Statistical Analysis of Introversion/Extroversion Among Different Hair Colors
How can we test for differences among blonde-haired people, brown-haired people, and redheads in terms of introversion/extroversion?
The researcher selected random samples from a college campus and obtained the following data:
- Blonde-haired: 8, 10, 6, 6, 5, 3
- Brown-haired: 3, 5, 2, 4, 3, 5
- Redheads: 2, 1, 7, 2, 2, 3
Answer:
To test for differences among the groups, a one-way ANOVA can be used. After performing the ANOVA, if the p-value is less than the chosen significance level, we reject the null hypothesis and conclude that there is a significant difference among the groups. If the ANOVA indicates a significant difference, a Tukey's post hoc test can be conducted to compare each group pair-wise.
To test for differences among the groups, a one-way ANOVA can be used. ANOVA tests whether there is a significant difference in means between multiple groups. In this experiment, the groups are blonde-haired, brown-haired, and redheads. The null hypothesis is that there is no significant difference in mean introversion/extroversion scores among the groups. The alternative hypothesis is that at least one group differs from the others.
If the ANOVA indicates a significant difference among the groups, a Tukey's post hoc test can be conducted to compare each group pair-wise. The Tukey's test determines which specific group pairs differ significantly. It adjusts for multiple comparisons to avoid increasing the risk of a type I error. The results of the Tukey's test will show which groups are significantly different from each other and which are not.