.

Figure ##: Research groups and subgroups located on the Dyslexia-ness Continuum

 

4.4 Comparing ABC levels

Mean levels of Academic Behavioural Confidence between non-dyslexic students and dyslexic students overall, and between the Test, Control and Base subgroups of quasi-dyslexic, strongly dyslexic, and strongly non-dyslexic students, respectively, (Table 9), have enabled the research hypotheses to be addressed (see sub-section 1.4):

1. In comparison with their non-dyslexic peers, (RG:ND), students with a declared dyslexic learning difference (RG:DI) present a significantly lower mean ABC (67.21, 58.45, respectively), indicated by a moderate-to-large effect size ( g = 0.604, [0.287, 0.919]), supported by a significant difference in sample means ( t(134) = 3.75; < 0.001). Thus, sufficient evidence is presented to reject Null Hypothesis (1), in favour of Alternative Hypothesis (1) that non-dyslexic students present a higher, overall level of ABC than their non-dyslexic peers.

2. In comparison with their strongly non-dyslexic peers in the Base subgroup, students in the Control subgroup of identified, dyslexic students also present a significantly lower mean ABC (72.31, 57.56, respectively), indicated by a large effect size ( g = 1.061 [0.616, 1.500]), supported by a significant difference in sample means ( t(86) = 5.05; p < 0.001).

3. In comparison with students in the Control subgrop of identified, dyslexic students, quasi-dyslexic students in the Test subgroup present a significantly higher mean ABC (57.56, 64.92, respectively), indicated by a moderate effect size ( g = 0.506 [-0.048, 1.056]), supported by a significant difference in sample means ( t(38) = 1.99; p = 0.0268). Thus sufficient evidence is presented to reject Null Hypothesis (2), in favour of Alternative Hypothesis (2) that quasi-dyslexic students present a higher overall level of ABC than their dyslexic peers.

 

Table 9: Summary of ABC mean values by research group and subgroup

4.5 Dimension reduction

Applying dimension reduction to the Dx Profiler and ABC Scale.

Both the Dx Profiler and the ABC Scale are multi-dimensional, linear scales. Although complete-scale outcomes have enabled the research hypotheses to be address and conclusions drawn, precedents set for the ABC Scale (see sub-section 4.1(II/3) above) indicated that applying dimension reduction to explore any factor structure which may emerge could reveal more nuanced outcomes, subsequently permitting a deeper interpretation of the data collected in this current study.

Assumptions and preliminary work

 

The data in this project uses the two scales of ABC and Dyslexia Index which are each comprised of continuous variable, linear scale items. Of the many dimension reduction techniques available, Principal Component Analysis (PCA) was chosen as the most appropriate firstly, because all precedents for dimension reduction applied to the ABC Scale had used this process, and hence guidance was available; secondly, a factor structure that emerged from PCA on the data in this current study could then be considered alongside existing factor structures for the ABC Scale which had emerged through a similar process. For Dyslexia Index, also a linear scale, both to maintain a consistency of dimension reduction approach, and also to minimize computational complexity, PCA was the preferred choice.

Dyslexia Index comprises 20 scale item variables and the ABC Scale comprises 24. An analysis of the inter-variable correlation matrix for both metrics showed that for Dyslexia Index, of the 190 possible correlation outcomes, 80 returned a Pearson correlation coefficient of r ≥ 0.3 with all variables bar one returning at least one correlation of r ≥ 0.3 with any other variable. For the ABC Scale, 138 out of the 300 possible correlations returned a coefficient of r ≥ 0.3 with all variables returning at least one correlation of r ≥ 0.3. For PCA to be valid, it is considered that a scale-item variable that presents a correlation of r ≥ 0.3 with at least one other scale-item variable is worthy of inclusion in the analysis (Hinton et al., 2004). Furthermore, sufficient sampling adequacy is fundamental to PCA, but this adequacy is a function of the total number of observations rather than to the sample sizes(s) per se. Statistical conventions indicate that a sample size of ≥ 150 observations is a sufficient condition (Guadagnoli & Velicer, 1988) although a later study suggests that aspects of the variables and the study design have an impact on determining an appropriate level of sampling adequacy, recommending that this is improved with a higher number of observations (McCallum et al., 1999).

 

In this current study, 4,032 observations for ABC and 3,360 for Dyslexia Index were recorded. The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy produced a value of 0.866 for the Dyslexia Index metric and coincidentally, KMO = 0.866 for the ABC Scale. Measures of sampling adequacy for individual variables were examined to ensure that these also confirm the appropriateness for factor analysis. For the Dyslexia Index metric, the individual variable measures returned values of 0.605 ≤ KMO ≤ 0.919, and for ABC, returned values of 0.753 ≤ KMO ≤ 0.929. According to Kaiser's (1974) own classification, KMO values can range from 0 to 1, with a value of KMO ≥ 0.5 considered to be desirable (Hinton el.al, 2004). Finally, the null hypothesis that there are no correlations between any of the variables was tested using Barlett’s Test of Sphericity where a rejection is sought as determined by a p-value of p < 0.05. When applied to both the ABC Scale and to Dyslexia Index, the test returned values of p < 0.005. Thus for both metrics, the null hypothesis that there are no correlations between the metrics' variables is rejected, hence suggesting that there are correlations between the variables and therefore justification for running the PCA is met.

 

I      PCA on Dyslexia Index

 

1. Examining scale item redundancy

 

PCA has been used to help to identify scale items that might be considered as redundant - that is, are not contributing to the evaluation of the construct in a helpful way and hence might be discarded. This has been done through use of Cronbach's alpha (α) which is widely used to establish the internal reliability of data scales. It is important to note that the coefficient is a measure for determining the extent to which scale items reflect the consistency of scores obtained in specific samples and does not assess the reliability of the scale per se (Boyle et al., 2015), because it is reporting a feature or property of the individuals' responses who have actually taken part in the questionnaire process. This means that although the alpha value provides some indication of internal consistency it is not necessarily evaluating the homogeneity, that is, the unidimensionality of a set of items that constitute a scale.

