Academic confidence and dyslexia at university
Results & Analysis
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. 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).
2. Null-hypothesis significance testing; ANOVA
Notwithstanding (1) 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).
3. Principal Component Analysis
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 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). Specifically in this current study, 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.
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 were found to be small and not significant (see Table ## below).
However, just as Cronbach's 'alpha' 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.
However, it also remains unclear from the Sander and Sanders original and subsequent studies, whether the components analysis adopted for both the individual and the later, combined datasets, was 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 meet this criteria, it becomes difficult to decide which components to include and which to omit.
Early iterations of the process in this current study suggested that solutions of four, five, or six factors for both ABC and for Dx could be reasonably supported, based on 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 occured 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 the five-factor solution 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. 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. 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.
4. Multiple Regression Analysis
Finally, a tentative multiple regression analysis was conducted, not so much to determine whether a predictive relationship exists between Dyslexia Index and Academic Behavioural Confidence, but more so to add substance to the statistical evidence to address the research hypotheses generated thus far, by examining differences between observed and expected ABC outcomes according to Dx inputs.
Precedents have been set where multiple regression analysis has been used in education contexts, although usually, these have attempted to predict whether dyslexia exists amongst students with suspected dyslexia. For example, Tops et al. (2012) analysed data collected from a sample of 200 Dutch university students which was split equally between those with a known dyslexia and a Control subgroup of those with no known dyslexia nor any previous evidence of it. Based on several independent variables, such as for assessing STM, phonological awareness, and rapid-naming skills, a predictive model was generated. The subtests were drawn from the wide range of assessments regularly associated with attempts to identify dyslexia. An important element of the research design matched each dyslexic individual with a control-group data-partner using matching criteria of age, gender and field of study. Though not explicitly stated, it is presumed that this was intended to eliminate the likelihood of confounding analysis results that might otherwise be attributable to these variables. The main feature of the study was the derivation of a prediction equation that enabled a probability indicator of dyslexia to be generated, based on each individual's tests scores outputs. The research outcomes confirmed the view that the literacy difficulties associated with dyslexia extend into adulthood, indicated that the inherent phonological deficits persist in undergraduate students, and that these high-functioning adults were not able to compensate completely for them. However, it was also stated that since the process of regression analysis is data-driven, the results are applicable to the dataset from which it was derived and that generalizations could only be cautiously drawn.
But the most important concluding statement was that although the prediction model could be useful in educational settings, it did not indicate the causes of individuals’ dyslexia; and also that in comparison to the control group, students with dyslexia presented differences on just the variables in the model and there may be other measures that would be more optimal. It was claimed that this study was the first to bring prediction analysis to the field of dyslexia research (ibid) in order to convert multi-test data into interpretable dyslexia probabilities. Perhaps at the time, the authors were unaware of a prior study which had also attempted to create a multivariate predictive model for identifying dyslexia, albeit in young learners rather than for adults (le Jan et.al., 2009). Although there were methodological differences between the two studies, not least where le Jan's study utilized a combination of PCA together with logistic rather than multiple regression analysis, the outcome was also a predictive model. The research conclusions claimed high levels of sensitivity and specificity.
These examples suggest that multi-variable regression analysis can be valuable in dyslexia research, not least to complemen the rationales of the multi-factorial approaches to understanding dyslexia (Section 2.1(II/6)). Hence this analysis approach was considered to have value in this current study. However, rather than use the device to predict dyslexia, 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), and there is generally some danger of the analysis being descriptive 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.
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)
A total of n=183 questionnaire replies were received. Seventeen were discarded due to Dyslexia Index Profiler data less than 50% complete. 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.
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.
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 boardly 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).
Distribution by study level
Data about level of study was collected to determine whether the datapool represented a reasonable cross-sectional match to the wider community of students attending UK universities more generally. Although a wider selection of choices were 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)). It has been argued earlier that the outcome of a ‘disability diagnosis’ may lead individuals with dyslexia to perceive themselves to be valued less by their peers (Burden, 2008; Ridley, 2011; Shifrer, 2013; Gibby-Leversuch, et.al., 2019), or by society more generally, a characteristic typically associated with stigmatization (Goffman, 1963). At the same time, by associating diagnosis with treatments to effect a cure (or not), affective responses are known to influence compliance with remedial regimes constructed around the modification of behavioural intentions and actions (Schuettler & Kiviniemi, 2006). Translated into the dyslexia context, it is reasonable to suppose that individuals whose dyslexia is diagnosed to them as a learning disability are likjely to experience aversive emotional responses to this new information, not only about themselves, but also about how their new situation may impact on their ability and capacity to learn and study (e.g.: Dale & Taylor, 2001; Armstrong & Humphrey, 2009; Gwernan-Jones, 2010). Hence this may be part of the explanation for lower academic confidence in dyslexic students due to negative internalization of dyslexia into self-identity, perhaps even as an illness without a cure, when it is diagnosed and labelled as a disability. 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).
