Dyslexia Index Factor Profiles

 

In the previous blog-post I identified that the factor analysis of my Dyslexia Index metric generates different cohorts of students in each factor when regarding Dyslexia Index (Dx) as the independent variable – that is, the one I’ve fixed or chosen. This is because the process of considering the aggregate of the values for each of the dimensions that together constitute a factor generates a different Dyslexia Index (when scaled up to a value out of 1000) than it might for any other factor for any specific student respondent in my datapool. In other words, Student X will have a different Dx value for each Dx factor and this may mean that the student is included or not in any of the research subgroups of interest, ND-400, DNI, and DI-600 when these are established on the basis of that factor. The table below shows sample sizes when the research subgroups are determined according to Dx factor and also the subsequent, respective sample mean Factor Dx values for the two principal research subgroups (DNI and DI-600).

samplesizes_DxFactors

 

This is interesting not least because it demonstrates that for all of the Dyslexia Index Factors, the sample Dx means in each of the research subgroups DNI and DI-600 respectively are not significantly different from each other and that therefore it is reasonable to test differences between other parameters of these research subgroups when the datasets within them are established through this process. The matrix of results presented in the previous blog-post summarizes effect sizes and t-test results for differences in Academic Behavioural Confidence between the research subgroups when these are generated according to Dyslexia Index FACTOR values.

 

However, there remains considerable merit in exploring the Dx factor profiles of respondents in the original research subgroups which are sifted according to their overall Dyslexia Index with the boundary value set at Dx > 592.5. To recap, this process generates research subgroups:

The factor profile of a respondent is shaped by the five Dyslexia Index factor values which are calculated using just the Dyslexia Index dimensions that together constitute each factor. The weighted mean dimension-score aggregation process generates a Dx value between 0 and 1000, just as it does for the overall Dyslexia Index.

For example, consider respondent #96408048 from research group ND who presented an overall Dyslexia Index of Dx = 604.94, hence placing this respondent just above the boundary into research subgroup: DNI – that is, students with an unreported dyslexia-like profile. The Dyslexia Index values for each of the 5 factors of Dyslexia Index for this respondents are these:

Dx overall Student respondent Dx Factor 1 Dx Factor 2 Dx Factor 3 Dx Factor 4 Dx Factor 5
Reading, Writing, Spelling Thinking & Processing Organization & Time Management Verbalizing  & Scoping Working Memory
604.94 #96408048 824.11 746.99 512.26 80.00 489.51

When applying the same boundary criteria of Dx > 592.5, this respondent’s Dyslexia Index is greater than that value for only two of the factors. What it is interesting to note is that this respondent’s Dx values for those two factors is high, indicating that this particular individual is presenting a strongly dyslexic profile in these two (factor) areas – reading, writing, spelling, and processing – conventionally regarded throughout decades of dyslexia research with children as being key indicators of the syndrome. Exploring this has caused me to reflect on the ways in which the factor Dx values are contributing to the overall Dx value and additionally, how the factor profiles of the other respondents sifted into research subgroup DNI compare to each other.

The table below lists all 18 respondents who have been sifted from research group ND – that is, no reported dyslexia – into research subgroup DNI, the 18 respondents who present a dyslexia-like profile based on the boundary cut-off value of Dx = 592.5.

Dx overall Student respondent Dx Factor 1 Dx Factor 2 Dx Factor 3 Dx Factor 4 Dx Factor 5
Reading, Writing, Spelling Thinking & Processing Organization & Time Management Verbalizing & Scoping Working Memory
research subgroup DNI (sifted from research group ND)  n=18
597.39 #75931558 916.77 432.65 489.60 634.84 609.76
604.94 #96408048 824.11 746.99 512.26 80.00 489.51
619.58 #61624105 505.49 549.41 706.84 812.97 1000.00
639.45 #16730769 583.02 714.22 483.05 1000.00 390.24
642.01 #20048355 567.20 718.86 568.08 852.27 500.00
642.02 #57371454 635.70 546.16 753.05 976.64 648.78
642.26 #97653577 694.09 559.57 712.99 816.33 472.93
654.84 #99268333 840.57 472.01 493.79 666.09 749.02
655.32 #63726872 570.07 771.58 500.00 466.41 800.00
656.90 #14557932 786.18 646.99 576.10 835.23 269.27
659.87 #78323952 700.81 621.80 518.70 938.91 316.10
682.51 #18801333 851.97 604.32 445.99 549.45 753.90
708.61 #21388930 878.05 613.15 755.14 336.95 1000.00
731.52 #87083069 895.96 647.76 851.19 1000.00 339.02
746.04 #10498881 903.14 527.08 705.65 933.44 1000.00
753.67 #68379308 819.43 788.45 611.81 549.53 884.63
779.07 #84526262 781.43 821.46 755.25 774.53 878.29
909.43 #28565915 980.17 874.41 1000.00 1000.00 937.32
research group ND (subgroup DNI) summary
717.32  <-sample mean->  763.01 647.60 635.53 734.64 668.82
 sample SD  141.87 123.49 152.28 257.97 253.89
 95% CI for pop’n mean 696 < μ < 830  589 < μ < 706  563 < μ < 708 612 < μ < 857 548 < μ < 790
view this data as charts: graphicon_pink40  