Scale item redundancy in the Dx Profiler

It would be expected that a meta-analysis of several similar studies which all used the scale would be required before general confidence in the internal consistency of the scale could be established. Since the Dyslexia Index (Dx) metric has been especially developed for use in this current project this is not possible. Nevertheless, and with this caveat in mind, calculating Cronbach's alpha for the Dx metric can provide a useful indicator of its likely internal consistency.

 

The α value for the Dyslexia Index (Dx) 20-item scale computed to α = 0.852 which appears to indicate a high level of internal consistency. However, when the value of α exceeds 0.7, this may indicate that some scale items are not providing much additional contribution to the metric (Kline, 1986). When the potentially redundant Dx scale items were identified through this analysis and removed, the resulting 16-item scale returned a value of α = 0.889. The scale items that were removed were:

Dx 03: ‘I find it very challenging to manage my time efficiently;

Dx 05: ‘I think I am a highly organized learner’;

Dx 07: ‘I generally remember appointments and arrive on time’;

Dx 13: ‘I find following directions to get to places quite straightforward’.

The higher value of α appears to be indicating that the internal consistency of the scale is enhanced and hence suggests that discarding these 4 scale items from the Dyslexia Index Profiler may have little impact on the overall Dx values. However, this new value of α is even further above the apparently critical value of α = 0.7, suggesting that removing these four dimensions may be of dubious value.

 

By recalculating Dx for all datasets according to the reduced, 16-item scale, mean Dx values could be re-determined for the non-dyslexic, and dyslexic groups ,and for the Test, Control and Base subgroups. Differences between means, and also between respective medians and ranges emerged (Table 10), but were considered unlikely to have a substantial impact on the compositions of the subgroups. Nevertheless, differences in mean ABC values were examined (Table 11)  where the changes in both the sample sizes of the subgroups and the mean values of ABC data are small as to be reasonably considered negligible.

 
 

Table 10: Comparing basic statistics of groups and subgroups for the 20-item (Dx20) and 16-item (Dx16) Dyslexia Index Profilers.

Table 11: Impact on subgroup compositions and respective mean ABC values according to Dx20, Dx16 criteria.

 

Hence the full, 20-point scale has been retained for the further analyses, not least so that the scale items that would have been discarded could be retained to contribute to the more detailed, dimension-by-dimension comparisons that were subsequently conducted.

 

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Table 12:    Cronbach’s α and upper 95% confidence limit for α for the datapool and research groups ND, DI.

In conclusion, respectable values for both α and for the upper confidence limit for α have been established for the datapool and both research groups which adds evidence for the strong internal consistency for the Dyslexia Index (20-point) scale.

 

 

Proportion of variance explained

The prime objective of dimension reduction into factors through PCA is to determine how many factors are worth retaining in the final solution so that as much of the total variance as possible can be explained. Using the Eigenvalue-1 extraction criteria (Kaiser, 1960) typically used (Lund & Lund, 2018) five factors emerged from the analysis for the Dx Scale. Between them, these five factors accounted for 60.4% of the total variance (Table 13), respectively, 31.7%, 9.9%, 7.6%. 6.0% and 5.3% of the total variance for Dyslexia Index. Inspection of the scree plot (Figure 18) suggested that retaining these five factors would be appropriate although it can be seen that it is possible that a six-factor solution may be equally applicable because the initial eigenvalues for components 5 and 6 were both very close to 1, (1.06, 0.988); or even that a four-factor solution may be the most appropriate as the eigenvalue for the fourth component in the 5-factor solution stood at a value of 1.20.

Fig18.png

Figure 18:   Scree plot for total variance explained for Dyslexia Index scale, five-factor solution.

 
 
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Table 13:    Total variance explained for Dyslexia Index

To explore this, PCA was applied to the data twice more with a forced extraction of firstly six components and secondly with four components. Both of these produced similar outputs to the original, five-factor solution, although it was harder to determine a reasonable structure with six factors as the number of dimensions loading onto more than one factor was increased and hence the overall structure became less clear. With four factors in the extraction more than half of the dimensions loaded onto just one factor and hence it was felt the discriminative power of the scale would be reduced were this solution to be adopted. Thus, it was considered that the five-factor solution could be accepted as the most reasonable structure for the metric Dyslexia Index.

Table 14 shows the complete, Rotated Component Matrix that was finally adopted, presents the factor loadings of each of the Dyslexia Index dimensions onto their respective factors and also how each of the factors were subsequently labelled to reflect the overall characteristics of the respective dimensions within them. The loading is the correlation between the variable and the factor and this is the figure presented in line with each dimension in the respective factor column. For example, in Table 11, for the first dimension 3.20: I get really anxious if I'm asked to read 'out loud', the communalities extraction value of 0.573 indicates that 57.3% of this dimension's variance can be explained by the all of the factors. According to research convention, serious attention is paid to loading factors of > 0.32 and that a loading of > 0.71 is 'excellent' (Comrey & Lee, 2013). Note that although loadings are calculated for all dimensions in all factors, only factor loadings > 0.3 are presented in Table 14 to make it less congested and easier to comprehend. Thus, the row of data for dimension 3.20 shows only the value of 0.829 for a loading onto Factor 1, Reading, Writing, Spelling because the loadings onto the other four factors are less than 0.3.

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Table 14:    Rotated Component Matrix for Dyslexia Index 20-dimension scale

These communalities are reported alongside the Rotated Component Matrix in Table 14 where this groups the 20 dimensions into the five components/factors, with dimensions listed in descending order according to loading. The table indicates 'rotated' components where this is the mathematical process that places the factors in the best (geometrical) position to enable easier interpretation. For these data varimax rotation was applied, being an orthogonal rotation method which assumes that the factors in the analysis are uncorrelated. Other rotations are possible and rather than exhaustively work through several of these, in the interests of expediency it was considered only necessary to check whether these data were best analysed using an orthogonal (eg: varimax) rather than an oblique (eg: direct oblimin) rotation. For these data, the factor correlation matrix (not shown) derived through an oblimin rotation showed only one correlation to be (marginally) > 0.32, considered as the critical factor for determining whether an oblique rather than an orthogonal rotation is the most appropriate (Tabachnik & Fiddel, 2007).

