Statistics

Statistics

1. Chi Square Distribution: unimodal, right-skewed, non-negative. Used to determine difference between observed and expected values.

   • Null: specified proportion distribution fits data well. Alt: ... does not fit data well
   • Standardized Residuals: # of sds observed count is from expected count
     • d=(observed-expected)/ root expected
       • > 2: obs. and hyp. values are significantly different. 1<x<2: somewhat unusual, not sufficient evidence proportions are significantly different. <1: obs. & hyp. values are quite close
     • Tests for independence: are 2 categorical variables independent?
       • Null: are independent. Alt: not independent
       • Expected count >= 10

2. F-distribution: unimodal, right-skewed, non-negative, 2 parameters for df (numerator and denominator). Compares ratio of 2 sources of variability

   • Large F-stat = evidence against null
   • ANOVA (one-factor analysis of variance): compares means of 3+ populations, has 2 sources of variability
     • Between group variation: variability between sample means of groups. Within group variation: variability within samples
       • Between group variation: Small: means are close (20,30,40). Large: means far apart (20,40,60)
       • Within group variation: Small: obs. close together (range is approx. 10). Large: obs. far apart (range is approx. 40)
     • Null: mu1=mu2=... mu k. Alt: at least 2 means are significantly different
     • Conditions: sample distributions must be approx. Normal, Spreads of samples must be approx. equal
     • Grand mean: mean of all obs. (disregarding groups)
       • Sources of variation

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