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Understand the difference between independent and dependent samples.
Understand how to conduct a statistical test concerning \(p_1-p_2\).
Understand how to compute a confidence interval to estimate \(p_1-p_2\).
Understand how to conduct a statistical test concerning \(\mu_1-\mu_2\).
Understand how to compute a confidence interval to estimate \(\mu_1-\mu_2\).
Understand the advantages of dependent (matched) samples.
Understand why we might use the alternative standard error for \(\bar{x}_1-\bar{x}_2\).
Understand the concepts we discussed concerning causal inference including confounding variables, conditioning, randomization, instrumental variables, the placebo effect, the observer-expectancy effect, single-blind studies, and double-blind studies. You might find it useful to understand these concepts in terms of the causal diagrams.
Understand the survey sampling designs covered in lecture: simple random sampling, stratified random sampling, and cluster sampling (one- and two-stage), and systematic sampling. Also understand the advantages and/or disadvantages of these designs.
Understand the misconceptions and limitations of statistical tests discussed in lecture.
Formulas/expressions you should understand when and how to use.
\[ \hat{p}_1 - \hat{p}_2 \pm z \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}} \]
\[ z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}} \]
\[ \bar{x}_1 - \bar{x}_2 \pm t \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \]
\[ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]