 

Hence the orthogonal (varimax) rotation was preferred for these data. In the event, the varimax and the oblimin rotations generated the same distribution of dimensions into the emergent factors, implying that either would have been appropriate. However, the factor structure in both cases was such that some dimensions loaded onto more than one factor. Where this occurred, the troublesome dimension was assigned to the factor onto which its loading was greatest - that is, where there was the greatest correlation between the dimension and the factor (Lund & Lund, 2016-2018).

 

Kline (1986) suggests that more often than not a single, simple factor structure is elusive and it remains the task of the researcher to establish the most appropriate interpretation of the analysis that makes sense in the context of the project. Thus, the first-conducted, varimax factor analysis for the Dyslexia Index Profiler seemed reasonable. Hence it was considered justifiable to retain the factor structure that emerged through this process for the remaining data analysis.

Hence the five factors that were considered as the most acceptable structure emerged as:

  1. Dx Factor: Reading, writing, spelling (dimension #)

    • #20: gets anxious when asked to read aloud

    • #08: when reading, repeats a line or misses out a line altogether

    • #01: remembers thinking of themselves as slower at learning to read than their peers

    • #06: in writing, frequently uses the wrong words for an intended meaning

    • #09: in writing, struggles to put ideas into a sensible order

    • #02: weak spelling

  2. Dx Factor: Thinking and processing

    • #15: considered by friends to be an innovative or creative problem-solver

    • #17: regularly gets ‘lefts’ and ‘rights’ mixed up

    • #18: often told by tutors that essays are confusing to read

    • #11: prefers mindmaps and diagrams over lists or bullet points when planning assignments or writing

    • #10: when at school, remembers mixing up similar-looking letters

    • #19: gets muddled when searching for information

    • #16: struggles when following lists of instructions or making sense of them

  3. Dx Factor: Organization and time-management

    • #05: considers themselves as a highly organized learner

    • #03: finds time-management challenging

    • #07: remembers appointments and arrives on time

  4. Dx Factor: Verbalizing and scoping

    • #14: prefers the big picture rather then focusing on detail

    • #04: considers themselves better at explaining things verbally rather than in writing

  5. Dx Factor: Working memory

    • #13: finds following directions to get to places easy

    • #12: is hopeless at remembering things, eg phone numbers

 

Visualizing Dx Factor Values

 

The factorial analysis for Dyslexia Index has enabled radar charts to be constructed which present an overview of the distribution of Dx factor values for the three research subgroups (Figures 19-21). These charts display the factor profile for every student with profiles overlaid to generate a composite profile map for each subgroup. (Note that in Figures 20, 21 only the first page of respondents are listed in the key). In ways that are much easier to spot than through inspection of the full data tables, these graphical representations of the five factor values for students in each subgroup firstly reveal stark contrasts between the factor profiles of non-dyslexic students in the Base subgroup and dyslexic students in the Control subgroup; and secondly identify the similarities in profile maps between students in the Test subgroup of quasi-dyslexic students and those for dyslexic students in the Control subgroup.

 

This implies strong dyslexia-ness similarities between students with known dyslexia and the quasi-dyslexic students. Both of these are notably different from the collective profile map for students in the non-dyslexic Base subgroup where it is clear to see the skew away from the two Dyslexia Index factors, 'Reading, Writing, Spelling' and 'Thinking, Processing. Furthermore, this profile map indicates reduced Dyslexia Index Factor values overall for students in the Base subgroup in comparison with students with declared dyslexia or quasi-dyslexia. Aside from more easily revealing differences in the subgroups at the factorial level, which will be discussed below (sub-section 4.6), this representation further underpins the Dyslexia Index Profiler as an effective discriminator for the purposes of this study.

Fig19.png

Figure 19:   Radar chart of Dx Factor distributions for respondents in the Base subgroup of non-dyslexic students.

Fig20.png

Figure 20:   Radar chart of Dx Factor distributions for respondents in the Control subgroup of dyslexic students.

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Figure 21:   Radar chart of Dx Factor distributions for respondents in the Test subgroup of quasi-dyslexic students.

Table 15 amplifies these differentiated characteristics in summary overview of the sample mean Dx factor values for each subgroup, together with corresponding 95% confidence intervals for population means. (See Appendix 8.4 for Tables 34-36 showing data for every student in each of the research subgroups).

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Table 15:    Dyslexia Index Factors for research subgroup DNI

These data demonstrates similarities in mean Dx Factor values across the factor range between dyslexic and quasi-dyslexic students. Furthermore, it is evident that in all factors except Dx Factor 3, mean Dx Factor values for the non-dyslexic subgroup are lower than for the dyslexic, and the quasi-dyslexic subgroups. These data are consistent with the visual patterns presented in the profile maps (Figures 19-21). Differences between the factor means of the Test and Control subgroups were tested (Table 16a); between the Base and the Control subgroups (Table 16b), and between the Base and the Test subgroups (Table 16c). The outcome adds support for the effectiveness of the Dx Profiler as a discriminator by identifying the similarities between the factor means for the Test and the Control subgroups where no significant differences were recorded with the exception of Factor 1, Reading, Writing, Spelling where the mean value for the dyslexic students was significantly higher than that for the quasi-dyslexic students. Although this may be taken as an indication of weakness in the Dx Profiler, it could also be a sample-size generated anomaly, indicating that further development of the Dx Profiler may be warranted with larger sample sizes. 

 

As for comparisons between the Base subgroup and the Control and Test subgroups, it can be seen that the converse outcome is established between the Control subgroup and the Base subgroup where, again with the exception of Dx Factor 3, Organization and Time Management, significant differences between the Dx Factor means are recorded indicating that overall, students in the Base subgroup are presenting very low levels of dyslexia-ness. It is of note that for Dx Factor 3, Organization and Time Management, the mean Dx Factor values for all three research subgroups are not significantly different from each other (Dx = 586.78 (Base); Dx = 615.72 (Control); Dx = 635.53 (Test)) and possible explanations are provided in sub-section 5.4 below.