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 hypothesis, one-tail test 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. This indicates that 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.
III Dyslexia Index Profiler Data
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 mean; together with outcomes for effect size difference between the sample means and the corresponding, supporting t-test.
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 that indicated 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)). These results indicate that 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.
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 outsomes 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, 723 respectively. Conducting a one-tail t-test determined a significant difference between these means although the outcome was marginal (t(164) = 1.69; p = 0.048). 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, an outcome that was considered satisfactory was established at Dx = 592.5. This was based on the t-test outcome of t(164) = 1.64, p = 0.053, which although equally marginal, did indicate no significant difference between the sample means of the Test and Control subgroups, which emerged as Dx = 685, 716, respectively. This 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, this adjustment increased the sample sizes of the Test subgroup 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 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 Principal Component Analysis (PCA)
Applying PCA to the datapool scales for Dyslexia Index and Academic Behavioural Confidence
Both the Dyslexia Index Profiler and the ABC Scale have been reduced through PCA into a set of factors (components) and these have been assigned name-labels that reflect which dimensions of their parent metrics are their respective contributors. Recall that Sander and Sanders also applied a process of factorial analysis to their original, 24-item ABC Scale and later, to their revised, 17-item Scale. With the exception of one study found to date (Corkery, 2011), all others that have used the ABC Scale have utilized the Sander and Sanders factor structure for their analysis, had they chosen to explore their findings in the greater detail that the use of ABC factors permits.
The original, together with Corkery's ABC factor structures were investigated as part of the analysis development (discussed in subsection 5.3), and the outcome encouraged development of a factor structure that is unique to this project. This generated an alternative set of project-specific factors for the ABC Scale that were more pertinent for exploring the interrelationships between components (factors) of academic confidence and components of dyslexia-ness that are the focus of this enquiry. The outcome of the factorial analysis of both metrics has enabled a Dx Factor X ABC Factor matrix to be constructed which, as expected, revealed interesting and meaningful relationships between the components of the two metrics. The matrix and a more detailed report is presented below in sub-section 4.6, with interpretations discussed in sub-section 5.4.
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 scale items.
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 in the metrics is also required for a PCA to be run. Having adequate sample sizes 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.
Hence the preliminary assumptions have been met for running a PCA on both the ABC Scale and Dyslexia Index for the data collected in this enquiry. Having set out the more general analysis results of the PCA above, the sub-sections which follow focus firstly on aspects of the PCA applied to the Dyslexia Index metric that are especially important to recount, not least because this metric has been devised and developed exclusively for this study; and secondly reports more briefly on the outcomes of the PCA applied to the ABC Scale which has already been field-tested in other studies.
I PCA on Dyslexia Index
Examining scale item redundancy in the Dyslexia Index Scale
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.
It would be expected that a meta-analysis of several broadly similar studies which had all used the scale being evaluated would be required before more 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 given that an alpha value within the range 0.3 < α < 0.7 is considered as acceptable with preferred values being closest to the upper limit in this range (Kline, 1986). However, Kline also indicated that when the value of α exceeds 0.7 this may indicate that some scale items are not providing much additional contribution to the metric. 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 being even further above the apparently critical value of α = 0.7, appears to suggest a process that may be of dubious value since repeating the reduction to determine whether redundant items now exist in the revised scale may lead to an even higher value of α.
In the interests of expediency, it was considered that by recalculating Dx for all datasets according to the reduced, 16-item scale, and recalculating the mean Dx values for each of the three subgroups, Test, Control and Base, it would be possible to examine whether any important differences were revealed. The outcome of this exercise showed some small differences: The mean Dx-20 = 531.25 for the complete datapool with a data range of 88 < Dx < 913 whereas the 16-item Dx scale generated a mean Dx-16 = 525.40 with a data range of 31 < Dx < 961. This suggests that the impact on the dataset composition of the three subgroups is likely to be marginal when these are derived from either the 20-item or the 16-item scale. The difference between these two mean values was confirmed as not significant at the 5% level using a 2-tail independent samples t-test assuming homoscedastic variances ( t(164) = 0.288 , p=0.771).
Nevertheless, it was still felt important to consider the actual differences in mean ABC values of the subgroups that were generated through use of both Dx scales since establishing the most appropriate composition of these subgroups was key to exploring differences in ABC. These data are presented in Table 11 which shows that the changes in both the sample sizes of the subgroups and the mean values of ABC data in the subgroups are so small as to be reasonably considered negligible.
Table 11: Comparison of sample sizes and mean ABC for subgroups Test, Control, Base when adjusted according whether the 16-item or 20-item Dyslexia Index is used.
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.
Reporting more than Cronbach’s Alpha
Further reading about internal consistency coefficients revealed studies which identify persistent weaknesses in the reporting of data reliability in research, particularly in the field of social sciences (e.g.: Henson, 2001; Onwuegbuzie & Daniel, 2000; 2002). Furthermore, useful frameworks are suggested for a better process for reporting and interpreting internal consistency estimates which, it is argued, then present a more comprehensive picture of the reliability of data collection procedures, particularly data elicited through self-report questionnaires.
