Major Points An exampleAn example Sampling distributionSampling distribution Hypothesis testingHypothesis testing  The null hypothesis  Test statistics and their distributions  The normal distribution and testing Important conceptsImportant concepts

The effect of violence in video games Do violent video games affect children’s behavior? (Independent Variable)Do violent video games affect children’s behavior? (Independent Variable) XHypothetical experiment XTwo groups of 100 subjects played video games XViolent video game versus nonviolent video game Then gave free associations to words which could have both violent and non violent meanings.Then gave free associations to words which could have both violent and non violent meanings. Xe.g. cuff, mug, plaster, pound, sock

ResultsResults XNumber of aggressive free associates as a function of type of video game: Xplayed violent gamemean = 7.10 Xplayed non violent gamemean = 5.65 Is this difference large enough to conclude that type of game affected results?Is this difference large enough to conclude that type of game affected results?

A Simplified Version of Study One-group study is easier to start with than two-group study.One-group study is easier to start with than two-group study. Convert to one-group studyConvert to one-group study XPeople normally give 5.65 aggressive associates to words (a pop. parameter) XA group who watched violent videos give 7.10 aggressive associates (a sample statistic) XIs this sufficiently more than expected to conclude that violent video has effect?

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?Is the difference between 7.10 and 5.65 large enough to lead us to conclude that it is a real difference? XWould we expect a similar kind of difference with a repeat of this experiment? Or... XIs the difference due to “sampling error?”

Sampling Error The normal variability that we would expect to find from one sample to another, or one study to anotherThe normal variability that we would expect to find from one sample to another, or one study to another

How Could we Assess Sampling Error? Take many groups of 100 subjects who did not see a violent video.Take many groups of 100 subjects who did not see a violent video. Record the number of aggressive responses to 25 ambiguous words.Record the number of aggressive responses to 25 ambiguous words. Plot the distribution and record its mean and standard deviation.Plot the distribution and record its mean and standard deviation. This distribution is a “Sampling Distribution.”This distribution is a “Sampling Distribution.”

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

What can we infer? When people don’t view violent video, they average between about 4.5 and 6.5 aggressive interpretations of homonyms.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 violent video group averaged 7.10 aggressive interpretations.

Distribution ranges between 3.76 and 7.25Distribution ranges between 3.76 and 7.25 Mean is 5.65, SD is.45Mean is 5.65, SD is.45 Mean of 4.00 is not likely, mean of 5 is likelyMean of 4.00 is not likely, mean of 5 is likely

How likely is it to get score as low as 4.25 by chance. Convert score to z score (z distribution has a mean of 0 and standard deviation of 1)Convert score to z score (z distribution has a mean of 0 and standard deviation of 1) X= score - mean / standard deviation XLook up Table E10, smaller portion 4.25 =-3.1 = = -.11 = =3.5 =.0002

Hypothesis Testing A formal way of testing if we should accept results as being significantly different or notA formal way of testing if we should accept results as being significantly different or not Start with hypothesis that subjects are normal.Start with hypothesis that subjects are normal. XThe null hypothesis Find what normal subjects do.Find what normal subjects do. Compare our subjects to that standard.Compare our subjects to that standard.

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

Null and Alternative Hypothesis Hypothesis: Every crow is blackHypothesis: Every crow is black Sample: 3000 crowsSample: 3000 crows Results: all are blackResults: all are black Conclusion: Are all crows black?Conclusion: Are all crows black?

Observation: One white crowObservation: One white crow Conclusion: Statement :Every crow is black” is falseConclusion: Statement :Every crow is black” is false It is easier to prove things to be false than to prove things to be trueIt is easier to prove things to be false than to prove things to be true

Hypothesis: Shopping on Amazon.com is different than on BN.comHypothesis: Shopping on Amazon.com is different than on BN.com Study: 100 usability tests comparing the two shopping process on bothStudy: 100 usability tests comparing the two shopping process on both Results: Both sites performed similarlyResults: Both sites performed similarly Conclusion: ?Conclusion: ?

Observation: On Test No:101 Amazon did betterObservation: On Test No:101 Amazon did better Conclusion: Amazon.com and BN are different.Conclusion: Amazon.com and BN are different.

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

Important Concepts Concepts critical to hypothesis testingConcepts critical to hypothesis testing XDecision XType I error XType II error XCritical values XOne- and two-tailed tests

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

Possible Scenarios

Type I Errors Assume violent videos games really have no effect on behaviorAssume violent videos games really have no effect on behavior Assume our results show that they do.Assume our results show that they do. This is a Type I errorThis is a Type I error XProbability set at alpha (  )  usually at.05  usually at.05 XTherefore, probability of Type I error =.05

Type II Errors Assume violent video games make a differenceAssume violent video games make a difference Assume that we conclude they don’tAssume that we conclude they don’t This is also an errorThis is also an error XProbability denoted beta (  ) We can’t set beta easily.We can’t set beta easily. We’ll talk about this issue later.We’ll talk about this issue later. Power = (1 -  ) = probability of correctly rejecting false null hypothesis.Power = (1 -  ) = probability of correctly rejecting false null hypothesis.

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

One- and Two-Tailed Tests Two-tailed test rejects null when obtained value too extreme in either directionTwo-tailed test rejects null when obtained value too extreme in either direction XDecide on this before collecting data. One-tailed test rejects null if obtained value is too low (or too high)One-tailed test rejects null if obtained value is too low (or too high) XWe only set aside one direction for rejection.

One- & Two-Tailed Example One-tailed testOne-tailed test XReject null if violent video group had too many aggressive associates Two-tailed testTwo-tailed test XReject null if violent video group had an extreme number of aggressive associates; either too many or too few.

The Design of Experiments Sources of variances in an experimentSources of variances in an experiment NotationNotation Experimental Manipulation Individual Differences Random Variance

Example: Readability of PDA’s and Laptops IV: Device (PDA, and Laptop) DV: Reading time Design: Test 10 subjects on PDA and 10 on Laptop

Between Subject Design: Sources of variance Experimental Manipulation: Effect of device Individual Differences between users Random Variance

Readability of PDA’s and Laptops (within subject design) Experimental Manipulation: Effect of device Random Variance IV: Device (PDA, and Laptop) DV: Reading time, errors