4. Subjects from the general population of Central Prison,...

4. Subjects from the general population of Central Prison, Raleigh, NC, volunteered for an experiment involving an ""isolation"" experience. (Those convicted of felon offenses are housed in this facility.) The experimental treatment exposed inmates to combined sensory restriction and suggestion. The intent was to reduce the psychopathic deviant T scores (Pd T), Scale 4 of the Minnesota Multiphasic Personality Inventory (MMPI) test. Briefly, the three treatments consisted of Four hours of sensory restriction plus a 15 minute ""therapeutic"" tape advising that professional help is available. Four hours of sensory restriction plus a 15 minute ""emotionally neutral"" tape on training hunting dogs. Four hours of sensory restriction but no taped message. Forty-two subjects were assigned to one of the three treatment groups (for a total of 14 in each treatment group). For each subject the MMPI was administered before and after the experimental treatment. Distributions of pre-treatment and post-treatment values of Pd T scores are given below for the 42 individuals. Tr 1 Tr 2 Tr 3 Mean 6.21 2.86 -3.21 SD 12.3 7.94 8.57 n 14 14 14 https://stat.duke.edu/resources/datasets/prison-isolation a. State the appropriate null and alternative hypotheses for this test. b. The ANOVA resulting from doing this test is below. Use the F-distribution to find the p-value for the test. Using ? = 0.05, does the Pd T score differ by treatment? Make a conclusion in context. Df Sum Sq Mean Sq F value treatment 2 639.48 319.74 3.33 Residuals 39 3740.43 95.91 c. Are the conditions for using ANOVA reasonably satisfied? Explain briefly.

Transcript

00:01 All right, so today we're looking at a study that was conducted and it was prisoners who had volunteered for an isolation experience.

00:14 And the experimental treatment exposed inmates to combined sensory restriction as well as a suggestion.

00:26 So what we mean by that is, so there's three treatment groups, one, two, and three.

00:32 And there were 42 subjects, n is 42, and they were broken into the three groups evenly.

00:40 So there's a sample size of 14 in each.

00:42 So i guess this should be big n of 42.

00:45 And so the sensory restriction, they were all, all treatment groups were exposed to sensory restriction and this was a voluntary experiment.

00:57 But the treatments were as follows.

00:59 So treatment one had a 15 minute therapeutic tape advising them that professional help was available.

01:10 So that was treatment one, as well as the four hour sensory restriction.

01:13 Treatment two, there was a 15 minute emotionally neutral tape of training, training hunting dogs.

01:22 And then treatment three was this restriction, but no message at all.

01:26 So there's no message here.

01:27 This is like your control.

01:29 We call that the control.

01:32 And like we said, this one was, it was neutral tape.

01:37 It's like, hey, here's some hunting dogs being trained.

01:39 And this one, the treatment was, was a professional help.

01:46 So we're, and here, these are the, the mean scores.

01:50 They were given the, a, an assessment on their t scores, which is, it's a measure of psychopathic deviance.

02:05 And this is the mean and standard deviation for the scores in the three groups and standard deviations in the sample sizes.

02:13 And essentially what we'd be doing is running an anova to see if there's a difference in the group.

02:16 So a one -way anova has the following hypothesis.

02:19 So we've got the null hypothesis is that the, the mean of group one is equal to the mean of group two is equal to the mean of group three.

02:27 The alternative hypothesis is that the means are not all equal.

02:31 Those are our, our, our hypotheses.

02:46 And the anova was run and this is the result of it.

02:57 We have the source, we have the treatment, which is also like your between groups observation between looking at the difference between the groups and then the residuals looking within the groups.

03:07 So this is between here, this is within.

03:17 Degrees of freedom, sum of squares, mean square and the f statistic.

03:21 And the p value is here.

03:22 There's the p value and i got using the spreadsheet function fdist where you put in your f statistic.

03:27 And then this two is the degrees of freedom of the treatment.

03:31 And this 39 is the degrees of freedom of the residuals.

03:36 And then you get your p value, 0 .046.

03:39 And then we're testing these hypotheses at the alpha of 0 .05 level of significance.

03:45 And then the general rule is to reject h naught, reject h naught if our p value is less than this alpha of 0 .05.

03:59 Indeed, it is less than 0 .05.

04:01 So we'd reject the hypothesis or we have evidence to reject the hypothesis and say that the means are not all equal.

04:09 All right.

04:09 Now the last question we're asked is about the conditions for using an anova.

04:16 Are they reasonably satisfied? so the conditions for anova are right here.

04:20 These are our assumptions.

04:21 Let me bring these down.

04:22 I put them at the top because they're important.

04:24 I wanted you to see them and we'll get to them now...

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