. You are running an a single variable ANOVA with five levels of the variable, such as comparing IQ on 5th, 6th, 7th, 8th and 9th graders and the F-value is very large. The significance for the F value is equal to .0003. What can you conclude about the overall effect and what do you now have to do to determine differences among the five levels? (Be specific.)
To interpret the results of the single variable ANOVA, we first look at the F-value. A large F-value suggests that there is a significant overall effect of the independent variable (in this case, the grade level) on the dependent variable (IQ scores).
In your case, the significance level for the F-value is stated to be 0.0003. This means that the probability of obtaining such a large F-value by chance alone is very low (less than 0.03%). Therefore, we can conclude that there is a significant overall effect of grade level on IQ scores.
To determine the differences among the five levels of grade (5th, 6th, 7th, 8th, and 9th graders), we need to conduct post-hoc tests. The purpose of these tests is to compare each level of the independent variable against every other level and determine which pairs are significantly different from each other.
There are different methods for conducting post-hoc tests, and the choice of method depends on factors such as sample size, study design, and desired level of control for Type I error rate. Some common post-hoc tests include Tukey's Honestly Significant Difference (HSD), Scheffe's test, and Bonferroni correction.
To determine the differences among the five levels, you should consult with a statistician or use statistical software that provides post-hoc tests. These tests will conduct pairwise comparisons and identify the specific grade levels that differ significantly in terms of IQ scores.