STAT120C: Final Review

Scope The final is comprehensive T test ANOVA Linear regression One-sample or paired t-test Two-sample ANOVA One-way Two-way Linear regression Categorical analysis Fisher’s exact test The general idea of chi-squared test One random sample Multiple random samples McNemar’s test for matched pairs Other appropriate situations … Nonparametric test Wilcoxon signed rank test Mann-Whitney-Wilcoxon test

T tests Know how to construct a t distributed random variable: (1) …, (2), …, and (3) … Be able to explain why the T statistic follows a t distribution under the null hypothesis Be able to find the degrees of freedom Know how to make conclusion in the context of the situation Know how to construct confidence intervals Understand the difference between two-sample t test and paired t-test

One-Way ANOVA Balanced and unbalanced situation Know the model assumptions Understand the interpretations of parameters Be able to derive MLEs Know how to construct an F distributed r.v. Be able to show SSTO=SSB+SSW the distribution of SSW/σ2 the distribution of SSB/σ2 when the null hypothesis is true The independence between SSW and SSB Know how to find the degrees of freedom and make conclusions

Two-way ANOVA (balanced design) Know the model assumptions Understand the interpretations of parameters, especially the meaning of interactions Be able to derive MLEs Know how to construct an F distributed r.v. Be able to show the distribution of SSW/σ2 The distributions of SSA/σ2 and SSB/σ2 under their null hypotheses Know The distribution of SSAB/σ2 under its null hypothesis how to find the degrees of freedom and make conclusions

Linear regression Know the model assumptions Understand the interpretations of parameters Be able to derive least squares estimate / maximum likelihood estimates Know the distribution of RSS/σ2 the LSE/MLE of the coefficients Be able to show unbiasedness Be able to derive variances An expected value given x and predict the outcome given x Understand their difference Know how to make statistical inference

Fisher’s exact test Know the test statistic Know the distribution of the test statistic under the null hypothesis When given the null distribution of the test statistic, know how to calculate p-value

Pearson’s Chi-squared Test: the general setting Know the formula of the test statistic Understand how to find the df of the test statistic Understand that this is a large-sample test

Pearson’s Chi-squared test: One random sample Know the model assumptions Be able to write down the likelihood, log-likelihood under both the full and reduced/null models Know how to derive MLEs under the null hypothesis Be able to provide a heuristic argument of the df Be able to apply the test and make conclusion

Pearson’s Chi-squared test: One random sample per subpopulation Know the model assumptions Be able to write down the likelihood, log-likelihood under both the full and reduced/null models Know how to derive MLEs under the null hypothesis Be able to provide a heuristic argument of the df Be able to apply the test and make conclusion

McNemar’s Test for Matched Pairs Under which scenarios should the test be used? What is the model? Be able to Write the likelihood, log-likelihood under both full and reduced models Know how to derive MLEs under the null hypothesis Know the large-sample distribution of the test statistic when the null hypothesis is true Make conclusions

Wilcoxon Signed Rank Test Understand that the test is a nonparametric alternative to the one-sample t-test Know which test statistic to use Understand how to state the null hypothesis Know the distribution of the test statistic under the null When given the null distribution, be able to calculate p-value Be able to derive the large sample distribution under the null hypothesis

Mann-Whitney-Wilcoxon test Understand that the test is a nonparametric alternative to the two-sample t-test Know which test statistic to use Understand how to state the null hypothesis Know the distribution of the test statistic under the null When given the null distribution, be able to calculate p-value

Good luck!