P553 Statistics, Prof. Kruschke, Homework 6

P553 Statistics in Psychology, Prof. Kruschke

Homework 6. Due Tuesday 16 October 2007.

  1. (5 pts) F distribution: Use the linked SPSS syntax file to explore sampling distributions of F. The file generates 5 different sampling distributions of F. For each of the five distributions, there is (a) a table of "Descriptive Statistics", (b) a table of "Statistics" that shows critical percentiles for F, and (c) a histogram. Please run the file in SPSS and do the following.
    • The output includes 5 histograms of F sampling distributions. The graphs have titles and subtitles with some missing numbers, indicated by underlines like this: ___. Write in the appropriate values in all the blanks. In particular, the blanks in F(__,__) refer to the df for the numerator and denominator of F. For each graph that was generated by populations with all means=0, write next to it the words "Null Hypothesis". For each other graph, write next to it the words "Alternative Hypothesis"
    • The output includes 5 tables of "Statistics" that specify the percentiles in the F distributions. If the population corresponds to a null hypothesis, then write the corresponding critical values from the F tables (in the textbook appendix) next to the SPSS output values. (The SPSS output values should be close to the tabled critical values.)
    • The output includes 5 tables of "Statistics" that specify the percentiles in the F distributions. For the two populations that are NOT null hypotheses, determine the power of the experiments (to within the nearest 5%) assuming a Type I error rate of .05. Describe in writing next to the table of percentiles how you arrived at your answer. For the case with a sample size of 10, assume that the alternative hypothesis corresponds to a "large" effect size, and report the corresponding power listed in Table 9-9, p. 355 of the textbook.
    • The output includes 5 tables of "Descriptive Statistics" that show the means of MSB, MSW, F, and RSQ. The (mean of) MSW is the (average) unbiased estimate of the population SD obtained by pooling the samples. Next to each table, write the expected value of MSW, like this: E(MSW)=____ (and fill in the blank with the appropriate value). When the null hypothesis is true, the MSB is also an unbiased estimate of the population SD. Next to each table for a null hypothesis, write the expected value of MSB, like this: E(MSB)=____ (and fill in the blank with the appropriate value).
    • For your personal edification, look at the various F distributions you have generated. Notice how they change depending of df_B and df_W. Visualize diagrams of the corresponding populations that generated the distributions. (Your thoughts are being continuously monitored by satellite-borne fMRI machines, so no cheating on this one. ;-)

    In all SPSS analyses of variance below, please
    * Include Descriptive Statistics and the test of Homogeneity of Variance. Do this as part of Analyze -> Compare Means -> One-Way ANOVA by checking the boxes of the Options dialogue.
    * Make a bar graph of the group means with error bars that indicate 1 SE. Do this separately from the ANOVA by using Graphs -> Interactive -> Bar and then the Error Bars tab.

  2. (5 pts.) Suppose an experiment has three conditions with three subjects each, with scores as follows:
    Group A: 1, 2, 3 Group B: 2, 3, 4 Group C: 5, 6, 7
    Conduct an omnibus ANOVA completely by hand, showing your work. Then verify your computations with SPSS, including your printout. (See note above regarding what to include in your SPSS output!)

  3. (5 pts.) P. 376, #15. Do these two omnibus ANOVAs with SPSS, not by hand (so, in particular, don't bother with part (d) as a separate part).
    DO answer the part about effect size.
    Also answer this: Notice that all that differs between data (a) and data (b) is the mean of Group 2, but the range of group means is the same. What component(s) of the F statistic is affected by this change in group mean?

    GroupScore
    1 3
    1 5
    2 4
    2 6
    2 8
    2 10
    3 3
    3 4
    3 5
    4 8
    4 10

  4. (5 pts.) For the data in the table at the right, conduct an omnibus ANOVA completely by hand, showing your work. HINT: Keep all the data in a single column like the one at right, and then include columns for the group mean Mj, (x-Mj)^2, GM, and (Mj-GM)^2.
    Verify your computations with SPSS, including your printout. See note above regarding what to include in your SPSS output!

  5. (5 pts.) P. 377-378, #21 AND #22.