Methods of data analysis :

The tests for addressing question 1 and 2 are Application of Cognitive Function Scale (ACFS) classification subscale, norm-referenced Raven‟s Coloured Progressive Matrices (RCPM) Brigance Diagnostic Inventory of Early Development II (IED-II) standardised academic/cognitive domain assessment and Brigance Diagnostic Inventory of Early Development (IED-II) criterion referenced assessment

To answer the above research questions, an analysis was conducted using a series of tests/measures that examine the responses of the participants in both the experimental and control groups. The design of the study used a 2 x 2 ANOVA with the treatment as a between-subject factor (Experimental vs. Control group) and pre- post tests (time element) as the within-subject factor. ANOVA is preferred over t-

143 tests because it is a repeated measure to detect the main and interaction effects between the factors over time, therefore to test more complex hypotheses about reality. While t-test compares only the means of two groups, ANOVA examines two factors simultaneously; in this research study, the two factors were between-subject factor (experimental vs. control) and within-subject factor (time element in pre-post tests). The effect of each of the above factor as well as interaction effect of the two factors were examined.

Effect size was used to report the significance of the difference between the experimental and control groups. According to Coe (2002), one of the main problems associated with the use of p-value is that it depends on the size of the effect and the size of the sample. But most important of all, statistical significance does not tell the size of the effect. The use of effect size is particularly valuable in quantifying the effectiveness of this particular intervention (Coe, 2002). This is also consistent with the encouragement of this approach given by the American Psychological Association to report effect size in research studies (Wilkinson et al., 1999).

There are many ways of calculating effect sizes. For this research study, the Hedges g effect size, with its adjustment for sample size, was used to quantify the size of the difference between the experimental and control groups (Coe, 2002).

The labeling used to name the dependent variables in this study are listed in Table 4.1.

Table 4.1: The variables

Variable

Name Variable label/Value Label

Group The group participants are in; either in the experimental group (eg) or control group (cg)

RCPMpre RCPM, pre test RCPMpost RCPM, post test

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ACFSpre ACFS, pre test ACFSpost ACFS, post test Brigancepre Brigance, pre test Brigancepost Brigance, post test Brig2pre Brig2, pre test Brig2post Brig2, post test

To answer the two primary questions listed above, initial comparisons have to be made between the mean and standard deviation in relation to each of the test (subscale) as a source of information with regards to the relevance of this procedure for this population.

To investigate if there were significant differences across these subscales and time, the SPSS General Linear Model (GLM); Repeated Measures ANOVA was used. The assumptions of Repeated Measures ANOVA are similar to those for ANOVA in terms of normality and homogeneity of variances. However, in addition to the variances, which involve deviations from the mean of each person‟s rating on one subscale, the repeated measures design also takes into account of more than one measure of subscales for each person.

4.1.1.1Data Assumptions

We need to assume the relationships between pair of experimental conditions are similar (i.e. the level of dependence between pairs of groups is roughly equal). This assumption is more commonly known as sphericity. The null hypothesis test of the test of sphericity is: the variance-covariance structure has the Huynh-Feldt structure, so called Type H structure.

4.1.1.2Effects of meeting sphericity assumption

If the sphericity test is not significant then we cannot reject that null hypothesis that the variance-covariance structure has Type H structure.

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4.1.1.3 Effects of violating sphericity assumption

If, however, the sphericity test is significant then we reject that the variance- covariance structure has a Type H structure. The effect of violating sphericity is a loss of power (i.e. increased probability of a Type II error) and a test statistic (F- ratio) that cannot be compared to tabulated values of the F-distribution (XXX). One will need to further investigate the severity of departure from the sphericity assumption; using SPSS Mauchly‟s test.

1. If Mauchly‟s test is significant (p<0.05), we can infer that there are

significant differences between the variance of differences: the condition of sphericity is not met. We cannot trust the F-ratios produced by SPSS.

2. If Mauchly‟s test is not significant (p>0.05), it is reasonable to infer variance of differences are roughly equal; condition of sphericity is met.

4.1.1.4 Corrections for violation of sphericity assumption

There are several corrections that can be applied using SPSS to produce a valid F- ratio. All of these corrections involve adjusting the degree of freedom associated with the F-value. In all cases, the degree of freedom is reduced based on an estimate on how spherical the data are; by reducing the degree of freedom to make the F- ratio more conservative. There are three different estimates of sphericity used to correct the degree of freedom in SPSS

 Greenhouse and Geisser‟s (1958)

 Huynh and Feldt‟s (1976)

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Which one to use?

1. When estimates of spehericity ( ε) >0.75, then use Huynh and Feldt‟s 2. When estimates of spehericity ( ε) <0.75, then use Greenhouse and Geisser‟s

correction

For this research study, the F value or degree of freedom has been adjusted with the use of Greenhouse and Geisser (1958) because there were several violations in relation to the co-variances for the main dependent variables for the experimental and control groups. Please see Appendix O for the detailed output of the data.