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Table 16a:    Comparing Dx Factor mean values between the Test and Control subgroups.

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Table 16b:    Comparing Dx Factor mean values between the Base and Control subgroups.

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Table 16c:    Comparing Dx Factor mean values between the Base and the Test subgroups.

 
 
 
 
 

Comparing differences in Dyslexia Index dimensions between research subgroups at a dimensional level

 

Further to examining differences in Dyslexia Index Factors, Dyslexia Index has been explored on a dimension by dimension basis as part of the process of trying to tease out which characteristics might account for the differences in ABC between the three research subgroups.

 

Table 17 lists all 20 dimensions of Dyslexia Index (Dx) and shows the mean Dx levels firstly between the two, main research groups - students who declared their dyslexia, and students who declared no dyslexic learning difference; and secondly across all three subgroups. Note that the values are all 0 < Dx < 100 and that for each respondent it has been the mean of the weighted aggregates of these dimensional values, scaled to 0 < Dx < 1000 which generates the respondent's overall Dyslexia Index (Dx). Underneath the actual mean values, both the t-test p-values and the Hedges 'g' effect size differences between pairs of groups and subgroups are shown.

It can be seen that for most of the dimensions, the differences in mean Dx values between dyslexic and non-dyslexic students (RG:DI and RG:ND) are substantial with the largest absolute difference being for Dimension 20, I get really anxious if I'm asked to read out loud, with a Dx difference of 32.57 points (RG:DI Dx=77.40, RG:ND Dx=44.83) corresponding to a ‘large’ effect size of 0.965. For the corresponding difference in mean Dx values between the Control (strongly dyslexic) and Base (strongly non-dyslexic) subgroups, there arises an even greater absolute difference of 62.11 Dx points in values for this dimension (Control: Dx=83.38, Base: Dx=21.27) which is as we would expect given that traditional beliefs about dyslexia strongly associate it with reading difficulties. This considerable absolute difference in Dx points resonates with Dimension 1, When I was learning to read at school I often felt I was slower than others in my class, where the greatest difference of 65.29 Dx Index points is recorded (Control: Dx=78.34, Base: Dx=13.05). Dimension 5, I think I’m a highly organized learner, presents the smallest absolute difference in Dx mean values between the Control and the Base subgroups of 3.27 Dx points (Control: Dx=43.32; Base: Dx=46.59) suggesting that differences in organizational capabilities between the strongly dyslexic and strongly non-dyslexic students in this sample is marginal.

 

This is supported by the result for Dimension 7, I generally remember appointments and arrive on time, where the second lowest absolute difference in mean Dx values (4.88 Dx points) between the Control and the Base subgroups is shown (Control: Dx=68.51; Base: Dx=73.43). In both examples (Dimensions 5 and 7) the t-test outcome shows no significant differences between these pairs of mean values, however, this outcome is interesting because the difference in Dx values is reversed which is indicating that strongly non-dyslexic students are on average (slightly) more disorganized than their strongly dyslexic peers. For all dimensions in the two Dx Factors 1: Reading, Writing, Spelling, and 2: Thinking and Processing almost all of the differences in mean Dx values are significant and present moderate or large effect sizes between dyslexic and non-dyslexic students with all dimensions presenting large to very large effect sizes between the strongly dyslexic and strongly non-dyslexic students. This and other notable differences are discussed in sub-section 5.2(II).

 
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Table 17:    Mean Dyslexia Index values by dyslexia dimension and research group and subgroup, showing effect size differences and t-test outcomes.

II     PCA on Academic Behavioural Confidence

The original Academic Confidence Scale (ACS) was formulated to explore stark differences in confidence observed between two very different student groups (Sander & Sanders 2003). The data collected was factor-analysed to reveal six subscales:  Studying, Understanding, Attendance, Grades, Verbalizing and Clarifying. Because some statements in the ACS did not load on to a single factor it was stated that this resulting factor structure was a best-compromise. The ACS was later renamed as the Academic Behavioural Confidence Scale to acknowledge that it was more sharply focused on measuring students' confidence in actions and plans related to academic study (Sander & Sanders, 2007).

 

The later, factor analysis of the aggregated data demonstrated that this revised scale also consisted of six factors:  Studying, Understanding, Attendance, Grades, Verbalising, and Requesting, which was deemed a better representation of the subscale structure than the earlier 6-factor analysis. The factor loadings of the earlier PCA is not published however, so it is not possible to comment on how scale item loadings may have shifted in generating the later factors other than to note that the sixth factor in the ACS, ‘Clarifying’ was renamed in the later scale as ‘Requesting’. For the original ABC 24-item Scale, a value of Cronbach’s α = 0.88 was reported (Sander& Sanders, 2006), which suggested a strong internal consistency but also that some items may be redundant. This led to 7 items being removed from the existing, 24-item ABC Scale. The remaining 17 scale items were unrevised. A further factor analysis on the 17-item scale was then conducted which revealed a new structure with scale items loading onto only four factors, these being described as: Grades, Verbalizing, Studying and Attendance. Scale items in the 24-item scale which comprised the factors Understanding and Requesting were either identified as redundant or were absorbed into the factors of the 17-item, 4-factor scale.

 

The data collected in this project have been acquired using the original 24-item scale and since Sander and Sanders' revised, 17-item scale had discarded 7 earlier scale items leaving the remainder unchanged it has enabled both ABC-24 and ABC-17 outputs to be generated from the current data. Table 18 reveals little absolute difference between the mean ABC24 and mean ABC17 values for the three subgroups showing that a slightly greater effect size exists between the Test and the Control subgroups when using data from the 17-item ABC Scale. In both cases (ABC24 and ABC17) Student's t-test reveals that a significant difference (t(38)=1.91, p=0.032; t(39)=2.10, p=0.021 respectively) is present between the sample means (one-tail test, 5% level) of the Test and the Control subgroups. This outcome supports a rejection of the Null Hypothesis that there is no difference in ABC between the Test subgroup and the Control subgroup.

