Week 6: Introducing Inferential StatisticsType I Error and Statistical SignificanceType II Error and Statistical PowerWeek 7: t-TestsEffect Size and PowerWhen and Why to Use a t-TestEffect Sizes and Confidence Intervals for t-TestsIndependent Samples t-TestWeek 8: t-Tests, cont., and ANOVADependent-Samples t-TestWriting About t-TestsWhen and Why to Use ANOVAOne-Way ANOVAWeek 9: ANOVA, cont.Planned Contrasts and Post Hoc ComparisonsWeek 10: InteractionsPlotting and Interpreting InteractionsWriting About InteractionsWeek 6: Introducing Inferential StatisticsNull and Alternative Hypotheses:- What’s a hypothesis? How do we define it? - What roles do samples and populations play in hypothesis testing? o How do we get from population parameters to sample statistics and vice versa? Describe thegeneral process, as outlined in your text. - Explain the idea of the “unknown population.” What does it mean if we conclude that our sample is more likely to have come from the unknown population than the known one? - What is the definition of the null hypothesis? What symbol do we use to represent the null?- What is the definition of the alternative hypothesis? What symbol do we use to represent it?- By default, which hypothesis do we always assume is true unless we have evidence to the contrary?- What is the alpha level? What is the critical region? How are these related?o Is alpha always = .05? Why or why not?- When do we reject the null hypothesis? When (if ever) do we prove it?Type I Error and Statistical Significance- What is the difference between Type I and Type II error? How is each one defined? o Be able to identify examples of each. - What are the consequences of Type I error? Why do we worry about it?o Should we aim to eliminate Type I error or minimize it? Why? - How is our alpha level related to Type I error? Be as specific as you can here. o How does the alpha level relate to the likelihood that we will reject the null hypothesis?- What do we mean when we say that a finding is statistically significant? Be precise here – this is a case where it’s a good idea to memorize the exact phrase. o What two common misconceptions about significance did we discuss in class? Why are these wrong? How is the correct definition different? - What is a p-value? What does the p stand for? (If nothing, then what will it fall for?) o This is another place where it’s important to be precise – what is the correct way to interpreta p-value?- What is practical significance? How is it related to statistical significance (if at all)? o How do we determine whether our results are practically significant?Type II Error and Statistical Power- What are the consequences of a Type II error? o Should we be more worried about Type I error or Type II? Or does it depend? If so, what does it depend on?o Historically, which error have we given more emphasis to?- What is the connection between Type II error and research design? o How does research design affect our likelihood of Type II error? - Can we quantify the probability of Type II error as we do Type I error? - What is statistical power? o What is an effect size, in general terms?- In very broad terms, how do we estimate power, and how do we estimate the sample size we need?o What three pieces of information do we need in order to estimate the power of our analysis? Week 7: t-TestsGeneral Framework for Inference Tests- What do we mean by inference tests, or inferential statistics? What inference are we making?- What four steps do we go through every time we conduct an inferential test? - As discussed in lecture and your text, what are the four assumptions underlying all of our inference tests?o What happens if these assumptions are not met?- In class (and your text), we discussed three factors that tend to make it more likely that we will obtain a large test statistic (e.g., z-score) and thus reject the null hypothesis – what are they?o These recur over and over in all of our inference tests, so they’re rather important!- What is the difference between a directional hypothesis and a nondirectional hypothesis? o Be able to identify examples of each. - What is a one-tailed test? What is a two-tailed test? When would you use each one? o What does the critical region look like for each type of test? Can you draw them?o How does the decision to use a one- vs. a two-tailed test affect your power to reject the null?Effect Size and Power- What is the definition of an effect size?- How are effect sizes related to practical significance?- What is the conceptual definition of Cohen’s d? o When do we use Cohen’s d? o How do you interpret d values? What do we consider a small, medium, or large effect?- Is Cohen’s d affected by sample size? If so, how? If not, why not?- Do we need to report both a significance test and an effect size? Why or why not?- How does the effect size we expect to find affect the statistical power of our study?o What other factors affect our power?When and Why to Use a t-Test- In what situations would it be appropriate to use a t-test? o Identify the three different kinds of t-tests and the specific circumstances in which it would be appropriate to use each one. o Why (or when) would we use a t-test instead of a z-score?- In general terms, what are degrees of freedom? (A broad definition is OK for now). o Why do we need to figure out the degrees of freedom in order to use a t-test?- How is the t distribution different from the z distribution? How is it similar?- What is the general conceptual formula for all three kinds of t-tests? This is another one you should commit to memory!- When would you use a one-sample t-test?o Identify realistic research situations in which it would be appropriate to work with just one sample. - What do the four basic steps look like in a one-sample t-test? o What are the null and alternative hypotheses? o How do you find the critical region? What information do you need to determine this? o How do you calculate your test statistic? What information do you need?o How do you decide whether or not to reject the null hypothesis?o If I give you an example of a one-sample t-test, including the alpha level, degrees of freedom, critical value, and test statistic, you should be able to reach a correct decision about whether or not to reject the null. - What changes if you use a one-tailed t-test instead of a two-tailed t-test? When and why would you do this?Effect Sizes and Confidence Intervals for t-Tests-