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Unformatted text preview: 6. Statistical Inference: Significance Tests Goal: Use statistical methods to test hypotheses such as “For treating anorexia, cognitive behavioral and family therapies have same mean weight change as placebo” ( no effect) “Mental health tends to be better at higher levels of socioeconomic status (SES)” (i.e., there is an effect) “Spending money on other people has a more positive impact on happiness than spending money on oneself.” Hypotheses : For statistical inference, these are predictions about a population expressed in terms of parameters (e.g., population means or proportions or correlations) for the variables considered in a study A significance test uses data to evaluate a hypothesis by comparing sample point estimates of parameters to values predicted by the hypothesis. We answer a question such as, “If the hypothesis were true, would it be unlikely to get data such as we obtained?” Five Parts of a Significance Test • Assumptions about type of data (quantitative, categorical), sampling method (random), population distribution (e.g., normal, binary), sample size (large enough?) • Hypotheses : Null hypothesis ( H ): A statement that parameter(s) take specific value(s) (Usually: “no effect”) Alternative hypothesis ( H a ): states that parameter value(s) falls in some alternative range of values (an “effect”) • Test Statistic : Compares data to what null hypo. H predicts, often by finding the number of standard errors between sample point estimate and H 0 value of parameter • Pvalue ( P ): A probability measure of evidence about H 0. The probability (under presumption that H true) the test statistic equals observed value or value even more extreme in direction predicted by H a . – The smaller the Pvalue, the stronger the evidence against H 0. • Conclusion : – If no decision needed, report and interpret Pvalue – If decision needed, select a cutoff point (such as 0.05 or 0.01) and reject H if Pvalue ≤ that value – The most widely accepted cutoff point is 0.05, and the test is said to be “ significant at the .05 level” if the Pvalue ≤ 0.05. – If the Pvalue is not sufficiently small, we fail to reject H (then, H is not necessarily true, but it is plausible) – Process is analogous to American judicial system • H : Defendant is innocent • H a : Defendant is guilty Significance Test for Mean • Assumptions : Randomization, quantitative variable, normal population distribution (robustness?) • Null Hypothesis : H : µ = µ 0 where µ 0 is particular value for population mean (typically “no effect” or “no change” from a standard) • Alternative Hypothesis : H a : µ ≠ µ 0 2sided alternative includes both > and < H value • Test Statistic : The number of standard errors that the sample mean falls from the H value where / y t se s n se μ = = When H is true, the sampling dist of the t test statistic is the t distribution with df = n  1....
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This note was uploaded on 07/12/2011 for the course STA 3030 taught by Professor Agresti during the Spring '11 term at University of Florida.
 Spring '11
 Agresti

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