Statistical Analysis with R For Dummies
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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

Data: FarKlempt.data2

Test Statistic: Chi-Squared = 12.9812

Test Statistic Parameter: df = 9 P-value: 0.163459 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. . . .

About This Article

This article is from the book:

About the book author:

Joseph Schmuller, PhD, has taught undergraduate and graduate statistics, and has 25 years of IT experience. The author of four editions of Statistical Analysis with Excel For Dummies and three editions of Teach Yourself UML in 24 Hours (SAMS), he has created online coursework for and is a former Editor in Chief of PC AI magazine. He is a Research Scholar at the University of North Florida.

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