Statisttics Questions

1):    Basic definitions and reasons for using this test.

a) What are the assumptions of between-subjects analysis of variance?

b) Why not just compute t-tests among all pairs of means instead computing an analysis of variance?

c) How is it that estimates of variance can be used to test a hypothesis about means?

2):  See if you can apply this analysis.

If an experiment is conducted with 5 conditions and 6 subjects in each condition, what are dfn and dfe?

3):  This has all the calculations involved.  Can you find the critical F-value from the Table?  The p-value can also be approximated from that Table.  (Find an F-Table that you like on line)

The Table asked for has these headings:   SOURCE (with these categories down the side:  age, time, age x time, error and total), then continuing across the top:  df, SSQ,  MS, F and P.  Go ahead and fill it in.

The following data are from a hypothetical study on the effects of age and time on scores on a test of reading comprehension. Compute the analysis of variance summary table.

4.) PROBLEMS # a through h (count as ONE problem):  This is all about knowing the why and when about this test.

PROBLEMS #9 through 15 (count as ONE problem):  This involves working a basic F-test problem.  Can you find the critical F-value and compare the test statistic to it to see if we accept or reject (you pick an alpha).  You also can approximate the p-value from the table (find table on web if necessary). 

One-Way ANOVA

Use the following information to answer the next five exercises. There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?

F Distribution and One-Way ANOVA

a) Write one assumption.

b) Write another assumption.

c) Write a third assumption.

d) Write a fourth assumption.

e) Write the final assumption.

f) State the null hypothesis for a one-way ANOVA test if there are four groups.

g) State the alternative hypothesis for a one-way ANOVA test if there are three groups.

h) When do you use an ANOVA test?

The F Distribution and the F-Ratio

Use the following information to answer the next eight exercises. Groups of men from three different areas of the country are to be tested for mean weight. The entries in the table are the weights for the different groups. The one-way ANOVA results are shown in Table 13.13.

Table 13.13

a) What is the Sum of Squares Factor?

b) What is the Sum of Squares Error?

c) What is the df for the numerator?

d) What is the df for the denominator?

e) What is the Mean Square Factor?

f) What is the Mean Square Error?

g) What is the F statistic?

5.) BONUS:  see if you have this concept (F-test) down

Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that Table 13.26 shows the results of a study.

Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.