1. STAT120C: Final Review

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. Good luck!