Testing a Variance in R
You might think that the function
chisq.test() would be the best way to test a variance in R. Although base R provides this function, it’s not appropriate here. Statisticians use this function to test other kinds of hypotheses.
Instead, turn to a function called
varTest, which is in the
EnvStats package. On the Packages tab, click Install. Then type EnvStats into the Install Packages dialog box and click Install. When EnvStats appears on the Packages tab, select its check box.
Before you use the test, you create a vector to hold the ten measurements:
FarKlempt.data2 <- c(12.43, 11.71, 14.41, 11.05, 9.53, 11.66, 9.33,11.71,14.35,13.81)
And now, the test:
varTest(FarKlempt.data2,alternative="greater",conf.level = 0.95,sigma.squared = 2.25)
The first argument is the data vector. The second specifies the alternative hypothesis that the true variance is greater than the hypothesized variance, the third gives the confidence level (1 – ɑ), and the fourth is the hypothesized variance.
Running that line of code produces these results:
Results of Hypothesis Test
Null Hypothesis: variance = 2.25
Alternative Hypothesis: True variance is greater than 2.25
Test Name: Chi-Squared Test on Variance
Estimated Parameter(s): variance = 3.245299
Test Statistic: Chi-Squared = 12.9812
Test Statistic Parameter: df = 9
95% Confidence Interval: LCL = 1.726327
UCL = Inf
Among other statistics, the output shows the chi-square (12.9812) and the p-value (0.163459). (The chi-square value in the previous section is a bit lower because of rounding.) The p-value is greater than .05. Therefore, you cannot reject the null hypothesis.
How high would chi-square (with df = 9) have to be in order to reject? Hmmm. . . .