Academic confidence and dyslexia at university
Results & Analysis
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.
4.2 Analysis summary
To enable the research hypotheses to be addressed, firstly ABC data from the research groups of dyslexic and non-dyslexic students was compared; secondly data from participants in the Control subgroup was compared with data from participants in the Base group; finally, students with previously unidentified, dyslexia-like study profiles, (participants in the Test subgroup, RG:DNI) termed quasi-dyslexic students, was compared with those in the Control subgroup.
Effect size measures were the main points of statistical evidence used to consider against the Null Hypotheses with these data analysis outcomes supported by measures of statistical difference between independent sample means through the Student's t-test. A one-tail test was conducted because the alternative hypotheses were that i) the mean ABC values for the Base subgroup are higher than the mean values for the Control subgroup and ii) the mean values for Test subgroup are higher than the mean values for the Control subgroup. Homogeneity of variances was established using Levene's Test and according to the output, the appropriate p-value was taken. Hedges 'g' effect size wass used because the sample sizes are significantly different in all comparison cases which requires the weighted, pooled standard deviations to be used.
A total of n=183 questionnaire replies were received. Of these, n=17 were discarded because data for the Dyslexia Index Profiler were more than 50% incomplete, hence it was not possible to accurately determine these respondents’ Dyslexia Index. The demographic distribution of all participants according to dyslexia status, gender; home residency, and study level is presented 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.
It is evident that for the complete datapool, female participants (n=113, 67%) outnumbered male participants 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. Student participants recruited through the open invitation to all students and who subsequently formed research group ND (n=98), were distributed by gender, such that female = 60 (61%): male = 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.
Participants were asked to identify whether they were a 'home' student or an 'international/overseas' student - that is, without separating non-UK EU students from all overseas students. Tables 4 and 5 include the distribution of research participants by domicile. For comparison, national data from HESA for 2016/17 are shown. Although this demonstrates a similar distribution it must be added that the HESA figures are 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. However, it is reasonable to accept that the ratio of 'home' students to non-UK students would not be significantly different were an aggregated figure used, given that it were available.
It was considered useful to obtain data relating to the level of study of students participating in the research not least to determine whether the datapool constituted a reasonable cross-sectional match to the wider student community.
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 study for Professional or Vocational qualification
If so, then it follows that conclusions derived from the research outcomes might reasonably be considered as a representative of students attending UK universities more generally.
Tables 4, 5 include the distribution of participants by their level of study programmes. Nationally collected data for 2016/17[HESA 2016/17 available at: , accessed on: 16 April 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. 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. To enable a like-for-like comparison as far as is possible, 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).
From these, note that in comparison to national data where study at level 6 or lower accounted for 66% of the student population, undergraduate respondents in this study (n=124, 75%) are slightly over-represented.
II How students with dyslexia learned of their dyslexia
The impact of a diagnosis of dyslexia on Academic Behavioural Confidence
One aspect of the enquiry aimed to explore how dyslexia becomes known to participants who have declared it. The research hypotheses imply that the dyslexia label may be one of the contributing factors to reduced ABC in students with dyslexia. The sub-hypothesis was that students whose dyslexia was diagnosed to them as a disability have significantly lower levels of academic confidence when compared with students who were told about their dyslexia by reference to neither diagnosis nor to disability. Thus leading to a null sub-hypothesis to test against an alternative:
H0: the way in which dyslexic students learn of their dyslexia has no impact on their academic confidence;
AH: students whose dyslexia is diagnosed to them as a disability or a difficulty tend to show lower levels of academic confidence in comparison to those who are told about their dyslexia in other ways.
It was considered that if evidence emerged to reject the null hypothesis then this would suggest that the way in which dyslexic students learn of their dyslexia may have a negative impact on their academic confidence. The outcome of a ‘disability diagnosis’ to an individual may be that they will perceive themselves to be valued less by their peers or society more generally, a characteristic typically associated with stigmatization (Goffman, 1963). Hence this may be part of the explanation for lower academic confidence in dyslexic students, as a consequence of negative internalization of dyslexia into self-identity when it is diagnosed and labelled as a disability.
Respondents 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
A reasonable assumption was that such students had participated in a formal dyslexia screening and/or assessment at university, or during their earlier years in education. Altogether, 64 of the 68 declared dyslexic students returned a result (Table 6). It is notable that 22 respondents said that their dyslexia was diagnosed to them as a disability, and that 40 respondents said that their dyslexia was diagnosed to them as a difficulty or a disability. These represent 34% and 63% of the sample respectively. This left a remainder of 14 students (22%) who learned of their dyslexia by one of the other alternatives offered.