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Table 18:    Comparing mean ABC values, effect size and t-test outcomes for ABC24 and ABC17 Scales.

On the basis of the differences in outcomes from use of the 24-item as opposed to the 17-item ABC Scale being marginal, PCA was applied to the 24-scale-item ABC Scale to explore the structure of the scale for data in this current study.  A varimax rotation was used and as shown by component matrix in Table 19, the table of variances (Table 20) and the scree plot (Figure 22) the five-factor structure that emerged was not as simple as desired because some dimensions (scale items) loaded on to more than one factor. The output from the analysis indicated a KMO measure of sampling adequacy of 0.866, regarded as 'meritorious' (Kaiser, 1974), and the Bartlett test of sphericity showed a level of significance of p < 0.001, indicating that applying PCA to the data is likely to reveal a useful factor structure

Fig22.png

Figure 22:   Scree plot for the total variance explained for Academic Behavioural Confidence, five-factor solution.

Hence again, by applying an element of best reasonable judgement, it was considered that there was justification for accepting these outcomes and in accordance with the 'type' or 'sense' of scale items that emerged as sensibly loading onto each of the five factors, these have been categorized as:

  1. ABC24 Factor 1: - Study Efficacy

    •  #21: plan appropriate revision schedules

    •  #01: study effectively in independent study

    •  #04: manage workload to meet deadlines

    •  #13: prepare thoroughly for tutorials

    •  #22: remain adequately motivated throughout my time at university

    •  #19: make the most of university study opportunities

    •  #14: read recommended background material

  2. ABC24 Factor 2: - Engagement

    •  #03: respond to lecturers' questions in a full lecture theatre

    •  #10: ask lecturers questions during a lecture

    •  #12: follow themes and debates in lectures

    •  #05: present to a small group of peers

    •  #02: produce your best work in exams

    •  #11:understand material discussed with lecturers

    •  #17: ask for help if you don't understand

  3. ABC24 Factor 3: - Academic Output

    •  #16: write in an appropriate style

    •  #15: produce coursework at the required standard

    •  #07: attain good grades

    •  #20: pass assessments at the first attempt

    •  #23: produce best work in coursework assignments

  4. ABC24 Factor 4: - Attendance

    •  #06: attend most taught sessions

    •  #24: attend tutorials

    •  #18: be on time for lectures

  5. ABC24 Factor 5: - Debating

    •  #08: debate academically with peers

    •  #09: ask lecturers questions in one-one settings

 

Proportion of variance explained

 

As outlined above for the PCA conducted for the Dyslexia Index metric, the process attempts to account for all the variance in each of the variables if all of the components are retained. Using the same, Eigenvalue-1 extraction factor, the five components (factors) which emerged from the analysis accounted between them for 62.6% of the total variance (Table 20), with the most significant influence being from Factor 1, study efficacy which explained 35.0% of the total variance.

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Table 19:    Rotated Component Matrix for Academic Behavioural Confidence (24-point scale) and Table of Communalities (varimax rotation).

Table20_edited.png

Table 20:    Total variance explained for Academic Behavioural Confidence

 
 
 
 
 

4.5  Results and analysis outcomes

Table 21 presents a results overview for the data analysis conducted so far. Against the mean Dx value for the two, principal research groups, DI, ND, and for the Test, Control and Base subgroups, the corresponding mean values of ABC both overall are shown, together with the mean values of ABC on a factor-by-factor basis. Also shown are the mean Dyslexia Index values for all groups and subgroups.

Hedges g effect sizes and t-test outcomes between all combination-pairs of groups and subgroups are shown. Effect size differences that present g values considered as at least ‘moderate’, and statistically significant results from t-test outcomes, are indicated in bold typeface. T-test t, p values for independent sample means were derived from one-tail tests. († in Table 21 indicates a two-tail test). Levene’s Test was used to determine homogeneity of population variances and where this was violated, a result assuming unequal population variances is presented (indicated * in Table 21).

Table21_edited.png

Table 21:    Summarizing Academic Behavioural Confidence mean values per research group and subgroup, by overall ABC and by ABC factor means.

The results shown in this summary of outcomes enables the research hypotheses stated earlier (see sub-section 2.3) to be addressed thus:

1. In comparison with their non-dyslexic peers (RG:ND), students with a declared dyslexic learning difference (RG:DI) present a significantly lower level of ABC, with a moderate-to-large effect size difference (g=0.61) between the mean values (RG:ND: ABC24=67.21; RG:DI: ABC24=58.45). The t-test conducted between these independent sample means using a one-tail test indicated a highly significant difference (t(164)=3.825, p < 0.001). Therefore sufficient evidence is presented to reject the Null Hypothesis (1), and accept the Alternative Hypothesis (1) that non-dyslexic students present a higher overall level of ABC than their non-dyslexic peers.

2. Furthermore, in comparison with their strongly non-dyslexic peers in the Base subgroup, students in the Control subgroup of identified, dyslexic students also present a significantly lower level of ABC, with a large effect size difference (g=1.03) between the mean values (Base: ABC24=72.31; Control: ABC24=57.89). The t-test conducted between these independent sample means using a one-tail test also indicated a significant difference (t(89)=4.938, p < 0.001).

3. Supposedly non-dyslexic students who show levels of dyslexia-ness of comparable levels to their dyslexic peers, that is, the quasi-dyslexic students in the Test subgroup, present a significantly higher level of ABC in comparison to the Control subgroup of their identified dyslexic peers, with a moderate effect size difference (g=0.48) between the mean values (Test: ABC24=64.92; Control: ABC24=57.89). The t-test conducted between these independent sample means using a one-tail test indicated a significant difference (t = 1.743, p = 0.043), indicating sufficient evidence to reject the Null Hypothesis (2) and accept the Alternative Hypothesis (2) that quasi-dyslexic students present a higher overall level of ABC than their identified, dyslexic peers.

