P553 Statistics, Prof. Kruschke, Homework 5

P553 Statistics in Psychology, Prof. Kruschke

Homework 5. Due 14 October 2008.

This homework might use a lot of paper to print all the output. To save paper, perhaps print two output pages per side of paper if it is still legible and neat. Please keep your answers in order, and clearly label what you are doing where.

  1. (6 pts) t distribution: Use the linked SPSS syntax file to explore sampling distributions of t. The goal of this exercise is for you to see how the t distribution is (or is not) affected by unequal variances or unequal sample sizes. Please run the file in SPSS, print the output, and do the following.
    • Find the lines in the SPSS code (displayed in the output) that compute t with pooled or unpooled variance. Mark these lines and annotate which line computes which t (pooled or unpooled).
    • Equal variances and equal sample sizes: The first sampling distribution assumes normal populations of equal means, equal variances, and equal sample sizes. This is the null hypothesis on which are based the critical values of t in the table in the appendix of the textbook. From the "statistics" output table, average the magnitudes of the 2.5 and 97.5 percentiles, and average the magnitudes of the 5 and 95 percentiles. Write these averages next to the table. Now look up the corresponding critical values of t in the t table in the textbook, and write these critical values next to the corresponding average percentile values. Make sure to specify the df with your critical t values.
    • Equal variances and unequal sample sizes: Do the same thing for the next sampling distribution. Is there much influence on the critical values from the unequal sample sizes? In particular, has the Std. Deviation of the sampling distribution been much influenced?
    • Unequal variances and equal sample sizes: Do the same thing for the next sampling distribution. Is there much influence of the unequal variances on the critical values (relative to the first "textbook" distribution above, not the second)? In particular, has the Std. Deviation of the sampling distribution been much influenced? Discuss how this relates to the corrected or adjusted df provided in SPSS t-test output when the variances are unequal.
    • Unequal variances and unequal sample sizes: Near the top of p. 298 in Aron and Aron, it says "it turns out that in practice the t test gives pretty accurate results even when there are fairly large differences in the population variances, particulalrly when there are equal or near equal numbers of scores in the two samples." How does the fourth histogram relate to this statement?

  2. (6 pts.) p. 315 #19. Don't bother with parts (a)-(c), instead, do this: Compute the t-test by hand and annotate your work. Then verify in SPSS, and include the printout. Notice that N1 does not equal N2 in this case; are the t values different for pooled and unpooled variance (mark this on the printout)?

  3. (6 pts.) We are interested in knowing whether girls' names tend to be longer than boys' names, in terms of number of letters. Go to the Social Security Administration list of most popular baby names: http://www.ssa.gov/OACT/babynames/ . Scroll down the page to the section where you can retrieve a list of the top baby names for a given year. Choose a year of your choice and get the list of the top 50 names from the male and female lists. Enter the data into SPSS and conduct the t-test (include the printout). Hint: To get the names into SPSS, try the following. First, on the SSA web page, drag the cursor over the table to highlight all the names. Copy and paste into a blank text document (e.g., Notepad in Windows). In the text document, make sure you have properly pasted all the names in three columns of 50 rows. Save the text document. Then in SPSS use File -> Read_Text_Data. Once the names are in your SPSS spreadsheet, compute their lengths using Transform -> Compute and the formula namelength = LENGTH(LTRIM(RTRIM(name))). ALSO: Determine the effect size and power. Click here for detailed power tables.

    Litter Female Male
    A 6 6
    B 5 7
    C 4 8
    D 3 9
    E 2 10

  4. (7 pts.) Suppose you are interested in the weights of newborn gerbils. From each litter, you measure the weight of one female and one male. Here are the results (at right):

    (a) Is there a significant difference between the mean weights of newborn females and newborn males? Conduct this test by considering the female and male samples to be independent. Do this by hand and verify with SPSS. What is the effect size and power of this test? Finally, is it logically reasonable to suppose that the males and females within a litter have independent weights?

    (b) Is there a significant difference between the weights of newborn females and newborn males littermates? Conduct this test by considering the female and male littermates to be matched pairs, and compute a difference for each litter. Do this by hand and verify with SPSS. What is the effect size and power of this test?

    (c) Do you notice any relationship between weights of littermates that is not captured by the comparisons of means?