 

The table below summarizes results for the other two research subgroups. The complete datasets are not presented due to the respective sample sizes (n=47, n=44) but links to these are provided.

Also shown are effect size and t-test outcomes

summary for research subgroup DI-600 n = 47  (sifted from research group DI) – full dataset and chart here
Dx overall Student respondent Dx Factor 1 Dx Factor 2 Dx Factor 3 Dx Factor 4 Dx Factor 5
Reading, Writing, Spelling Thinking & Processing Organization & Time Management Verbalizing  & Scoping Working Memory
684.75  <-sample mean->  794.50 700.42 615.74 772.72 589.20
 sample SD  106.33 131.07 145.72 165.11 227.14
 95% CI for pop’n mean  764 < μ < 825  663 < μ < 738  574 < μ < 658  725 < μ < 820 524 < μ < 655
Hedges’ g effect size and t-test, one-tail @5% level between sample means research group ND(DNI) and DI-600
 0.4552  <- g ->  0.2692 0.4092 0.1341 0.1957 0.3393
 t=1.642 p=0.0527;
not significant
 <- t=, p=, sig? ->  t=0.971 p=0.168;
not significant
t=1.476 p=0.072;
not significant
t=0.484 p=0.315;
not significant
 t=0.706 p=0.241;
not significant
t=1.224 p=0.113;
not significant
view this data as charts: graphicon_pink40  
summary for research subgroup ND-400 n = 44  (sifted from research group ND) – full dataset and chart here
Dx overall Student respondent Dx Factor 1 Dx Factor 2 Dx Factor 3 Dx Factor 4 Dx Factor 5
Reading, Writing, Spelling Thinking & Processing Organization & Time Management Verbalizing  & Scoping Working Memory
304.00  <-sample mean-> 276.43 214.38 586.78 458.02 377.68
 sample SD  118.78 103.08 151.32 218.03 206.19
 95% CI for pop’n mean 241 < μ < 312  184 < μ < 245 542 < μ < 632 393 < μ < 523 316 < μ < 419
Hedges’ g effect size and t-test, one-tail @5% level between sample means research group ND(ND-400) and DI-600
6.030  <- g ->  4.604 4.106  0.1951  1.62  0.974
 t=28.72 p<0.00001;
significant
 <- t=, p=, sig? ->  t=21.95 p<0.00001;
significant
t=19.57 p<0.00001;
significant
t=0.9301 p=0.1774;
not significant
t=7.793 p<0.00001;
significant
t=4.641 p<0.00001;
significant
view this data as charts: graphicon_pink40  

This is interesting and looking at the summaries first of all, there appear to be a number of key points that emerge:

The complete data tables of Dyslexia Index Factors are available on the project webpages here, where additional discussion points are presented about the emerging interrelationships between Academic Behavioural Confidence and Dyslexia Index.

It is also useful here to provide a list of which dyslexia dimensions are the constituent parts of each dyslexia factor:

Dx Factor: Reading, writing, spelling

Dx Dimensions:

Dx Factor: Thinking and processing

Dx Dimensions:

Dx Factor: Organization and time-management

Dx Dimensions:

Dx Factor: Verbalizing and scoping

Dx Dimensions:

Dx Factor: Working memory

Dx Dimensions:

 

to be continued…

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