 

Notable other features of the data analysis results emerge from Table 21: In respect to differences in ABC between the declared dyslexic group (RG:DI) and the declared non-dyslexic group (RG:ND), moderate to large effect sizes arose between the ABC factor means for the three factors, Study Efficacy, (g=0.37), Engagement (g=0.73), and Academic Output (g=0.62). These results were supported by t-test outcomes indicating significant differences were present between the factor means (t(120)=2.273, p=0.012; t(164)=4.61, p<0.001; t(164)=3.89, p<0.001 respectively).

 

Thus as would be expected, respective outcomes were more extreme between the Control subgroup of dyslexic students and the Base subgroup of non-dyslexic students. In both cases, differences in mean ABC values for the two remaining factors, Attendance, and Debating, were slight or negligible, indicating that there was little or no difference in attendance at teaching sessions amongst all students in this datapool, with only a small effect size difference in student peer-interactions (ABC24-5, Debating) indicated between the non-dyslexic and dyslexic subgroups (g=0.26).

A similar picture is observable between quasi-dyslexic students in the Test subgroup and their dyslexic peers in the Control subgroup where effect size differences between ABC mean values in the three factors Study Efficacy, Engagement, and Academic Output were more disparate, (g=0.25, g=0.61, g=0.41 respectively) which although only statistically significant according to t-test outcomes for the factor, Engagement (t(63)=2.197, p=0.016), indicate measurably higher levels of academic confidence between students in these two subgroups for these ABC factors. This observation appears to be showing that dyslexic students’ confidence in engaging with their academic studies can be uniquely identified as a factor which may be the most adversely affected by attributes of their dyslexia in comparison to their quasi-dyslexic peers who present similar levels of unidentified dyslexia-ness.

 
 

4.6  Dx Factor x ABC Factor Matrix

Emerging from the PCA above (sub-section 4.4) is that the structure of the metric, Dyslexia Index broadly loads onto 5 factors:

  1. Reading, Writing, Spelling

  2. Thinking and Processing

  3. Organization and Time-management

  4. Verbalizing and Scoping

  5. Working Memory

 

and that the PCA applied to data collected on the 24-item ABC Scale has also loaded onto 5 factors:

  1. Study efficacy

  2. Engagement

  3. Academic output

  4. Attendance

  5. Debating

 

The dimensions that constitute all of these factors are listed again in Table 22 for easy reference as these will be referred to in the analysis which follows to explore the interrelationships between these two sets of factors. The purpose of this deeper analysis is to determine whether it is possible to formulate a reasonable conjecture about which aspects of dyslexia may have the most notable impact on which aspects of academic confidence. The intention to pursue this avenue of deeper analysis was set out as an extension of the research questions in sub-section 2.3, above.

I      Factor Matrix Overview

 

Table 22 demonstrates that linkages might be identified between factors across the two metrics. For example, ABC Factor 1, Study Efficacy, includes the dimension ‘study effectively in independent study’ which might be related to dimensions in Dx Factor 2, Thinking and Processing, for instance ‘I get in a muddle when searching for learning resources or information’ and/or dimensions in Dx Factor 3, Organization and Time Management, such as ‘I find it very challenging to manage my time efficiently’. In devising a method to explore these factor interrelationships a five-by-five cell matrix has been constructed (Table 26, sub-section 4.6(II) below) which cross-compares all factors of ABC with all factors of Dx by setting out Hedges' 'g' effect size and t-test outcomes between the Test, Control and Base subgroups.

 

The purpose was to establish a mechanism for exploring the impacts of specific groups of dyslexia dimensions on not only academic confidence overall but also on the components of ABC. This analysis draws on the more recent view that dyslexia, such as it can be defined, is most likely to be multifactorial and that the relative balances of the factors can be significantly different from one dyslexic individual to another whilst both are still identified as dyslexic. The examples from datasets in this current study (below) provide evidence to support the multifactorial approach which has been developed most lately by Tamboer, Vorst and Jon (2017), building on the earlier ideas of Pennington (2006), Le Jan et al. (2011) and Callens et al. (2014). These studies are referred to above in sub-section 2.1(II).

Table22.png

Table 22:    Summary of all Academic Behavioural Confidence and all Dyslexia Index Factors and factor dimensions

Redistribution of datasets into research subgroups

 

Before constructing the factor matrix, it was necessary to reconsider the distribution of datasets into the Test, Control and Base subgroups. This was because when each Dyslexia Index factor was taken in turn as the independent variable with the other Dx factors ignored, any particular dataset may then appear in different subgroups according to the Dx value for that factor, according to whether the factor value falls above or below the Dx boundary values used to determined the subgroups. Recall that a Dx value of <400 sifts a dataset into the Base subgroup and Dx>592.5 sifts it into the Test or the Control subgroup depending on whether the dataset originates from the non-dyslexic, or the dyslexic group respectively.

 

This process is best illustrated with an example: Consider the data obtained from respondent, #63726872. Table 23 shows this student’s Dyslexia Index values both overall (Dx=655.32) and for each of the five, Dyslexia Index Factors. The overall Dx value placed him at approximately the median point of the Test subgroup. This was considered an appropriate choice for an example because the same criteria could be applied to datasets in each of the other subgroups for a further comparison and comment.

Table23_edited.png

Table 23:    Dx Factor values for respondent #96408084 and research subgroups that these would correspondingly place this respondent into.

This student’s questionnaire data first sifted him into research group ND because no reported dyslexia was declared. Once calculated, the overall Dyslexia Index of Dx = 655.32 subsequently sifted him into the Test subgroup of students with a quasi-dyslexic profile. However, this student’s Dx factor mean values span a range from Dx = 800.00 in Dx Factor 5, Working Memory, to Dx = 466.41 in Dx Factor 4, Verbalizing and Scoping. Thus, although this respondent was sifted into the Test subgroup overall, when the factor values are considered in turn, this dataset is in the Test subgroup for Factors 1, 2 and 5 only, as Dx values for the remaining factors are below the boundary value of Dx=592.5. Indeed, with a Dx Factor 4 value of Dx = 466.41, (for Verbalizing and Scoping) this value placed this individual quite close to being included in the Base subgroup of non-dyslexic students (where Dx < 400).

