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UA PSY 230 - Study Notes

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Psych 230 Psychological Measurement and StatisticsThis Time….Statistical TestingSlide 4Slide 5Analysis of VarianceSlide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22ANOVASlide 24Slide 25Slide 26Slide 27Slide 28ANOVA - assumptionsANOVA - why bother?ANOVA - experiment-wise errorSlide 32Slide 331. Decide which test to use2. State the Hypotheses3. Calculate the obtained value (Fobt)Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Slide 61Slide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68Slide 69Slide 70Slide 71Slide 72Slide 73Slide 744. Calculate the critical valueFcrit and Fobt5. Make our Conclusion6. Conduct post-hoc testsSlide 79Slide 80Slide 81Slide 82Slide 83Slide 84Slide 85Slide 86Slide 87Slide 88Slide 89Slide 90Slide 91Slide 92Slide 93Slide 94Slide 95Slide 96Slide 97Slide 98Slide 99Slide 100Slide 101Slide 102Slide 103Slide 104Slide 105Slide 106Slide 107Slide 108Slide 109Slide 110Slide 111Slide 112Slide 113Slide 114Slide 115Slide 116Slide 117ProblemSlide 119Slide 120Slide 121Slide 122Slide 123Slide 124Slide 125Slide 126Slide 127Slide 128Slide 129Slide 130Slide 131Slide 132Slide 133Slide 134Slide 135Slide 136Slide 137Slide 138Slide 139Slide 140Slide 141Slide 142Slide 143Slide 144Slide 145Slide 146Slide 147Slide 148Slide 149Slide 150Slide 151Slide 152Psych 230Psychological Measurement and StatisticsPedro WolfNovember 18, 2009This Time….•Analysis of Variance (ANOVA)•Concepts of variability•Why bother with ANOVA?•Conducting a testStatistical Testing1. Decide which test to use2. State the hypotheses (H0 and HA)3. Calculate the obtained value4. Calculate the critical value (size of )5. Make our conclusionStatistical Testing1. Decide which test to use2. State the hypotheses (H0 and HA)3. Calculate the obtained value4. Calculate the critical value (size of )5. Make our conclusion6. Conduct post-hoc testsAnalysis of Variance (ANOVA)Analysis of Variance•In this statistical test, we are interested in seeing if there are significant differences between more than two groups •In an experiment involving only two conditions of the independent variable, you can use either a t-test or the ANOVAAnalysis of Variance•We will look at the variance within each group and compare that to the variance found between the groups•Remember: Variance is the degree to which scores are dispersed in our dataAnalysis of Variance•Remember: H0 is that all the group means in our experiment are the same–any difference between them is due to random chance •H1 is that there is a difference between our group means–a difference that is so unlikely to have happened by chance that we conclude it is due to the independent variableAnalysis of Variance•There is always variability in our data•This variability can be due to two factors:1. The independent variable•Systematic factors2. Error variance•Random factorsAnalysis of Variance•So, to draw a conclusion about whether the independent variable makes a difference to the dependent variable, we need to know what kind of variance there is in our data–variance due to the independent variable (systematic)–variance due to random factors (error)Analysis of Variance•To assess this, we need to look at the variance both within each of our experimental conditions and also at the variance between each of our experimental conditions•Assume H0 is true - there is no effect of our independent variable•What type of variance might we expect to see?Analysis of Variance•Example: we want to see if people differ in their shoe size by where they sit in the class–three groups of students: front row, middle row and back row–expect to find significant differences in shoe size?•Front row: vary in their shoe size: 6,8,5,4,7•Middle row: vary in their shoe size : 9,9,4,6,7•Back row: vary in their shoe size : 4,6,12,10,8Analysis of VarianceBack Middle Front6 9 48 9 65 4 124 6 107 7 86 7 8 Mean=7Analysis of VarianceBack Middle Front6 9 48 9 65 4 124 6 107 7 86 7 8 Mean=7Total varianceAnalysis of VarianceBack Middle Front6 9 48 9 65 4 124 6 107 7 86 7 8 Mean=7Variance within the groupsTotal varianceAnalysis of VarianceVariance between the groupsBack Middle Front6 9 48 9 65 4 124 6 107 7 86 7 8 Mean=7Variance within the groupsTotal varianceAnalysis of VarianceBack Middle Front6 9 48 9 65 4 124 6 107 7 86 7 8 Mean=7Total Variance = Variance between + Variance withinVariance within the groupsTotal varianceVariance between the groupsAnalysis of Variance•So, when H0 is actually true, we should expect the same amount of variance both within each group and between the groups•If we divide Variancebetween by Variancewithin, we should get?•If H0 is true, this ratio should be close to 1Analysis of Variance•How about if H1 is actually true? •In this case, we know the independent variable is having some effect•So, we should expect more variance between each group than there is within each groupAnalysis of Variance•Example: we want to see if people differ in their attendance by where they sit in the class–front row, middle row and back row–expect to find significant differences in attendance?•Front row: vary in their attendance: 6,5,7,6,6•Middle row: vary in their attendance: 7,8,6,7,7•Back row: vary in their attendance: 8,8,7,9,8Analysis of VarianceVariance between the groupsBack Middle Front6 7 85 8 87 6 76 7 96 7 86 7 8 Mean=7Total Variance = Variance between + Variance withinVariance within the groupsTotal varianceAnalysis of Variance•When HA is true, we have more variance between each group than there is within each group•If we divide Variancebetween by Variancewithin, we should get?•If HA is true, this ratio should be more than 1–the F-ratioANOVA•A one-way ANOVA is performed when only one independent variable is tested in the experiment•Example: we are interested in the differences between freshmen, sophomores and juniors on tests of socialization–dependent variable: socialization scores–independent variable: class standingANOVA•A two-way ANOVA is performed when two independent variables are tested in the experiment•Example: we are interested in the differences between male and female freshmen, sophomores and juniors on tests of socialization–dependent variable: socialization


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UA PSY 230 - Study Notes

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