were unable to fulfil the criterion of ‘homogeneity of variance’ in the groups being studied. Welch’s ANOVA corrects for these problems in the data and otherwise performs much the same function as the standard ANOVA. Both the standard ANOVA and Welch’s ANOVA are known as ’omnibus tests’. That is, where three or more groups of data are being simultaneously studied, they can detect whether a significant difference occurs somewhere between the groups, but omnibus tests cannot locate which pairs of groups are different in relation to each other. To fix this, a variety of ‘post-hoc’ tests are available to pinpoint which pairs are significantly different from each other. Post-hoc tests Several post-hoc tests are available for use, each of which are appropriate in different circumstances depending on the data being studied. This report accompanies ANOVA testing with either a Games-Howell test or a Hochberg’s GT2 test. The Games-Howell post-hoc test is appropriate for use if the data do not fulfil the ‘homogeneity of variance’ criterion, while Hochberg’s GT2 test is appropriate for use if the studied groups each have a very different sample size (for example, if the group ‘indicating a guilty plea during the committal stage’ is vastly larger than the group ‘pleading guilty at the door of the court’). Post-hoc testing is not required if only two groups of data were examined in the initial ANOVA or Welch’s ANOVA. Reporting the results of significance testing When the result of a z-test is stated in this report, it will be displayed in the following manner: (z = test score, p-value). When the result of ANOVA is stated, it will be displayed in the following manner: (F(degrees of freedom between groups, degrees of freedom within groups) = test score, p-value). The explanation for the test scores and degrees of freedom for these tests are technical and not central to understanding the results of the data analysis for this report. The p-value, however, is the most important output from these tests as it determines whether a result is significant or not.
were unable to fulfil the criterion of ‘homogeneity of variance’ in the groups being studied. Welch’s ANOVA corrects for these problems in the data and otherwise performs much the same function as the standard ANOVA. Both the standard ANOVA and Welch’s ANOVA are known as ’omnibus tests’. That is, where three or more groups of data are being simultaneously studied, they can detect whether a significant difference occurs somewhere between the groups, but omnibus tests cannot locate which pairs of groups are different in relation to each other. To fix this, a variety of ‘post-hoc’ tests are available to pinpoint which pairs are significantly different from each other. Post-hoc tests Several post-hoc tests are available for use, each of which are appropriate in different circumstances depending on the data being studied. This report accompanies ANOVA testing with either a Games-Howell test or a Hochberg’s GT2 test. The Games-Howell post-hoc test is appropriate for use if the data do not fulfil the ‘homogeneity of variance’ criterion, while Hochberg’s GT2 test is appropriate for use if the studied groups each have a very different sample size (for example, if the group ‘indicating a guilty plea during the committal stage’ is vastly larger than the group ‘pleading guilty at the door of the court’). Post-hoc testing is not required if only two groups of data were examined in the initial ANOVA or Welch’s ANOVA. Reporting the results of significance testing When the result of a z-test is stated in this report, it will be displayed in the following manner: (z = test score, p-value). When the result of ANOVA is stated, it will be displayed in the following manner: (F(degrees of freedom between groups, degrees of freedom within groups) = test score, p-value). The explanation for the test scores and degrees of freedom for these tests are technical and not central to understanding the results of the data analysis for this report. The p-value, however, is the most important output from these tests as it determines whether a result is significant or not.