 

For this student, the Dx values for Dx Factors 1, 2 and particularly 5, are high, suggesting a strongly dyslexic profile in the three (factor) areas of Reading, Writing, Spelling; Thinking and Processing, and Working Memory – considered throughout decades of dyslexia research with children as being amongst the key indicators of the syndrome. Although this quasi-dyslexia is only implied through the self-report output of the Dyslexia Index Profiler, which, as has been established earlier is not, and is not claiming to be a dyslexia screener, it is nevertheless possible that this output may be indicating that this student does present a dyslexia that so far has been unidentified.

 

A central claim of this research project is that such a student may be better left alone to pursue their studies rather than be formally screened and possibly identified as dyslexic because to do so may have a detrimental impact on his academic confidence. To support this conjecture, consider the outputs that his responses to the ABC Scale generated and how these compare to the mean ABC Factor values for the groups of non-dyslexic students (RG:ND) and dyslexic students (RG:DI) (Table 24):

Table24_edited.png

Table 24:    Respondent #63726872 overall ABC24 value and ABC24 Factor values.

Aside from being an interesting snapshot of this student's ABC values both overall and at a factorial level, by viewing these in relation to the mean values of both the non-dyslexic (RG:ND) and the dyslexic (RG:DI) groups a picture emerges which shows that his academic confidence is approximately at or above the mean values for non-dyslexic students, with values ranging from -0.06SD to +1.15SD. When compared with mean values for the dyslexic group which are all depressed relative to the non-dyslexic means (although only very marginally for the ABC Factor 4, Attendance), an even starker contrast is indicated, where this student's mean ABC values range from +0.66SD to +1.20SD above the dyslexic group's mean values.

 

This appears to suggest that although this student’s results are indicating quasi-dyslexia overall, generated by particularly high levels of dyslexia-ness in three of the Dyslexia Index Factors, Reading, Writing and Spelling (Dx=611.64), Thinking and Processing (Dx=771.58), and Working Memory (800.00), his academic confidence is at comparable or higher levels to his non-dyslexic peers and generally substantially higher than students in the dyslexic subgroup. Although it is not being claimed that not knowing about his possible dyslexia is the sole reason for this individual’s higher than (dyslexia)-peer group ABC average, it is nonetheless being suggested that this may be part of the explanation.

Hence by taking a collective view across the complete datapool, where factor means are calculated and compared across the subgroups, the Factor Matrix could be constructed.

 

Thus, it was considered that enabling the re-organization of the subgroups so that this is possible would permit a deeper investigation into cross-factorial relationships that may emerge, what their interpretation may mean, and how such analyses might be useful in a university context. However, in the first instance, the results from analysis of this student’s data were compared to similarly derived results from students in the Base and Control subgroups to examine whether likely differences would be revealed. These data are presented and discussed below (sub-section 5.3) as a reflective commentary which leads to recommendations about how such information may constitute a comprehensive insight into students’ academic learning management strengths and weaknesses, and how this may impact on learning development provision at university.

 
 
 
 
 

Effect of Dx Factor sifting on subgroup sample sizes

Thus, the student respondent in the example above shows how a dataset may appear in different subgroups depending on which Dx Factor is used as the determining criteria. One consequence of sifting datasets into the three subgroups according to weighted mean Dx values for each Dx factor was that the sample sizes of the subgroups varied (Table 25). This meant that fresh mean values of ABC had to be calculated for each of the five ABC Factors for each subgroup according to whichever Dx Factor determined the composition of the subgroups. Hence it was these outputs that generated the summaries presented in the Factor Matrix below (Table 26).

Table25_edited.png

Table 25:    Subgroup sample sizes following Dx Factor-based sifting of datasets.

 

II     The Factor Matrix

 

Figure 26 is an extract of Table 26 with cell contents labelled so that the complete table may more easily understood:

Fig23.png

Figure 23:   Explaining the meaning of each cell entry in the Factor Matrix (Table 26).

Two sets of comparators are important: firstly, between the non-dyslexic students in the Base subgroup and those others considered to be dyslexic in the Control subgroup; and secondly between the Control subgroup and the quasi-dyslexic students in Test subgroup.

 

Given that data for the Control subgroup was common to both comparisons, in each of the Dx Factor row-sets, ABC data for the Control subgroup is presented centrally with the corresponding data for the Base and Test subgroups above and below it respectively.

 

Absolute ABC values are provided to contextualize the effect size values. The overall, key findings of the complete analysis which relate back to the research hypotheses are again indicated in the bottom-right of the matrix (bordered red) corresponding to the results presented in Table 20 above. To aid clarity, t-test outcomes for differences between factor mean ABC values of the Base and Control subgroups have been omitted, not least because it has been established above (sub-section 4.4) that both overall, and in three of the five ABC factors, ABC values for non-dyslexic students in the Base subgroup are substantially higher than corresponding values for dyslexic students in the Control subgroup. However, where apposite, these data are provided in the discussion (sub-section 5.4) where notable features from Table 26 are discussed.

Table26_edited.png

Table 26:    Matrix of ABC Factor mean values relative to Dx Factors.

 
 
 

4.7  Applying multiple regression analysis

The scatterplot (Figure 24) shows the distribution of the datapool variables resulting from a simple linear regression analysis. An association between ABC and Dyslexia Index is indicated by the line of best fit overlaid through the distribution, with an R-squared value (effect size) of 0.2052, derived from Pearson’s coefficient of correlation, r = 0.453 (a moderate correlation). Given that the Dyslexia Index (Dx) scale comprises 20 scale items, it was considered that a multiple regression analysis may be a better model for the data and may reveal more about the interrelationship between ABC and Dyslexia Index. Rather than using this procedure to explore whether it is possible to predict ABC from Dx more generally – which although is valid and relevant, was considered to be more appropriate as the topic of a further study later – the aim has been to determine whether a multiple regression analysis might add further weight to the hypothesis that students with a quasi-dyslexia present higher levels of ABC than their dyslexia-identified peers by showing that the observed results differ from those expected.

