hypothesis testing in R

The R language has built-in support for a lot of hypothesis testing methods. Though we can also compute it manually.

One-sampled Proportion Test

See: Z-test > One Sample Proportion Test

prop.test(x, n, p, alt = "two.sided", conf.level = 0.95, correct = TRUE)

• where x is the observed count of success (a count rather than proportion!)
• n is the sample size
• p is the probability of success according to the null hypothesis
• alt is the direction of the alternative hypothesis. Can be less, greater, or two.sided
• conf.level = 0.95
• correct = True is whether to apply Yates’ continuity correction

For example:

prop.test(19, 220, 0.1, alt = "two.sided", correct = FALSE)

To compute the p-value manually, we first need to compute the test statistics according to the formula

box = ... # expected population distribution e.g. c(rep(0, 9), 1)
n = ... # Sample size. e.g. 42
OV = ... # observed value
 
box_mean = mean(box)
box_sd = rafalib::popsd(box) # Note that we need population standard deviation!
 
# EV and SE of the sample sum
EV = n * box_mean
SE = sqrt(n) * box_sd
 
# calculate test statistic
test_stat = (OV - EV)/SE

Then we use pnorm to calculate the chance of getting a test statistic as or more extreme. The exact formula depends on the side of alternative hypothesis and whether we are doing one-tailed and two-tailed tests:

p_value = 2 * pnorm(test_stat) # if 2-sided, t < 0

T-Test

Use t.test()

Check Normality: Shapiro-Wilk Test

see: Shapiro-Wilk Test

shapiro.test(vec)