What’s your sign? The University of Chicago’s General Social...

What’s your sign? The University of Chicago’s General Social Survey (GSS) is the nation’s most important social science sample survey. For reasons known only to social scientists, the GSS regularly asks a random sample of people their astrological sign. Here are the counts of responses from a recent GSS: If births are spread uniformly across the year, we expect all 12 signs to be equally likely. Are these data inconsistent with that belief? Carry out an appropriate test to support your answer. If you find a significant result, perform a follow-up analysis.

What’s your sign? The University of Chicago’s General Social Survey (GSS) is the nation’s most important social science sample survey. For reasons known only to social scientists, the GSS regularly asks a random sample of people their astrological sign. Here are the counts of responses from a recent GSS:
If births are spread uniformly across the year, we expect all 12 signs to be equally likely. Are these data inconsistent with that belief? Carry out an appropriate test to support your answer. If you find a significant result, perform a follow-up analysis.

Key Concepts

Null and Alternative Hypotheses

The null hypothesis in this context asserts that the categorical data (such as counts of responses) follow a specified distribution (for example, a uniform distribution across categories). The alternative hypothesis contends that the observed frequencies deviate significantly from this expected distribution, indicating a potential difference in the underlying population distribution.

Post-Hoc Analysis

Post-hoc analysis refers to additional testing performed after an initial statistical test, particularly when the overall test indicates a significant difference. It involves examining individual components or categories (often through standardized residuals) to identify specifically which categories deviate from expectations and contribute most to the overall significant result. This helps in understanding the detailed structure of the deviation from the expected distribution.

Hypothesis Testing

Hypothesis testing is a statistical method used to evaluate the evidence provided by sample data against a claim or hypothesis about the population. It involves formulating a null hypothesis, which posits no difference or effect, and an alternative hypothesis, which reflects the presence of a difference. Decisions are made based on calculated probabilities and test statistics to determine if observed deviations are significant enough to reject the null hypothesis.

Chi-Square Goodness-of-Fit Test

The Chi-Square goodness-of-fit test is a nonparametric statistical test used to determine whether the frequency distribution of a categorical variable matches an expected distribution. This test compares observed frequencies with those expected under a specific theoretical distribution, such as a uniform distribution, and calculates a chi-square statistic to assess whether any discrepancies are likely to have occurred by chance.

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