Difference Detectives
Which test compares the means of two independent groups when data are normal?
Independent samples t-test
What correlation test is used for normally distributed interval data?
Pearson’s r
What type of data is required for the chi-square test of independence?
Categorical data
What assumption does the Durbin–Watson statistic test?
Independence of residuals (no autocorrelation).
In the equation Ŷ = a + bX, what does “b” represent?
The slope: change in Y for every one-unit increase in X.
Which nonparametric test replaces the paired t-test when data are not normal?
Wilcoxon signed-rank test
When data are ordinal or not normal, which correlation test should be used?
Spearman’s rho / Kendall's tau B
What does a significant chi-square result indicate?
There is an association between the two categorical variables.
What does the residuals vs. predicted plot help check?
Linearity and homoscedasticity of residuals.
What does R² = 0.70 mean in a regression model?
70% of the variance in Y is explained by X.
What are the two key assumptions before using ANOVA?
Normality and homogeneity of variances
What does a correlation coefficient of r = –0.78 indicate?
A strong negative linear relationship
A chi-square test gives p = 0.02. What does this mean at a 0.05 level of significance?
There is a significant association between the variables; the null hypothesis of independence is rejected.
What indicates possible multicollinearity among predictors?
High VIF values (typically above 5).
If p < 0.05 for the slope coefficient, what can we conclude?
The predictor has a significant linear relationship with Y.
When comparing more than two groups with normal distribution and unequal variances, which test should you use?
Welch’s ANOVA
If two variables have r = 0.45, how would you describe the relationship?
There is a moderate positive linear relationship between the two variables.
What is the alternative hypothesis in a chi-square test of independence?
The two categorical variables are dependent or associated.
Residual plots show a clear funnel shape, where variance increases as predicted values rise. What assumption is likely violated?
The assumption of homoscedasticity (constant variance of residuals).
What does a negative slope mean in regression?
As X increases, Y decreases.
After finding a significant Kruskal–Wallis result, which test determines where the differences lie?
Dunn’s post hoc test
A correlation test yields p = 0.09. What should the researcher conclude at a 0.05 level of significance? Is there enough evidence against null hypothesis?
The correlation is not statistically significant; there’s not enough evidence to claim a relationship.
A chi-square test gives χ² = 9.21, df = 2, and p = 0.01. What decision should the researcher make, and what does it mean?
Reject the null hypothesis; there is a significant association between the two variables.
Two predictors in a regression model are highly correlated with each other. What problem might this cause?
Multicollinearity, which makes it hard to determine each predictor’s unique contribution.
A researcher adds more predictors and R² rises slightly, but adjusted R² drops. What does this suggest?
The new predictors do not meaningfully improve the model.