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PSY515 - Homework One | Tests with One IV | Fall 2023

This homework involves conducting several different kinds of tests with one independent variable. We will be using a large nationwide survey dataset that I have trimmed way down to make this easier to analyze. The responses and data are real. To help you find things in the data file, I will list the name of the variables that I want you to use in all-caps, but I will not explicitly tell you which is the IV and which is the DV, as you should be able to figure that out from the context of the question. Note when looking at variable values: things coded IAP, NAP, DK, or NA are automatically counted as missing data and can be ignored.

You may use SPSS or Jamovi for this assignment. Please indicate which software and version you are using, however. If you use Jamovi, you should also install the GAMLG package (click the modules + button in the upper right). Using that analysis button (vs the generic ANOVA one) will allow you to get uncorrected & Bonferroni post-hoc tests.

QUICK PROLOGUE: ONE GROUP TESTS

We didn’t explicitly cover this, but sometimes you simply want to know whether a group of people significantly differ from a known criterion (e.g., a population mean). This is accomplished via a one-sample t-test. You will find this test in SPSS under Analyze->Compare Means (And in Jamovi under the T-Test option). All you need to do is select the appropriate variable, and enter the appropriate reference number (e.g., 26 in the first question) into the Test Value area. The results will tell you if your data significantly differs from that value.

1) The average age at which people first get married (AGEWED) is approximately 26 years. Does our entire sample differ from this average? What is the average age at which people in our sample first got married?

2) I have three siblings (SIBS). Is that significantly different from the people in our sample?

3) Assuming this is your first year of graduate school, then all of you have about 17 years of education (EDUC). Does this significantly differ from the people in the sample?

TWO GROUP TESTS

In some cases, the IVs will have only two possible levels (e.g., 0 and 1 – you will need to look at the variable coding info to see the codes). However, in other cases, the IVs have multiple levels, and you will need to select only the groups you want to compare (e.g., by specifying group 2 vs 5).

4) Did divorcees (DIVORCE) get married at a younger age (AGEWED) than people who were still married? Is there significantly greater variability among the marriage age of divorcees vs. still-marrieds? Which line of the t-test results will you then use?

5) Does the age at first marriage (AGEWED) differ by sex (SEX)? Who gets married earlier?

6) Does the highest year of education (EDUC) differ by sed (SEX)? Who has more?

7) Do private-sector or government employees (WRKGOVT) earn more money (RINCOM06)? Which have higher levels of education (EDUC)?

8) Does the number of siblings you have (SIBS) relate to whether you’re married or single (MARITAL; single=never married)?

9) Are people with graduate degrees (DEGREE) more or less than politically conservative (POVIEWS) than people with only a high school degree?

THREE+ GROUP TESTS

Now for some ANOVAs. Just for this section, you do NOT need to run post-hoc tests. Be sure to ask for Descriptive Statistics and Means Plots to help you see what’s going on.

10) Overall, does the age at first marriage (AGEWED) differ by educational degree (DEGREE)?

11) Compare income (rincome06) for each level of educational degree (DEGREE).

12) Is there a relationship between religion (RELIG) and the number of siblings (SIBS) each participant has?

POST HOC TESTS

13) We’ll start off with just a basic one-way ANOVA. Let’s figure out if the size of the town you’re from influences how early you’re likely to have children. The IV is the variable RES16 (where the person’s residence was when they were 16 years old), and the DV is the variable AGEKDBRN (age at which they first had a child).

14) Now, I want to know something more specific, and we are going to try a number of different ways of getting at this info. I am from a large town (CITY GT250000, as listed in the data file). I want to know what types of locations contain people that have children at a significantly different age than city folks like me. You already know of one way to do this: Re-run the analysis conducting both Tukey, Bonferroni, and LSD/Uncorrected post-hoc tests. Focus on only the rows that compare CITY GT250000 to each of the other locations. Indicate what differences you find separately for each post-hoc test type.

15) Let’s try a different way of getting at this same information. Because post-hoc tests compare pairs of groups at a time, conduct a series of independent samples t-tests comparing CITY GT250000 to each of the other categories (so you will run five different t-tests). FOR THE PURPOSES OF THIS QUESTION, IN SPSS USE THE TOP ROW OF RESULTS REGARDLESS OF THE OUTCOME OF THE VARIANCE TEST. Report the results of each of the tests in APA format.

16) Compare the results of the t-tests—particularly the significance levels—to each of the sets of post-hoc tests you ran earlier. The t-test results will closely resemble one of the post-hoc results. Which one? If you decided to run t-tests instead of Tukey post-hoc tests, would it be easier or harder to find significant results?

Now we’ll take another look at what I asked you in questions 10-12. Re-run those analyses (the questions below) but this time do the full analysis including Tukey HSD post hoc tests. Report which groups differ from which other groups.

17) Overall, does the age at first marriage (AGEWED) differ by educational degree (DEGREE) – Report the Post Hoc Differences, telling me which degrees differ from which other degrees.

18) Compare income (rincome06) for each level of educational degree (DEGREE) – Report the Post Hoc Differences, telling me which degrees differ from which other degrees.

19) Is there a relationship between religion (RELIG) and the number of siblings (SIBS) each participant has?  – Report the Post Hoc Differences, telling me which religions differ from each other.

Additional Instructions and Hints:

For the primary tests (t-test, F-test), respond in a sentence to the question and provide the APA-format statistical results, including the test type, degrees of freedom, text value, p-value, and effect size. For example:

Yes, the number of hours that a person works during each week differs based on their
industry, F (1, 24) = 3.42, p = .02, η² = .04.
or
No, women are not more likely to live in cities compared to suburbs, t (254) = 1.23, p = .54, d = .14

For the post-hoc tests, to make things easy for you (just for the homework), you only need to provide p-values for SIGNIFICANT tests. Follow that up with a statement saying that no other tests were significant. For example:

Post-hoc tests using the Tukey HSD correction found that the Midwest was significantly poorer than the West (p=.03), the Northeast was significantly poorer than the South (p=.01), and the Southwest was significantly poorer than the Northwest (p<.001). No other comparisons were statistically significant.

You have the choice of pasting the relevant output into your homework. It is not required (just the above information is), but it might help us understand what happened if your answer is incorrect.

When conducting an independent-samples t-test, remember that you may use uncorrected (or “equal variances assumed”) for this class regardless of whether the levine’s test is significant.

Remember to provide EXACT p-values to at least two decimal places. The only exception is when you see a value of “p=.000”– those results should be labeled “p<.001”

Also remember that, if you need to hand calculate Cohen’s d, the formula is