Henson (op cit) argued that “internal consistency coefficients are not direct measures of reliability, but rather are theoretical estimates derived from classical test theory” (2001, p177). This resonates with Boyle's (2015) interpretation about the sense of this measure being relational to the sample from which the scale data is derived rather than directly indicative of the reliability of the scale more generally. However, Boyle's view about scale item homogeneity contrasts with Henson's, which persists with the view that internal consistency measures do indeed offer an insight into whether or not scale items are combining to measure the same construct. Henson strongly advocates that when (scale) item relationship correlations are of a high order, this indicates that the entire scale is gauging the construct of interest with some degree of consistency – that is, "that the scores obtained from this sample at least, are reliable" (Henson, 2001, p180).
This apparent perversity is less than helpful. Some light is shed on this by a study by Onwuegbuzie and Daniel (2002) which, although based on much of Henson's work, goes further by suggesting that it is useful to report an estimate for a confidence interval for alpha in addition to the single-point value, paying particular attention to the upper-tail limit. 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), as it pertains to that particular sample. 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 to be applied to the background population. Hence Onwuegbuzie and Daniel argued that the upper-limit confidence interval should be reported in addition to the point-value of Cronbach's α because this will be a more comprehensive report about the internal consistency of data, hence providing a better, interval estimate of the true value. This principle is adopted in this current study.
It is known that confidence intervals are most usually specified to provide an interval estimate for the population mean based on an observed sample mean as this constitutes a point estimate for the population mean. From this, the confidence interval estimate is built on the assumption that the background population follows the normal distribution. It follows, therefore, that a sample-based, point estimate of any population parameter might also have a confidence interval estimate constructed around it provided the most underlying assumption that the distribution of that parameter is normal can be accepted.
For example, a correlation coefficient between two variables in a sample is a point estimate of that parameter in the background population. If a distinct sample from the population it taken, it is likely that a different correlation coefficient would be generated although there is a good chance that it would be of a similar order. Hence a distribution of correlation coefficients would emerge in a similar fashion to the distribution of sample means that constitutes the fundamental tenet of the Central Limit Theorem.
It is on this basis that confidence intervals for a background population parameter can be established. Fisher (1915) developed a transformation that maps the Pearson Product-Moment Correlation Coefficient, r, onto a value, Z', which he showed to be approximately normally distributed and hence, confidence interval estimates could be constructed. Given that Cronbach's alpha (α) is derived from values of r, it follows that Fisher's Z' can be used to transform Cronbach's alpha and subsequently create confidence interval estimates for of alpha. Fisher showed that in these circumstances, the standard error (SE) of Z', which is obviously required in the construction of confidence intervals, is solely related to the sample size such that SE = 1/√(n-3).
Thus it becomes possible to generate the upper-boundary limit for the confidence interval for alpha by transforming α to Z', calculating the standard error for Z' so that the upper confidence interval for Z' can be derived, and lastly reversing the transformation to arrive at the upper confidence interval limit for α. This process enabled a more complete reporting of the internal consistency of scales for not only the datapool, but also for each of the research groups, ND, DI (Table 12).
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.
Figure 18: Scree plot for total variance explained for Dyslexia Index scale, five-factor solution.
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.
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:
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
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
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
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
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.
Figure 19: Radar chart of Dx Factor distributions for respondents in the Base subgroup of non-dyslexic students.
Figure 20: Radar chart of Dx Factor distributions for respondents in the Control subgroup of dyslexic students.
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).
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.
Table 16a: Comparing Dx Factor mean values between the Test and Control subgroups.
Table 16b: Comparing Dx Factor mean values between the Base and Control subgroups.
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).
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.
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
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:
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
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
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
ABC24 Factor 4: - Attendance
#06: attend most taught sessions
#24: attend tutorials
#18: be on time for lectures
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.
Table 19: Rotated Component Matrix for Academic Behavioural Confidence (24-point scale) and Table of Communalities (varimax rotation).
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).
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:
Reading, Writing, Spelling
Thinking and Processing
Organization and Time-management
Verbalizing and Scoping
and that the PCA applied to data collected on the 24-item ABC Scale has also loaded onto 5 factors:
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).
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.
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):
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).
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:
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.
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.
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:
to predict ABC based on the regression equation derived from Dyslexia Index (Dx) using data from the complete datapool;
to predict ABC for students in Research Group ND based on the regression equation derived from Dx data from that research group;
to predict ABC for students in Research Group DI based on the regression equation derived from Dx data from that research group;
to predict ABC for students in the Base subgroup, based on the regression equation derived from Dx data for that research subgroup;
to predict ABC for students in the Control subgroup, based on the regression equation derived from Dx data for that research subgroup;
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.
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.