Sampling Distributions and Hypothesis Testing Chapter 8 Sampling Distributions and Hypothesis Testing Fundamental Statistics for the Behavioral Sciences, 4th edition David C. Howell ©1999 Brooks/Cole Publishing Company/ITP     

Chapter 8 Sampling Distributions Major Points An example Sampling distribution Hypothesis testing The null hypothesis Test statistics and their distributions The normal distribution and testing Important concepts

Chapter 8 Sampling Distributions Media Violence Does violent content in a video affect later behavior? Bushman (1998) Two groups of 100 subjects saw a video Violent video versus nonviolent video Then free associated to 26 homonyms with aggressive & nonaggressive forms. e.g. cuff, mug, plaster, pound, sock The reference for this study is Bushman, B.J. (1998) Priming effects of media violence on the accessibility of aggressive constructs in memory. Personality and Social Psychology Bulletin, 24, 537-545. The author presented one group of subjects with a video containing a lot of violence (Karate Kid III) and another group with a nonviolent video (Gorillas in the Mist). He then presented them with 26 homonyms (which had both an aggressive and a nonaggressive meaning) and 26 nonaggressive words, and asked for free associates. My example only uses the homonyms for simplicity. He also broke his sample by gender, but I won’t talk about that until we get to factorials. The dependent variable was the number of aggressive associations given to the homonyms (and nonaggressive control words, which I’m ignoring). I modify this study several times for examples, but the study as described above is the real one. The modifications are done to convert it to a design with one same, sigma known, one sample with sigma unknown, two independent samples, and then an ANOVA with two factors. Cont.

Chapter 8 Sampling Distributions Media Violence Results Number of aggressive free associates to the homonym as a function of video: saw violent video mean = 7.10 saw nonviolent video mean = 5.65 Is this difference large enough to conclude that type of video affected results? The means and standard deviations for all conditions are given below for the instructor who wants to play with them. (The standard deviations are in parentheses.) I averaged across gender in the example

A Simplified Version of Study Chapter 8 Sampling Distributions A Simplified Version of Study One-group study is easier to start with than two-group study. Convert to one-group study People normally give 5.65 aggressive associates to homonyms. (a pop. parameter) A group who watched violent videos give 7.10 aggressive associates. (a sample statistic) Is this sufficiently more than expected to conclude that violent video has effect? I have provided a simplified version of the study because it is much easier to begin by comparing a sample mean with a population mean. You will probably need to explain why I did this. You can come back and work with the two-sample example later.

Chapter 8 Sampling Distributions What is the Question? Is the difference between 7.10 and 5.65 large enough to lead us to conclude that it is a real difference? Would we expect a similar kind of difference with a repeat of this experiment? Or... Is the difference due to “sampling error?”

Chapter 8 Sampling Distributions Sampling Error The normal variability that we would expect to find from one sample to another, or one study to another Random variability among observations or statistics that is just due to chance

How Could we Assess Sampling Error? Chapter 8 Sampling Distributions How Could we Assess Sampling Error? Take many groups of 100 subjects who did not see a violent video. Record the number of aggressive responses to 26 homonyms. Plot the distribution and record its mean and standard deviation. This distribution is a “Sampling Distribution.”

Sampling Distribution Chapter 8 Sampling Distributions Sampling Distribution The distribution of a statistic over repeated sampling from a specified population. Possible result for this example. See next slide. Shows the kinds of means we expect to find when people don’t view a violent video.

Chapter 8 Sampling Distributions

Chapter 8 Sampling Distributions What Do We Conclude? When people don’t view violent video, they average between about 4.5 and 6.5 aggressive interpretations of homonyms. Our violent video group averaged 7.10 aggressive interpretations. Our subjects’ responses were not like normal. Conclude that the violent video increased aggressive associations.

Chapter 8 Sampling Distributions Hypothesis Testing A formal way of doing what we just did Start with hypothesis that subjects are normal. The null hypothesis Find what normal subjects do. Compare our subjects to that standard.

Chapter 8 Sampling Distributions The Null Hypothesis The hypothesis that our subjects came from a population of normal responders. The hypothesis that watching a violent video does not change mean number of aggressive interpretations. The hypothesis we usually want to reject.

Steps in Hypothesis Testing Chapter 8 Sampling Distributions Steps in Hypothesis Testing Define the null hypothesis. Decide what you would expect to find if the null hypothesis were true. Look at what you actually found. Reject the null if what you found is not what you expected.

Chapter 8 Sampling Distributions Important Concepts Concepts critical to hypothesis testing Decision Type I error Type II error Critical values One- and two-tailed tests

Chapter 8 Sampling Distributions Decisions When we test a hypothesis we draw a conclusion; either correct or incorrect. Type I error Reject the null hypothesis when it is actually correct. Type II error Retain the null hypothesis when it is actually false.

Chapter 8 Sampling Distributions Type I Errors Assume violent videos really have no effect on associations Assume we conclude that they do. This is a Type I error Probability set at alpha ()  usually at .05 Therefore, probability of Type I error = .05

Chapter 8 Sampling Distributions Type II Errors Assume violent videos make a difference Assume that we conclude they don’t This is also an error Probability denoted beta () We can’t set beta easily. We’ll talk about this issue later. Power = (1 - ) = probability of correctly rejecting false null hypothesis.

Chapter 8 Sampling Distributions Critical Values These represent the point at which we decide to reject null hypothesis. e.g. We might decide to reject null when (p|null) < .05. Our test statistic has some value with p = .05 We reject when we exceed that value. That value is the critical value.

One- and Two-Tailed Tests Chapter 8 Sampling Distributions One- and Two-Tailed Tests Two-tailed test rejects null when obtained value too extreme in either direction Decide on this before collecting data. One-tailed test rejects null if obtained value is too low (or too high) We only set aside one direction for rejection. Cont.

One- & Two-Tailed Example Chapter 8 Sampling Distributions One- & Two-Tailed Example One-tailed test Reject null if violent video group had too many aggressive associates Probably wouldn’t expect “too few,” and therefore no point guarding against it. Two-tailed test Reject null if violent video group had an extreme number of aggressive associates; either too many or too few.

Chapter 8 Sampling Distributions Review Questions Define a sampling distribution. How would you create sampling distribution of mean number of aggressive associates if the null were true? What is sampling error? What does sampling error have to do with all of this? Cont.

Review Questions--cont. Chapter 8 Sampling Distributions Review Questions--cont. What are the steps in hypothesis testing? What is the probability we’d conclude violent videos cause aggression if they really don’t? Distinguish between Type I and Type II errors. Distinguish between one-tailed and two- tailed tests.