PSY 231 1st Edition Lecture 14 Outline of Last Lecture I. Error VarianceII. Two Ambiguities Caused by Selecting Subjects from a Varied PopulationIII. Measures of Variances Help us Diagnose Overlap Outline of Current Lecture II. Inferential StatisticsIII. Type 1 Error Risk’a. Acceptable Type 1 Error RiskIV. How Inferential Statistics Generates its Advicea. A Thought Experimentb. Data InputsCurrent LectureInferential Statistics● Inferential Statistics-- “advice” on whether to believe the mean difference, operational definition of “too much” variance/overlap● Input-- data from the study (and some guesses about population distributions)● Output-- p( probability) value, range form 0-1.00● Estimate of probability (p) that..○ group differences result from error variance○ if you reject the null hypothesis (and believe the scientific hypothesis) you will commit a type 1 errorType 1 Error Risk● Low p= statistically significant○ acceptable risk○ only error variance that makes the groups different○ rejecting null hypothesis creates type 1 error● High p = not statistically significant○ unacceptable risk ○ when p is high, we just pretend that the groups are not differentAcceptable Type 1 Error Risk● Alpha (usually .05)○ low risk is p is less than or equal to .05○ statistically significant○ 5% or lower risk that …■ error variance caused group differences■ rejecting the null hypothesis causes type 1 errorHow Inferential Statistics Generates its AdviceA Thought Experiment● Samples and populations● P is the probability that..○ a sample size N (your studies sample size)○ could be drawn from a single population(with variance (SD) like that of the sample)○ Without any manipulation○ yielding group differences as big as the one in your actual studyData Inputs● Differences between group means○ M1-M2○ if its really big..not likely due to error variance = low p○ really small...error variance could have caused it = high p● Standard deviation(SD) of samples○ really big...lots of overlap possible = high p○ really small...less overlap likely = low p● Variance creates overlap, overlap reduces confidence that the groups are really different● Sample size (N)○ the bigger the sample, the more likely the population it is■ big N= low p (more confidence)■ small N = high p (less confidence)● An Example○ t-test--used for experiments with 2 groups (or conditions)○ big t= statistically significant (low p)○ small t= not statistically significant (high p)○ the bigger t is the lower the p value● Hypotheses decisions depend on both direction of the effect (descriptive stats) and statistically significant effect (inferential
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