Normality of distribution

Figure 3 Academic self-perception scores for average/high attaining group N = 15

Figure 2 Academic self-perception scores for low attaining group N = 30

Figure 4 Attitudes towards teachers scores for low

attaining group N = 30 Figure 3 Attitudes towards teachers scores for average/high attaining group N = 15

Figure 5 Attitudes towards school scores for low

A visual inspection of figures 2 to 11 along with accompanying box plots (see Appendix 21) suggested there was a normal distribution of scores for the low attaining group on factors “attitudes towards teachers” and “motivation and self-regulation”. The average/high attaining group appeared to be normally distributed on the factors “academic self-

perceptions” and “attitudes towards teachers”. These sets of data were deemed normally distributed because their respective histograms were relatively symmetrical, had a single

Figure 8 Goal valuation scores for low attaining

group N = 30 Figure 7 Goal valuation scores for average/high attaining group N = 15

Figure 10 Motivation and self-regulation scores

clear peak and roughly followed the normal distribution curve. They also had box plots with no, or only one, outlier and relatively even whiskers (Field, 2009).

Although box plots for both groups on the factor “attitudes towards school” showed no outliers and had relatively even whiskers, their histograms suggested the data may not be normally distributed. The low attaining group’s data (figure 6) appeared platykurtic (flat and wide) in places, suggesting negative kurtosis. The average/high attaining group’s data (figure 7) displayed an uneven rather than smooth distribution with multiple peaks, again suggesting the kurtosis may deviate from the recommended normality level of zero (DeCarlo, 1997).

Both groups showed a distinct lack of symmetry in their distribution on the factor "goal valuation". Figures 8 and 9 show a clustering of scores towards the upper end of the distribution and trailing tails towards the lower end. This suggests there were very few scores in the lower range compared to the upper. The box plot for the low attaining group displayed a considerably longer lower than upper whisker and the average/high attaining group had no upper whisker at all, suggesting a high frequency of scores at the higher end and subsequently a severe skew in the distribution (see Appendix 21.4). A potential negative skew was identified in the data of the average/high group on the factor

"motivation and self-regulation". This was suggested by the presence of a notably longer lower whisker than the upper. The presence of two extreme outliers in the data of the low attaining group on the factor "academic self-perceptions." also suggested a skew in the data.

Due to the number of potential violations of normality observed in the frequency

distributions, the researcher chose to use the formulae; kurtosis/SE and skewness/SE = Z- score to check whether they were indeed violations - with Z-scores of +-1.96 indicating significant deviations from the norm.

Table 10 - Skewness and kurtosis measures of distribution with accompanying standard errors and Z-scores for low and average/high attaining groups on each of the factors of the SAAS-R, N = 45

Groups

Low attaining Average/High attaining

Skewnes s

SE Z Kurtosis SE Z Skewness SE Z Kurtosis SE Z

Academic self perceptions -.062 0.43 -1.44 0.17 0.83 0.20 -0.62 0.58 -1.07 0.06 1.12 0.05 Attitudes towards teachers -0.22 0.43 -0.51 -0.64 0.83 - 0.77 -0.65 0.58 -1.12 0.90 1.12 0.80

Factors Attitudes towards school -0.46 0.43 -1.07 -1.03 0.83 - 1.24 -0.16 0.58 -0.28 -0.88 1.12 -0.79 Goal valuation -1.43 0.43 -3.33 1.76 0.83 2.12 -2.27 0.58 -3.91 6.10 1.12 5.45 Motivation & self- regulation -0.28 0.43 -0.65 -0.77 0.83 - 0.93 -1.43 0.58 -2.47 2.13 1.12 1.90

Table 10 shows that based on the skew and kurtosis of both the low and average/high attaining groups, the factor "goal valuation" is not of normal distribution. The factor "motivation and self-regulation" was also found to be not normally distributed and negatively skewed for the average/high attaining group. A Kolmogorov-Smirnov test of normality in SPSS reported the scores on the factor “goal valuation” for the low attaining group, D (30) = 0.24, p = 0.00 and the average/high group, D (15) = 0.24, p = 0.02 were significantly non-normal at the level of <

0.05, as was the factor “motivation and self-regulation” for the average/high

attaining group, D (15) = 0.28, p = 0.002. All other distributions were found to be not significantly different from a normal distribution.