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.
Table 6: Summary of dyslexia self-report sentence: ‘My dyslexia was [ … ] to me as a learning [ … ]’
The mean average ABC both overall and for each of the five 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. Effect size differences in mean ABC between pairs of subgroups were calculated, together with t-test outcomes to support the effect size results (Table 7).
Comparing students in subgroup E with those in subgroups DF, DS and DS+DF combined, showed moderate effect size differences between mean ABC overall values of g=0.64, 0.58, 0.59 respectively, with these data being supported by t-test outcomes indicating significant differences between mean values (one-tail test; 5% critical value; Levene’s Test for homogeneity of variances was used).
Hence this shows that students whose dyslexia was diagnosed as a disability or as a difference, returned lower overall ABC mean values when compared with students who were told of their dyslexia in any of the alternative ways. Thus there is evidence to reject the null hypothesis in favour of the alternative.
It is somewhat surprising that the effect size was greater when dyslexia was diagnosed as a difficulty rather than as a disability, however given the small sample sizes it is likely that this is within margins of error and that effect sizes are broadly the same. To support this, the effect size was calculated for differences between subgroups DF and DS, with the outcome that this was ‘small’ (g=-0.16). Indeed, similar outcomes were established for all ABC Factor values between these subgroups.
When looking at the breakdown of ABC into its factors, it is notable that for all except Factor 5, Debating, the effect size between Factor mean values is generally ‘moderate’ with g-values that are broadly similar in comparisons between subgroup E and either subgroup DF or DS. For ABC Factor 4, Attendance, the effect size between subgroup E and both subgroups DF and DS is large with these results supported by t-test outcomes indicating significant differences between the factor mean values.
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. Also shown is the outcome of a t-test for differences between sample means’ Dx, indicating a significant difference (t(164)=8.71, p<0.001), and the 95% confidence interval for the effect size, g.
Table 8: Dyslexia Index summary according to research group
Figure 14 shows the representative distribution curves for the data of both research groups together with the key descriptive summaries of the mean Dx values and the 95% Confidence Interval Estimates for the population means, which suggests that both distributions are approximately normal by exhibiting the characteristic bell-shaped
outline. The Shapiro-Wilks test (p>0.05) provided confirmation of normality, which was further supported by an interpretation of Q-Q plots (Figure 15) where the datapoints for each research group are all positioned approximately along the diagonal. There are marked differences between Dx values for the two research groups where both the sample mean Dx and median Dx are much lower for the non-dyslexic students (RG:ND) than for the dyslexic students (RG:DI) and possible reasons for this are discussed in sub-section 5.2 below. An independent samples t-test conducted on the data revealed a significantly lower mean Dx for students with dyslexia in comparison with those with no declared dyslexia ( t(164) = 8.71, p<0.001). However, Levene’s test for homogeneity of variances was violated (F(164) = 7.65, p=0.006), so the revised output for equal variances not assumed was preferred (t(162) = 9.12, p<0.001).
Figure 14: Representative distribution curves for datapoints in both primary research groups suggesting normality.
Figure 15: Normal Q-Q plots for Dyslexia Index.
A one-tail test at the 5% critical value was implemented because the aim was to determine whether the sample mean Dx for students who offered no declaration of dyslexia would be lower than the mean for students who were declaring dyslexia. There were no outliers in the data for each research group, as assessed by inspection of boxplots. The effect size of g = 1.38 indicates a very large effect size (Sullivan & Feinn, 2012) for the difference in the Dx sample means, leading to an effect size confidence interval for the difference in Dx population means of 1.03 ≤ g ≤ 1.71. These results indicate that the Dyslexia Index Profiler is returning a high Dx value for the majority of students who declared their dyslexia and a much lower value for those who declared no dyslexic learning challenge. Thus, it was discriminating well between those two groups.
Setting boundary values for Dx
Setting the boundary value for Dyslexia Index in research group ND has been an essential element of the analysis process in order to filter student responses in this group into the Test subgroup, DNI. As the data analysis process has progressed, a critical evaluation of the setting of boundary values has been applied. A cursory inspection of the data suggested that setting Dx = 600 as the filter seemed appropriate because approximately two-thirds of students with declared dyslexia returned a value of Dx > 600 (45/68 = 66.2%).
