Updated: 12/29/2021

Statistical Measures

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  • 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 significantif 
      • 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 

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