Fig24.png

Figure 24:   Scatterplot of Academic Behavioural Confidence against Dyslexia Index for the complete datapool

Thus, a multiple regression analysis was constructed to generate a predictive model with ABC as the dependent ‘output’ variable and each of the 20 dimensions of the Dyslexia Index as multi-variable inputs. The objective was to compare each student’s predicted ABC against their observed ABC as derived from their questionnaire responses; and also to build mean-average ABC outputs for each research group and subgroup to enable further comparison to be possible.

 

The multiple regression analysis was applied to the datasets in each research group (RG:DI and RG:ND) separately to generate two predictive models. Since Research Group ND also contained the subset of students with quasi-dyslexia, (the Test subgroup), it would be possible to use the predictive model for dyslexic students to generate ABC outputs for students in the Test subgroup which could be compared with their observed ABC. 

In total, five multiple regression analyses were conducted to generate five distinct regression equations. The five analyses conducted sought six prediction outcomes:

  1. to predict ABC based on the regression equation derived from Dyslexia Index (Dx) using data from the complete datapool;

  2. to predict ABC for students in Research Group ND based on the regression equation derived from Dx data from that research group;

  3. to predict ABC for students in Research Group DI based on the regression equation derived from Dx data from that research group;

  4. to predict ABC for students in the Base subgroup, based on the regression equation derived from Dx data for that research subgroup;

  5. to predict ABC for students in the Control subgroup, based on the regression equation derived from Dx data for that research subgroup;

  6. to predict ABC for students in the Test subgroup, based on the regression equation derived from Dx data for the Control subgroup.

 

In each of the six cases, the objective was to compare the predicted mean ABC to the observed mean ABC where the closeness of match would be at least an ‘eyeball’ indicator of the predictive strength of the models. In case VI especially, it was hoped to demonstrate that students in the Test subgroup, the quasi-dyslexic students, presented on average, a higher level of ABC than expected, based on their Dyslexia Index.

According to the study design it was considered highly unlikely that observations would be related, hence it was not necessary to conduct the Durbin-Watson test for a (lack of) independence. Tests for linearity were conducted collectively by plotting scatterplots of the studentized residuals against the unstandardized predicted values for each of the five regressions. Since the residuals formed an approximately horizontal band in all

scatterplots, it was assumed that the independent variables collectively are linearly related to the dependent variable, (see Appendix 8.5, Figures 34-38). Homoscedasticity was demonstrated through a visual inspection of the scatterplots of studentized residuals against unstandardized predicted values. Interpretation of correlation tables showed that none of the correlation coefficients were > 0.7 for any of the regression models indicating no evidence of multicollinearity. This was further confirmed by consulting the Table of Collinearity Tolerances where none were less than the recommended critical value of 0.1 (Lund & Lund, 2016-18).

 

Significant outliers were not detected on the basis of standardized residuals being greater than +/- 3 standard deviations (SDs). Consulting the studentized deleted residuals also confirmed the unlikelihood of significant outliers as none were greater than +/- 3 SDs. Checking for any datapoints having undue influence on the regressions showed that 93% of the datapoints presented leverage values of <0.2, considered the boundary criteria between ‘safe’ and ‘risky’ (ibid), with all datapoints <0.289 leverage. As a further test for influential datapoints, Cook’s Distance values were examined and none showed a value >1, considered to be the criteria for testing influence (ibid).

 

Visual inspection of Normal P-P plots of the regression standardized residuals indicated that the distributions were approximately normal (see Appendix 8.5, Figure 43 for an example Normal P-P plot). To test the ‘goodness of fit’ of the regression models to the data, the proportion of variance explained by each regression model (adjusted R-squared) was I:43.6%; II:42.7%; III:31.6%; IV:42.3%; V:16.3% suggesting that all except model V were adequate. To determine the statistical significance of the models, that is, whether they are significantly better at predicating ABC than the mean model, the ANOVA outputs were consulted (Appendix 8.5, Table 39). All models returned a statistically significant result with the exception of model V: F(20,26)=1.447, p=0.186.

 

The summary of outcomes (Table 27) shows the mean ABC values for each of the research groups and subgroups calculated from observed data which is compared with the mean ABC values outputs from the predictive models. Given that these models were generated from the observed data it is of no surprise that the discrepancies between observed and predicated mean ABC values are generally small. For example, for research group DI, the dyslexic students, the observed mean ABC=58.45 is only 0.03 points adrift from the predicted mean ABC=58.42 using the regression equation built from this research group’s observed data.

Table27_edited.png

Table 27:    Comparisons of mean ABC between observed and predictive models.

It is of note that for the Test subgroup of quasi-dyslexic students, the observed mean ABC=64.92 is 3.08 points above the predicted mean ABC=61.84 using the predictive model built from Control subgroup, comprising students with similar levels of dyslexia-ness. However, the observed mean is 3.74 points above the predicted mean ABC=61.18 generated from the predictive model built from the complete datapool, and is 5.30 points above the predicted mean ABC=59.62 as generated from the model built from research group DI.  Interpretation of the ANOVA outputs for model V, derived from Dx data for the Control subgroup, indicated a result that was not significantly different from the mean model for that research subgroup. Hence these outputs suggest that using either model I, built from the complete datapool, or model III, built from research group DI, would be better predictors.

Although it is recognized that a much deeper inspection of these analysis outcomes is called for to properly understand their relevance and validity, at face value they appear to support the desired outcome that students with a quasi-dyslexia present better than expected levels of ABC.

 
 
 

Academic confidence and dyslexia at university

A PhD Research Project October 2014 - May 2019

Middlesex University, London

Andrew Dykes B.Ed, M.A, M.Sc, FHEA

ad1281@live.mdx.ac.uk; academic@ad1281.uk

+44 (0)79 26 17 20 26