Inference for a normal population: R code for Chapter 11 examples
Download the R code on this page as a single file here.
New methods on this page
Click on a function argument for a short description of its meaning. The variable names are plucked from the examples further below.
Other new methods:
Confidence intervals for the variance and the standard deviation.
Example 11.2. Stalk-eyed flies
Confidence intervals for the population mean, variance, and standard deviation using eye span measurements from a sample of stalk-eyed flies.
Read and inspect the data.
stalkie <- read.csv(url("http://www.zoology.ubc.ca/~schluter/WhitlockSchluter/wp-content/data/chapter11/chap11e2Stalkies.csv"))
stalkie
Histogram with options
hist(stalkie$eyespan, right = FALSE, col = "firebrick", las = 1, xlab = "Eye span (mm)", ylab = "Frequency", main = "")
95% confidence interval for the mean. Adding $conf.int after the function t.test causes R to give the 95% confidence interval for the mean.
t.test(stalkie$eyespan)$conf.int
99% confidence interval for the mean. Adding the argument conf.level=0.99 changes the confidence level of the confidence interval.
t.test(stalkie$eyespan, conf.level = 0.99)$conf.int
95% confidence interval for variance. R has no built-in function for the confidence interval of a variance, so must we compute it using the formula in the book:
df <- length(stalkie$eyespan) - 1 varStalkie <- var(stalkie$eyespan) lower = varStalkie * df / qchisq(0.05/2, df, lower.tail = FALSE) upper = varStalkie * df / qchisq(1 - 0.05/2, df, lower.tail = FALSE) c(lower = lower, variance = varStalkie, upper = upper)
95% confidence interval for standard deviation. Calculated from the confidence interval of the variance, which we just calculated above.
c(lower = sqrt(lower), std.dev = sqrt(varStalkie), upper = sqrt(upper))
Example 11.3. Human body temperature
Uses a one-sample t-test to compare body temperature in a random sample of people with the "expected" temperature 98.6 °F.
Read and inspect the data.
heat <- read.csv(url("http://www.zoology.ubc.ca/~schluter/WhitlockSchluter/wp-content/data/chapter11/chap11e3Temperature.csv"))
head(heat)
Histogram with options.
hist(heat$temperature, right = FALSE, breaks = seq(97, 100.5, by = 0.5), col = "firebrick", las = 1, xlab = "Body temperature (degrees F)", ylab = "Frequency", main = "")
One-sample t-test can be calculate using t.test. The mu arguemtn gives the value stated in the null hypothesis.
t.test(heat$temperature, mu = 98.6)