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# Statistical Measures

 Standard Deviation vs. Standard Error n = sample size Sigma (σ) = standard deviation SEM = standard error of the mean SEM = σ/√n SEM < σ SEM decreases as n increases z-scores 1 = +/- 1 σ around mean 2 = +/- 2 σ around mean 3 = +/- 3 σ around mean
 Confidence Interval (CI) Describes the range in which the mean would be expected to fall if the study were performed again and again = range from [mean - Z(SEM)] to [mean + Z(SEM)] 95% CI (alpha = 0.05) is standard  for 95% CI, Z = 1.96 Outcomes  if 0 falls within the CI when calculating the difference between 2 variables, H0 is not rejected and the result is not significant if 1 falls within the CI when calculating OR or RR, H0 is not rejected and the result is not significant T-test vs. ANOVA vs. χ2 T-test     compares the means of 2 groups on a continuous variable   ANOVA (analysis of variance) compares the means of 3 or more groups on a continuous variable χ2 ("chi-squared")  tests whether 2 nominal variables are associated used with 2x2 tables e.g., effect of treatment on disease Correlation Coefficient (r) Pearson coefficient, r, is always between -1 and +1 Absolute value indicates strength of correlation between 2 variables  Coefficient of determination = r2 Attributable Risk (AR) AR is incidence in the exposed (Ie) - incidence in the unexposed (Iu) = Ie - Iu  Ie = a/(a+b) Iu = c/(c+d) AR = a/(a+b) - c/(c+d) The AR percent (ARP) is the attributable risk divided by incidence in the exposed (Ie) ARP = 100* (Ie-Iu)/Ie = 100*[a/(a+b) - c/(c+d)]/[a/(a+b)]   note that relative risk (RR) = Ie/Iu = a/(a+b) DIVIDED BY c/(c+d) using math tricks ARP = (RR-1)/RR