The results of histogram of data of current study depicted the approximate normal distribution (figure 1), whereas the P-P plot displayed a linear relationship (figure 2) and the residual plot presented no set patterns and, therefore, the assumption of
homoscedasticity or homogeneity of variance of the effect of instructional leadership was not violated.
If there were statistically significant differences, it would be checked by the post-hoc LSD, taking into account
homoscedasticity. In case of heteroscedasticity, the ANOVA would be replaced by Welch's test, and if there were statistically significant differences, they would be checked by Tamhane's post-hoc T2.
Preliminary analyses were performed to ensure no violation of the assumptions of normality, linearity and
homoscedasticity. Table 1 shows the relevant descriptive statistics of language achievement and the independent variables: personality factors from the Big Five measure (neuroticism, extraversion, openness, agreeableness, & conscientiousness), and Gc.
The last assumption that is left to test is the equality of the variances of residuals, in other terms the existence of
homoscedasticity.
Homoscedasticity is tested by Scatterplot diagram where if there is a dispersion of data in the diagram, in other words if there cannot be noticed any correctness (order, scheduled data) that means that the
homoscedasticity exists.
The assumption of
homoscedasticity was checked by inspection of a plot of the unstandardized values against predicted values.
Data were checked for normality and
homoscedasticity, and if needed, were arcsine square-root or log-transformed before analysis by 1-way ANOVA (SAS Institute 2004).
As
homoscedasticity is already assumed for the random error, [[epsilon].sub.t], it is sufficient to verify whether the angular coefficient, [[beta].sub.1], is between the values of -1 and 1, exclusive.
The data of the index of chromatophores, the color value of the abdomen and cephalothorax, in each of the treatments, were compared to each other, for each case, variance analysis of one-way, previous tests of normality (Kolmogorov-Smirnov; a = 0.05) and
homoscedasticity (Bartlett; a = 0.05), all through the statistical software, SigmaStat V3.1 (2004).
The Shapiro-Wilk test and sphericity (Mauchly test) showed that all variables presented normal distribution and
homoscedasticity. Intraclass correlation coefficient showed high relation between test and retest (ICC=0.98).
And like the OLS model, the spatial lag model also violated the
homoscedasticity assumption.
Preliminary analyses ensured no violation of the assumptions of normality, linearity, and
homoscedasticity. There was a positive correlation between the results of the MCCTS and the MEIM-R, r = .41, n = 172, p < .01, suggesting a small positive relationship between MCC and EI.