This study guide is meant to help you prepare and organize for Exam 4 (Module/Week 8) for PSYC 354. The material is arranged by subject and not necessarily chronologically (according to chapter). It is recommended that you work through from beginning to end and let your instructor know if you have any questions. Also, remember that there is always a small percentage of cumulative material, so it will help to look over notes from previous modules/weeks.
Confidence Intervals:
1. Define a point estimate: is a summary statistic from a sample that is just one number used as an estimate of the population parameter.
2. Define an interval estimate: is based on a sample statistic and provides a range of plausible values for the population parameter.
3. What is the relationship between the two? In any estimation problem, we need to obtain both a point estimate and an interval estimate. The point estimate is our best guess of the true value of the parameter, while the interval estimate gives a measure of accuracy of that point estimate by providing an interval that contains plausible values.
a. Brief overview: The margin of error expresses an interval estimate and is often used in polling. Take the following values from a Gallup Poll conducted in June 2014
b. Only 7% of Americans report having a great deal or quite a lot of confidence in Congress.
c. Compare that to 74% of Americans who have the same level of confidence in the Military.
Both of the percentages above would be considered point estimates. The Gallup organization also reports a margin of error of +/-4 percentage points, or +/-4%, for these values. Using the point estimates and the margin of error, we can compute the interval estimate:
a. For Congress: 7 +/- 4 = 3 to 11% Our interval estimate is 3% to 11%
b. For the Military: 74 +/- 4 = 70 to 78%. Our interval estimate is 70% - 78%.
We can also work backwards from an interval estimate to a point estimate:
a. Gallup reported an interval estimate for confidence in small business ranging from 58% to 66%. What is the point estimate? To find the answer, just work in towards the center to find the median. Halfway between 58 and 66 is 62%, so 62% is our point estimate.
Also, if you know the point estimate and are given the interval estimate, you can calculate the margin of error simply by subtracting the point estimate from the upper value of the interval estimate, etc. So, if your point estimate is 45 and your interval estimate is 43 to 47, what is the margin of error?
4. Define a confidence interval: is an interval estimate, based on the sample statistic, that would include the population mean a certain percentage of the time if we sampled from the same population repeatedly.
5. Is it more like a point estimate or an interval estimate? Interval estimate
6. What value is the confidence interval usually centered around? Point estimate
7. Which is larger: a 95% confidence interval or an 85% confidence interval? 85% confidence interval
8. Confidence intervals can be useful in hypothesis testing. Say your null hypothesis states that the expected value on a measure is 15. You run the study, and the results give you a 95% confidence interval of 17.2 to 21.3 on the measure. Does the value of 15 lie within this confidence interval? In this case, would you reject or fail to reject the null hypothesis? What if the confidence interval were 13.5 to 18.3-reject or fail to reject the null?
Effect Size:
1. What is an effect size? Indicates the size of a difference and is unaffected by sample size.
Why are effect sizes useful? They tell us how much two populations do not overlap. The less overlaps, the bigger the effect size.
2. What is the formula for finding the effect size called Cohen's d? Does it rely on a distribution of scores or means?
3. What are Cohen's conventions for effect size?
4. Understand how effect size relates to the overlap of two distributions. For example, does a large effect size indicate more or less overlap between two distributions?
5. What could be said about results that are statistically significant (p < .05) but have a small effect size (d = .12)?
6. What is meta-analysis?
Statistical Power:
1. Define statistical power.
2. What is the minimal acceptable power for a study (percentage)?
3. Review the concepts of alpha, Type I error, and Type II error.
4. What are different methods of increasing power in a study?
The Single-sample t Test:
1. We use a one-sample t test when we know the population _____ but not the population _______.
2. How does the single sample t test compare to the z test? What is known in the z test that we do not know in the t test? If sample size were carried out to infinity, how would the t distribution compare to the z distribution?
3. If we are estimating the population standard deviation based on sample data, what formula do we use? How is it different from the usual formula for standard deviation?
4. Define degrees of freedom (df). How do we calculate df for a single-sample t test?
5. Review what kinds of letters represent sample statistics and what kinds of letters (what language?) represent population parameters.
6. Given a small group of scores, be able to compute the estimated standard deviation (see formula in #3).
7. Review computing the standard error (from last exam) and be able to do this in context of t test.
8. What is the formula for t in the single-sample t test?
9. Understand what the null and research hypotheses look like in parameter notation.
10. Know the steps of carrying out hypothesis testing with the single-sample t test.
11. What is the formula for effect size for the single-sample t test?
12. How do we write the results of a t test in current APA format?