Understanding Statistical Significance: Errors & Confidence Intervals in Logistics, Study notes of Political Science

Download Understanding Statistical Significance: Errors & Confidence Intervals in Logistics and more Study notes Political Science in PDF only on Docsity! THE MEANING OF STATISTICAL SIGNIFICANCE: STANDARD ERRORS AND CONFIDENCE INTERVALS LOGISTICS •  Homework #3 will be due in class on Wednesday, May 28 (not May 21) •  Note: Monday, May 26 is a holiday Problems in Sampling Ho for Sample Accepted Rejected Ho for Population True Type I False Type II Where Ho = null hypothesis Population parameter = Sample statistic + Random sampling error Random sampling error = (Variation component)/(Sample size component) Sample size component = 1/ √ n Random sampling error = σ / √ n where σ = standard deviation in the population SIGNIFICANCE MEASURES FOR REGRESSION ANALYSIS 1. Testing the null hypothesis: F = r2(n-2)/(1-r2) 2. Standard errors and confidence intervals: Dependent on desired significance level Bands around the regression line 95% confidence interval ±1.96 x SE POPDLAT 10N DISTRIBLTION 5 i = Kw SAMPLE DisTRIB UTION 2 X (#2) SAMPLING DISTRIBUTION a NK Srmupaed _ ERRoR =i\ Figure 5-1 The Normal Distribution 34% -2 Characteristics of the “Normal” Distribution • Symmetrical • Unimodal • Bell-shaped • Mode=mean=median • Skewness = 0 = [3(X – md)]/s = (X – Mo)/s • Described by mean (center) and standard deviation (shape) • Neither too flat (platykurtic) nor too peaked (leptokurtic) Random sampling error = standard error Refers to how closely an observed sample statistic approximates the population parameter; in effect, it is a standard deviation for the sampling distribution Since σ is unknown, we use s as an approximation, so Standard error = s / √ n = SE Establishing boundaries at the 95 percent confidence interval: Lower boundary = sample mean – 1.96 SE Upper boundary = sample mean + 1.96 SE Note: This applies to statistics other than means (e.g., percentages or regression coefficients). Conclusion: 95 percent of all possible random samples of given size will yield sample means between the lower and upper boundaries Postscript: Confidence Intervals (for %) Significance Level Sample Size .20 .10 .05 .01 2000 ±1.4 ±1.8 ±2.2 ±2.9 1000 2.0 2.6 3.2 4.4 500 2.9 3.7 4.5 5.8 50 9.1 12.0 14.1 18.0