The independent sample T test uses the based on the sample degree of freedom . The ANOVA test is based on the . This statistic relies on two degrees of freedom – Between groups (Transport here) and within groups (Residuals). Generally, a large value is associated with a rejection of the null hypothesis. The calculations are fairly complicated and most researchers do not considered them nor even understand them. All you need is the p-value which is given within SPSS or Jamovi. Reporting the ANOVA test: The test above show that the average time taken to get to the store between the three groups is statistically significant, . There are three types of effect size measures for this ANOVA test, The represents the amount of variance in the times taken to get to the store that is accounted for by the mode of transport used (The independent variable). Simulation studies have shown that the slightly overestimate the effect size in the population. Hence, it was suggested that the is a better an unbiased effect size. The standards for these effect sizes are as follows: Reporting the ANOVA test: The test above show that the average time taken to get to the store between the three groups is statistically significant, with a large effect size (0.177) Knowing that the difference in average time between the different mode of transport is statistically significant does not tell us which average if not all are different. To do this, we conduct the post-hoc test. These are tests between two groups similar to the independent sample T test. There are several post hoc tests. We use the Tukey test. Reporting the ANOVA test: The test above show that the average time taken to get to the store between the three groups is statistically significant, with a large effect size. A post-hoc test suggests that the average time for walkers to the store is significantly different (against private transport users) and (against public transport users). There is no significant time difference between public and private transport users.
