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UNDERSTANDING RESEARCH RESULTS: STATISTICAL INFERENCE

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Probabilistic Reasoning Most results are in probabilistic terms Exceptions to the rule The ‘Person Who’ argument Misuse of probabilistic information Base rates = the natural occurrence of some phenomenon with no other information Sample size

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Probabilistic Reasoning People aren’t very good at probabilistic reasoning Gamblers fallacy iPod shuffle

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SAMPLES AND POPULATIONS Inferential statistics are necessary because the results of a given study are based on data obtained from a single sample of researcher participants Allows conclusions on the basis of sample data

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INFERENTIAL STATISTICS Allows researchers to make inferences about the true difference in the population on the basis of the sample data Gives the probability that the difference between means reflects random error rather than a real difference

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NULL AND RESEARCH HYPOTHESES Null Hypothesis: Population Means are Equal Research Hypothesis: Population Means are Not Equal Statistical significance

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PROBABILITY AND SAMPLING DISTRIBUTIONS Probability: The Case of knocking ability Significance level Sample Size The larger the sample size, the more confidence you have in rejecting the null hypothesis

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THE t TEST t value is a ratio of two aspects of the data: the difference between the group means and the variability within groups t = group difference within group variability

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The t-test t = X 1 – X 2 √s 2 1 /N 1 + s 2 2 /N 2 t = 5.27

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Critical values of t-test Significance level.05.025.01 df.10.05.02 1 6.314 12.706 31.821 2 2.920 4.303 6.965 3 2.353 3.182 4.541 4 2.132 2.776 3.747 18 1.734 2.101 2.552

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SAMPLING DISTRIBUTION OF t VALUES

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The t-test Degrees of Freedom df = N 1 + N 2 - # of groups One-Tailed Versus Two-Tailed Tests One-tailed = directional hypothesis Two-tailed = no directional hypothesis

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SAMPLING DISTRIBUTION OF t VALUES -1.734

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Critical values of t-test Significance level.05.025.01 df.10.05.02 1 6.314 12.706 31.821 2 2.920 4.303 6.965 3 2.353 3.182 4.541 4 2.132 2.776 3.747 18 1.734 2.101 2.552

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The F-test F Test (analysis of variance) – ANOVA Used when you have 2 or more levels of an IV or when a factorial design with 2 or more levels Systematic variance = variability of scores between groups Error variance = variability of scores within groups

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