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Review of Chapters 6-9

# Review of Chapters 6-9 - Review for Exam 2 Some important...

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Review for Exam 2 Some important themes from Chapters 6-9 Chap. 6. Significance Tests Chap. 7: Comparing Two Groups Chap. 8: Contingency Tables (Categorical variables) Chap. 9: Regression and Correlation (Quantitative var’s)

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6. Statistical Inference: Significance Tests A significance test uses data to summarize evidence about a hypothesis by comparing sample estimates of parameters to values predicted by the hypothesis. We answer a question such as, “If the hypothesis were true, would it be unlikely
Five Parts of a Significance Test Assumptions about type of data (quantitative, categorical), sampling method (random), population distribution (binary, normal), sample size (large?) Hypotheses : Null hypothesis ( H 0 ): A statement that parameter(s) take specific value(s) (Often: “no effect”) Alternative hypothesis ( H a ): states that parameter value(s) in some alternative range of values

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Test Statistic : Compares data to what null hypo. H 0 predicts, often by finding the number of standard errors between sample estimate and H 0 value of parameter P -value ( P ): A probability measure of evidence about H 0 , giving the probability (under presumption that H 0 true) that the test statistic equals observed value or value even more extreme in direction predicted by H a . The smaller the P -value, the stronger the evidence against H 0. Conclusion : If no decision needed, report and interpret P- value
If decision needed, select a cutoff point (such as 0.05 or 0.01) and reject H 0 if P-value ≤ that value The most widely accepted minimum level is 0.05, and the test is said to be significant at the .05 level if the P-value ≤ 0.05. If the P -value is not sufficiently small, we fail to reject H 0 (not necessarily true, but plausible). We should not say “Accept H 0 The cutoff point, also called the significance level of the test, is also the prob. of Type I error – i.e., if null true, the probability we will incorrectly reject it. Can’t make significance level too small, because then run risk that P(Type II error) = P(do not reject null) when it is false is too large

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Significance Test for Mean Assumptions : Randomization, quantitative variable, normal population distribution Null Hypothesis : H 0 : µ = µ 0 where µ 0 is particular value for population mean (typically no effect or change from standard) Alternative Hypothesis : H a : µ µ 0 ( 2-sided alternative includes both > and <, test then robust), or one-sided Test Statistic : The number of standard errors the sample mean falls from the H 0 value 0 where / y t se s n se μ - = =
Significance Test for a Proportion S Assumptions: Categorical variable Randomization Large sample (but two-sided test is robust for nearly all n ) Hypotheses: – Null hypothesis: H 0 : π = π 0 – Alternative hypothesis: H a : π ≠ π 0 (2-sided) H a : π π 0 H a : π < π 0 (1-sided) (choose before getting the data)

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Test statistic:
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Review of Chapters 6-9 - Review for Exam 2 Some important...

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