Chapter 8 Sampling Distributions and Hypothesis Testing Fundamental

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

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

3 Chapter 8 Sampling Distributions Media Violence • Does violent content in a video affect later behavior? X Bushman (1998) • Two groups of 100 subjects saw a video X Violent video versus nonviolent video • Then free associated to 26 homonyms with aggressive & nonaggressive forms. X e. g. cuff, mug, plaster, pound, sock Cont.

4 Chapter 8 Sampling Distributions Media Violence • Results X Number of aggressive free associates to the homonym as a function of video: X saw violent video mean = 7. 10 X saw nonviolent video mean = 5. 65 • Is this difference large enough to conclude that type of video affected results?

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 X People normally give 5. 65 aggressive associates to homonyms. (a pop. parameter) X A group who watched violent videos give 7. 10 aggressive associates. (a sample statistic) X Is this sufficiently more than expected to conclude that violent video has effect? 5

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? X Would we expect a similar kind of difference with a repeat of this experiment? • Or. . . X Is the difference due to “sampling error? ” 6

7 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

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. ” 8

Chapter 8 Sampling Distributions Sampling Distribution • The distribution of a statistic over repeated sampling from a specified population. • Possible result for this example. X See next slide. X Shows the kinds of means we expect to find when people don’t view a violent video. 9

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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. X Our subjects’ responses were not like normal. • Conclude that the violent video increased aggressive associations. 11

Chapter 8 Sampling Distributions Hypothesis Testing • A formal way of doing what we just did • Start with hypothesis that subjects are normal. X The null hypothesis • Find what normal subjects do. • Compare our subjects to that standard. 12

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. 13

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. 14

Chapter 8 Sampling Distributions Important Concepts • Concepts critical to hypothesis testing X Decision X Type I error X Type II error X Critical values X One- and two-tailed tests 15

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

17 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 X Probability set at alpha ( ) • usually at. 05 X Therefore, probability of Type I error =. 05

18 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 X 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.

19 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. X Our test statistic has some value with p =. 05 X We reject when we exceed that value. X That value is the critical value.

Chapter 8 Sampling Distributions 20 One- and Two-Tailed Tests • Two-tailed test rejects null when obtained value too extreme in either direction X Decide on this before collecting data. • One-tailed test rejects null if obtained value is too low (or too high) X We only set aside one direction for rejection. Cont.

Chapter 8 Sampling Distributions One- & Two-Tailed Example • One-tailed test X 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 X Reject null if violent video group had an extreme number of aggressive associates; either too many or too few. 21

Chapter 8 Sampling Distributions 22 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.

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 twotailed tests. 23