Applying this boundary value to datasets in research group ND generated a subgroup of n=17 respondents with no previously reported dyslexia but who appeared to be presenting dyslexia-like characteristics which aggregated to similar levels of dyslexia-ness. Applying this boundary value indicated that nearly 20% (n=17) of the non-dyslexic students who participated in the research appear to be presenting unidentified dyslexia-like profiles. This is consistent with widely reported research suggesting 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 (Richardson & Wydell, 2003; MacCullagh et al., 2016; Henderson, 2017).
Conversely, setting a lower boundary value of Dx = 400 has been essential for establishing the additional comparator subgroup of students from research group ND who are highly unlikely to be presenting unidentified dyslexia - designated research subgroup ND-400, the Base subgroup group (Table 9). It is considered that this is justified through a similar but 'opposite tail' argument where the majority of students from research group ND who remained in this group after research subgroup DNI had been sifted out, presented a Dyslexia Index of Dx < 400 (n=44, 55%). 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) and although the analysis did not identify these as outliers to be excluded, it is possible that these remain anomalous results for other reasons, not least that the likely, conventional dyslexia identifying processes that were used with these individuals may have mis-identified them as dyslexic. In the absence of specific information about these two students, it is only possible to speculate that this may be a possible explanation.
Table 9: The first iteration for setting boundary values for Dyslexia Index
Figure 16 supports these boundary value conditions by presenting the basic statistics for each of the groups and subgroups including confidence interval estimates for the respective population mean Dx values. Thus it is argued that setting Dx filters at Dx = 400 and Dx = 600 was a reasonable starting point for the data sifting process. Note particularly the lower, 99% confidence interval boundary for the population mean Dx for students with identified dyslexia (RG:DI) falls at Dx = 606, and the 99% lower CI boundary for students with no previously reported dyslexia falls at Dx = 408, which suggests that the two students with declared dyslexia but whose Dx values fell below Dx = 400 may be safely considered as anomalous results.
Figure 16: Basic statistics for research groups and subgroups according to the first iteration for Dx boundaries
However, in order for the ABC for the subgroups to be justifiably compared, particularly those for the Test and Control subgroups, it is important that the defining parameter of Dyslexia Index for each of these two subgroups are sufficiently close so that it can be said, statistically at least, that the mean Dyslexia Index for the two subgroups is the same. Figure 16 shows the Test subgroup presenting a mean Dx = 690, some 33 Dx points below the mean for the Control subgroup (mean Dx = 723). Hence it was felt necessary to conduct a t-test for independent sample means to establish whether this sample mean Dx = 690 is significantly different from the sample mean Dx = 723. If not, then the boundary value of Dx = 600 would remain sensible for sifting respondents from research group ND into the Test subgroup.
However, should there be a significant difference between these sample means then this suggests that the two subgroups may not sharing the similar (background population) characteristic of mean Dx. Hence comparison analysis of other attributes between these two subgroups could not be considered so robustly, specifically the subgroups' ABC. An independent samples t-test was conducted on the Control(DI-600) and the Test(DNI) subgroups as established through the boundary Dx criteria of Dx=600. A one-tail test was used because it is known that the sample mean for the Control subgroup is higher rather than merely different from that for the Test subgroup.
The outcome returned values of t(164) = 1.69, p = 0.048 indicating that there is a significant difference between the sample means of the two subgroups although this is a marginal value. Following several further iterations of the t-test based on selecting different boundary Dx values close to Dx = 600, an outcome that was considered satisfactory was established using a boundary value of Dx = 592.5. This returned a t-test result of t(164) = 1.64, p = 0.053 which now suggests no statistically significant difference between the sample means, although again, this is marginally non-significant, and hence is indicating that this adjustment of the boundary Dx criteria is unlikely to have a substantial impact on the composition of the datasets, included into the Test subgroup.
Indeed, adjusting the Dx boundary value in this way 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 in the fresh subgroupings. This Dx boundary value adjustment has also resulted in small differences in the means and confidence intervals for these two research subgroups which is, of course, due to the revisions of datasets included in each subgroup. Figure 17 reflects these small differences and now clearly identifies the basic statistics for the Test, Control and Base subgroups that will be discussed throughout the remainder of the thesis. Table 10 sets out the final, defining criteria for the subgroups and their designation.
In summary, the process reported so far has demonstrated a robust approach towards exploring the nature of the Dyslexia Index metric. This is to justify its use in this project as the tool for finding students from amongst the datapool who are not identified as dyslexic, but who present dyslexia-like characteristics and study attributes in relation to their academic learning management strategies at university. This has enabled three subgroups to be clearly determined so that the examination of their respective levels of ABC can be conducted.
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.