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Class_11 - Hypothesis Testing(Statistical Significance...

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Hypothesis Testing (Statistical Significance Testing)
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Two Points to Emphasize: 1. Hypothesis testing ALWAYS involves a null hypothesis (H 0 ) whether one is explicitly stated or not. 2. The significance level (i.e., α -level) is chosen BEFORE the sample statistic is calculated.
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We have data from one of the General Social Surveys (GSS), a random sample of 2,013 individuals. Therefore, we know that the Central Limit Theorem can be applied. We are social psychologists interested in people’s image of themselves (i.e., self concept). Each participant in the survey was given a card with the following scale on it: 1 —2—3— 4 —5—6— 7 Respondents were asked to rate their own personal appearance. On this scale, 1 meant “way below average,” 7 meant “way above average,” and 4 meant “average.” Based on theories of self-concept, we hypothesize that in general people consider themselves “above average” in personal appearance.
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In this example, the expectation that “People in general rate their personal appearance as being above average” is the alternate hypothesis (H 1 ). Note that this is a statement about the universe (“People in general…”), not the sample. Thus, the symbolic representation of the alternate hypothesis is expressed as: H 1 : μ Y > 4.00 Why “ greater than 4.00 ”?; “ greater than ” because our alternate hypothesis states that the rating is above average ; “4.00” because, on this scale, 4.00 is average .
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Our null hypothesis (H 0 ), whether we state it or not, is “People in general rate their personal appearance as average.” This is the NEGATION of the alternate hypothesis. (To state that “People in general rate their appearance as below average” is to specify another alternate hypothesis, not a null hypothesis.) Symbolically, the null hypothesis is: H 0 : μ Y = 4.00
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1 —2—3— 4 —5—6— 7 Below Average Above Average Average
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No special statistical test is needed to test this null hypothesis since, with 2,013 cases in a random sample, we can assume that the Central Limit Theorem applies . Thus we can use our knowledge of the normal curve in testing this hypothesis. Let’s set the significance or α -level for our hypothesis test at α = 0.05. Since we can assume that the Central Limit Theorem applies in this case, we know that the sampling distribution of all possible (sample) mean self- appearance ratings is normally distributed . In other words, we can use Appendix 1, pp. 540-542.
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With Appendix 1, we can identify the critical value . We are making a test with an α -level of 0.05 , meaning that we want only a 5 percent chance of wrongly rejecting the null hypothesis (H 0 ). Alpha = 0.05 means 5 percent of the total area under the normal curve. Since our alternate hypothesis (H 1 ) is a directional one, pointing to scale values ABOVE the average score of 4.00, we are only dealing with the RIGHT HALF of the sampling distribution.
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