Estimating Population Variances

We use the var.test command to construct confidence interval estimates for the ratio of the population variances for two samples, and to test claims about two variances.  The difference will be the arguments we include.

To construct a confidence interval estimate for the ratio of two population variances we need a data set and a confidence level (conf.level).

Example: The table below provides data on the wind speeds (in knots) of hurricanes in the South Pacific and East Pacific in 2011.  Construct a 97% confidence interval estimate for the ratio of the population variances.

East Pacific	120	80	80	135	120	55	75	30	125	110	80	30	125
South Pacific	60	90	115	45	135	45	115	75

Source: weather.unisys.com

> east.pac = c(120, 80, 80, 135, 120, 55, 75, 30, 125, 110, 80, 30, 125)
> south.pac = c(60, 90, 115, 45, 135, 45, 115, 75)
> var.test(east.pac, south.pac, conf.level = .97)

        F test to compare two variances

data:  east.pac and south.pac 
F = 1.1047, num df = 12, denom df = 7, p-value = 0.9334
alternative hypothesis: true ratio of variances is not equal to 1 
97 percent confidence interval:
 0.1967649 4.6004064 
sample estimates:
ratio of variances 
          1.104662 

A fair amount of information is being output, but in this instance we are only concerned with the lines that tell us the 97 percent confidence interval estimate for ^σ2₁ ⁄ _σ²2 is 0.1967649 to 4.6004064.  Thus, the data suggests that σ²₁ = σ²₂.