SPSS Tests of Significance Discussion: Chi-Square Example With Hypotheses and Interpretation (GSS 2018)

SPSS Discussion: Tests of Significance on Project Variables (GSS 2018)

In Week 3 you used crosstabs to see whether a relationship between two variables was worth examining; in Week 4 you studied tests of significance. Now apply a test of significance to your project variables, chosen by level of measurement:

1. Briefly explain your topic and research question, then begin the five steps of hypothesis testing by stating the research and null hypotheses. State that alpha is .05.
2. Run the appropriate test (chi-square for two categorical variables; regression for two interval/ratio variables; independent-samples t test when a two-group categorical IV predicts an interval/ratio DV; ANOVA for three or more groups) and paste the table.
3. Identify the two-tailed p value and explain your findings. Is p < alpha? Do you reject or fail to reject the null hypothesis? Does your IV affect your DV?

Tests of significance tell us whether a relationship observed in the GSS 2018 sample is likely to generalize to the population of U.S. adults.

Original example for study purposes (about 380 words). All counts and statistics are illustrative, not real GSS output.

Topic and research question. My project examines gender differences in perceived neighborhood safety among U.S. adults. Research question: Is respondent’s sex related to fear of walking alone at night in the neighborhood? The independent variable is SEX (male, female; nominal), and the dependent variable is FEAR (“Is there any area right around here, that is, within a mile, where you would be afraid to walk alone at night?” yes, no; nominal).

Step 1: Hypotheses and alpha.

• Research hypothesis (H1): There is a relationship between sex and fear of walking alone at night; women are more likely than men to report fear.
• Null hypothesis (H0): There is no relationship between sex and fear of walking alone at night.
• Alpha level: .05.

Step 2: Test of significance. Because both variables are categorical, I ran a chi-square test (Analyze > Descriptive Statistics > Crosstabs, with Chi-square selected under Statistics and column percentages under Cells).

Crosstabulation: FEAR by SEX (illustrative)

Chi-Square Tests (illustrative)

0 cells (0.0%) have expected count less than 5. The minimum expected count is 287.00.

Step 3: Findings. The Pearson chi-square is 59.01 with 1 degree of freedom, and the two-tailed p value (Asymptotic Significance, 2-sided) is less than .001. Because p < .05, I reject the null hypothesis and keep the research hypothesis. In this illustrative sample, 50.1% of women reported fear of walking alone at night compared with 30.6% of men, a difference of about 20 percentage points. The result suggests that sex is related to fear of walking alone at night and that the relationship is unlikely to be due to sampling error, so it is likely to hold in the population of U.S. adults. A significant chi-square shows that a relationship exists, but it does not prove that sex causes fear; other factors such as age, neighborhood type and past victimization could also play a role and could be examined as control variables.

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