1. Question (3 scores): Explain the relationship between the significance level (α) chosen by researchers and the interpretation of p-values in the context of F-statistics. How does adjusting the alpha level influence the conclusions drawn from the results of an ANOVA test?

Response: If you raise alpha level to .05 from .01, your F-stat is more likely to be significant and more likely to reject the null hypothesis (1 point). You increase the Type I error rate or “False Positive” rate (1 point), which is the probability that a null hypothesis is rejected even though it is actually true (1 point).

2. Question (3 scores): Consider a scenario in which the F-statistic from an ANOVA yields a p-value less than 0.05 but greater than 0.01, making it significant at α = 0.05 but not at α = 0.01. Discuss the practical implications of this finding for interpreting the results, including how it should be reported and how it might influence decisions regarding the acceptance or rejection of the null hypothesis.

When a p-value falls between 0.01 and 0.05 (e.g., p = 0.03) in an ANOVA:

1. Reporting: State the exact p-value rather than just ‘significant’ (F = X.XX, df = X, p = 0.03).
2. Interpretation: The result is significant at α = 0.05 but not at α = 0.01, indicating moderate evidence against the null hypothesis but not as strong as if p < 0.01..
3. Decision: This highlights how significance thresholds are arbitrary. The same data leads to different conclusions depending on our chosen α level.
4. Practical approach: Consider both statistical significance and practical importance. Borderline results warrant cautious interpretation and possibly additional research before making consequential decisions

3. Question (4 scores): Critically evaluate why exclusive reliance on p-values (such as those derived from F-statistics in ANOVA) can lead to misleading conclusions in social science research. Propose additional statistical metrics or measures that should be reported to offer a more thorough and nuanced interpretation of the data.

Problem with p-values: (1) Sample Size Sensitivity; (2) Binary Decision Making; (3) No Information on Magnitude; (4) Vulnerable to P-Hacking.

1. Effect Size Measures: Cohen’s d, η² (eta-squared), or ω² (omega-squared) for ANOVA Standardized regression coefficients for regression models These quantify the magnitude of differences, enabling assessment of practical significance

2. Descriptive Statistics: Means, standard deviations, and distributions for each group. Visual representations (box plots, histograms) to reveal patterns not captured by significance tests

3. Confidence Intervals: Provide range estimates for parameters rather than single points. Communicate uncertainty and precision of findings

4. More Complex Models: Hierarchical/multilevel models to account for nested data structures. Structural equation models to examine relationships between latent variables. Mixed-methods approaches incorporating qualitative insights