All identified outliers were individually inspected and found to be acceptable and not the result of deliberate patterned selection e.g. circling "1" for all items on the questionnaire, or an erroneous selection. The researcher chose not to remove outliers from the data set due to the small sample size, which may have then had a greater detrimental effect on the power of the study to detect statistical differences. Also, the SAAS-R employs a rating scale where all responses from 1 – 7 are valid, and all identified outliers sat within this valid range (McCoach, 2002).

4.2.2.2 Homogeneity of variance

Homogeneity of variance, which is the assumption that the spread of scores on a variable is the same within different groups, was tested using the Levene’s test (Levene, 1960). The Levene's test tests the null hypothesis that there is no significant difference in the variances between groups.

The results of the Levene’s test conducted in SPSS revealed the factors: “academic self-perceptions”, “attitudes towards teachers”, “attitudes towards school” and “motivation and self-regulation” had equal variances at the level P > 0.05, between the low and average/high attaining groups. However, on the factor “goal valuation”

the low and high/average groups were found to have statistically significant

variances, F (43, 40) = 4.43, p = 0.04. Therefore, the null hypothesis of no significant difference could not be rejected. This means that the spread of scores on the factor "goal valuation" was different between the groups. An examination of the ranges within each dataset showed that there was a greater range of scores in the low attaining group than the average/high (see Appendix 21.4 for ranges).

4.2.2.3 Independence

The assumption of independence requires data from individual participants to be independent of each other, meaning that one person does not affect the data or information gathered from another participant.

The researcher was confident the assumption of independence was met in this study, as each participant completed the SAAS-R questionnaire independently, in silence, taking as much time as they needed and under the supervision of an adult to ensure answers were not shared, compared or influenced.

4.2.3 Significance Testing

As the factor “goal valuation” was found to violate the assumption of normality of distribution and homogeneity of variance, and the average/high-attaining group was also found to violate the assumption of normality of distribution on the factor "motivation and self-regulation", non-parametric testing was needed. Therefore, to

ensure that the statistical tests used with these factors were reliable and valid, and to be able to make confident conclusions about observed differences between groups, a Mann-Whitney-U test was used to investigate significant differences between groups on both the "motivation and self-regulation" and "goal valuation" factors. This test has greater power than T-tests to detect differences when data are not normally distributed. Two-tailed independent samples T-tests were run on the factors: academic self-perceptions, attitudes towards teachers and attitudes towards school.

The results of the T-test showed there was no statistically significant difference between the means of the low and average/high attaining groups on academic self- perceptions t (43) = -0.30, p > 0.05, attitudes towards teachers t (43) = -1.34, p > 0.05 nor attitudes towards school t (43) = -1.32, p > 0.05. Therefore, the null hypothesis of no significant difference between the groups must be accepted, and the

experimental hypothesis rejected.

The results of the Mann-Whitney-U test on goal valuation showed that average/high achievers had a higher mean rank (26.80) than low achievers (21.10), meaning the low achieving group had a greater number of low scores within it. However, these differences were not found to be significant, U = 168.00, Z = -1.39, p = 0.169, suggesting both groups reported comparable levels of goal valuation. The results of the Mann-Whitney-U test on motivation and self-regulation showed that

average/high achievers had a higher mean rank (26.07) than low achievers (21.47), meaning the low achieving group had a greater number of low scores within it.

However, as with “goal valuation”, these differences were not found to be significant, U = 179.00, Z = -1.11, p = 0.273 suggesting both groups reported comparable levels of motivation and self-regulation.