biostatistics summary lectures

Tests:
Anova: testing the difference among means of k groups simultaneously (variance is the
same, normally distributed)
H0: µ1 = µ2 = µ3, Ha: at least 1 µ differs
Sum of squares: 𝑆𝑆𝑔𝑟𝑜𝑢𝑝𝑠 = ∑ 𝑛(𝑌̅𝑖 − 𝑌̅)2 , 𝑆𝑆𝑒𝑟𝑟𝑜𝑟 = ∑ 𝑆12 (𝑛1 − 1)
𝑆𝑆𝑔𝑟𝑜𝑢𝑝𝑠 𝑆𝑆𝑒𝑟𝑟𝑜𝑟
Mean squares: 𝑀𝑆𝑔𝑟𝑜𝑢𝑝𝑠 = , 𝑀𝑆𝑒𝑟𝑟𝑜𝑟 = (k = number of groups)
𝑘−1 𝑁−𝑘
𝑀𝑆𝑔𝑟𝑜𝑢𝑝𝑠
Violence ratio: 𝐹 = → use online calculator to determine P
𝑀𝑆𝑒𝑟𝑟𝑜𝑟
𝑆𝑆𝑔𝑟𝑜𝑢𝑝𝑠
𝑅2 = → how much effect is explained by the treatment
𝑆𝑆𝑡𝑜𝑡𝑎𝑙

Binomial distribution: probability of getting X successes out of n trial (page 192)
𝑛
Pr[X successes] = ( ) 𝑝 𝑋 (1 − 𝑝)𝑛−𝑥
𝑥
𝑛
( ) on calculator: optn → F6 → F3 →F3
𝑥
Use binomial calculator online

Binomial test: does population proportion match the p of the H0 (page 193)
H0: the relative frequency of success is p0, Ha: the relative frequency of success isn’t
p0
Use binomial calculator (two sided) → compare with α
Confidence interval: 𝑝̂ − 1,96𝑆𝐸𝑝̂ < 𝑝 < 𝑝̂ + 1,96𝑆𝐸𝑝̂

F-test: test whether the variances of numerical variable of two populations are equal
(page 352)
H0: variance of group 1 equals the variance of group 2, Ha: variance of group 1 does
not equal the variance of group 2
𝑠2
𝐹 = 𝑠12 → df = (n1-1
2


Mann-Whitney U-test: nonparametric (based on ranks) compare frequency distributions
of 2 groups (page 400)
H0: two groups are the same, Ha: two groups are not the same
Rank all numbers
Add ranks up per group → R
𝑛 (𝑛 +1)
𝑈1 = 𝑛1 𝑛2 + 1 22 − 𝑅1 → 𝑈2 = 𝑛1 𝑛2 − 𝑈1 → use largest for U
Compare U with table

One sample t-test: compare a mean of numerical variable to a hypothesized value (page
318) (random sample, and normally distributed)
H0: true mean equals µ0, Ha: true mean isn’t µ0
𝑌̅−µ 𝑠
𝑡= → 𝑆𝐸𝑌̅ =
𝑆𝐸𝑌
̅ √𝑛
Use online calculator