When doing an experiment with many groups, what is the problem with doing t tests between all possible groups without any correction? Why does use of the analysis of variance avoid that problem?
The problem with utilizing a t-test with many groups is that there is an increase in the probability of a Type I error occurring. Yet, when we use the analysis of variance (ANOVA) method, it is specifically designed to be used when there are two or more groups. It allows researchers to evaluate the mean of the single hypothesis through an a-level and reduces the potential of a Type I error occurring.
8. What are the assumptions underlying the analysis of variance?
10. Find Fcrit for the following situations:a. df(numerator) = 2, df(denominator) = 16, ? = 0.05
b. df(numerator) = 3, df(denominator) = 36, ? = 0.05
c. df(numerator) = 3, df(denominator) = 36, ? = 0.01What happens to Fcrit as the degrees of freedom increase and alpha is held constant? What happens to Fcrit when the degrees of freedom are held constant and alpha is made more stringent?
12. What are the variables that affect the power of the one-way analysis of variance technique?
13. For each of the variables identified in Question 12, state how power is affected if the variable is increased. Use the equation for Fobt on p. 421 to justify your answer.
20. Assume you are a nutritionist who has been asked to determine whether there is a difference in sugar content among the three leading brands of breakfast cereal (brands A, B, and C). To assess the amount of sugar in the cereals, you randomly sample six packages of each brand and chemically determine their sugar content. The following grams of sugar were found:
a. Using the conceptual equations of the one-way ANOVA, determine whether any of the brands differ in sugar content. Use ? = 0.05.
b. Same as part a, except use the computational equations. Which do you prefer? Why?c. Do a post hoc analysis on each pair of means using the Tukey HSD test with ? = 0.05 to determine which cereals are different in sugar content.
d. Same as part c, but use the Scheffé test.
e. Explain any differences between the results of part c and part d.