Statistical Inference September 16, 20051Statistical Inference SamplingData SourcesPopulation Parameters vs. Sample Statistics Population Parameters Sample Statistics Greek Roman Proportion B ("pi") p Standard Deviation or F ("sigma") s Standard Error (S.E.) Variance F2 ("sigma squared") s2 Mean F ("mu") X_ ("X-bar") population/sample size N (Roman "N") n difference of means ) ("delta") D correlation D ("rho") r regression slope $ ("beta") b regression intercept " ("alpha") a It’s Greek to Me Just Greek generic population parameter 2 ("theta") The sum of E The product of A Other Odds and Ends estimate of a parameter is $^ ("beta hat") typically denoted by putting a ^ ("hat") above the parameter's symbol standard error (S.E.) is F$^ indicated by a subscript estimated standard error F^$^Statistical Inference September 16, 20052Feeling Thermometer-Bush.517.327eta2242.482.7Very Conservative1583.279.1Conservative1869.968.5Slightly Conservative1553.052.7Moderate531.033.3Slightly Liberal819.425.8Liberal3018.3Very Liberal(n)Mean by Ideology5555IQR32.933.6Standard Deviation6060Median52.354.9MeanSamplePopulationVote for Bush by Religion7250.050.0Total1250.047.1None0—53.8Other2(50.0)24.0Jewish1656.348.3Catholic4247.6%52.9%Protestant(n)SamplePopulationBush FT (y) by Liberals FT (x)Populationr = .366 y = 89.913 - .589xSample (n=86)r = .358 y = 93.844 - .645xStatistical Inference September 16, 20053Collecting Data• Experiments– Hawthorne effect– Random assignment• Quasi-experiments• Survey research– Sample designs• Other kinds of