Exam 15: Introduction to the Analysis of Variance

The higher is, the higher is power, other factors held constant.

A cancer researcher is interested in the effect of certain drugs on the growth rate of cancer cells. She grows 24 cultures of cancer cells and randomly divides them into four groups of 6 cultures each. Then she injects the cultures of each group with a different drug and counts the number of cells per square millimeter after 7 days. The following data are the results. a. Use one-way ANOVA to determine if any of the drugs has an effect ( a = 0.05). b. Use the HSD test to compare the 4 drugs ( a = 0.05).

It is possible to get significant differences between pairs of means using the HSD test that are not significant using the Scheffé test.

A clinical psychologist wants to know if there is any difference in the age of onset of paranoid schizophrenia, simple schizophrenia, or catatonic schizophrenia. The psychologist does a chart review and records the age of diagnosis for random samples of patients with the above diagnoses. a. Is there any difference in the age of onset for these three types of schizophrenia? (use a = 0.01). b. Make all post hoc pairwise comparisons possible, using a = 0.01 and the Scheffé test.

The value for Q _crit using the HSD test for 6 groups with 6 subjects in each group and a = 0.01 is _________.

If MS_between = 27.9 and MS_within = 54.2, what is the value of F _obt?

Using the HSD test, if there are 16 df associated with MS_within , and a = .05 and the number of groups = 3, Q _crit = _________.

If SS_within = 126, N = 28, k = 4, then what is the value of MS_within ?

The total variability of a set of data can be completely partitioned into the between-groups variability and the within-groups variability.

From an experiment the following data are obtained: a. Using a = 0.01 and the HSD test, compare the likelihood that and are random samples from the same population. b. What is the value of n ?

The HSD test is less powerful than planned comparisons.

Which of the following is(are) statistical test(s) for doing post hoc comparisons?

Which of the following tests hold the Type 1 error rate at a ?

It is not necessary to do an F test if one is only interested in doing planned comparisons between the groups.

A physiological psychologist suspects that the sweat gland activity decreases in people as they get older. The psychologist believes that the highest readings should occur in the youngest people and the lowest readings should occur in the oldest people. The sweat gland activity is assessed by measuring the electrodermal activity of the skin. The following data are electrodermal readings measured in micromhos/cm . The higher the value the more is the sweating. a. Using an a priori test and a = 0.05 1 tail , evaluate whether the young group sweats significantly more than the middle aged group. b. Using the HSD test, evaluate all possible pair-wise comparisons using a = 0.05. c. Would the results of part b have been different had we used the Scheffé test? Please show all work. d. Explain any differences in results between parts a , b and c .

When doing multiple comparisons, which method is the most powerful?

A t test for independent groups can be used to analyze the results from an experiment with k = 2 groups.

If one did a series of a priori pairwise t tests on k > 2 groups and analyzed the results using the t distribution, there would be a substantially lower risk of making a Type II error than if one used HSD or Scheffé tests.