This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 : = 0 where 0 is particular value for population mean (typically no effect or no change from a standard) Alternative Hypothesis : H a : 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  = = When H is true, the sampling dist of the t test statistic is the t distribution with df = n  1....
View
Full
Document
 Spring '11
 Agresti

Click to edit the document details