EnvStats (version 2.1.0)

varTest: One-Sample Chi-Squared Test on Variance

Description

Estimate the variance, test the null hypothesis using the chi-squared test that the variance is equal to a user-specified value, and create a confidence interval for the variance.

Usage

varTest(x, alternative = "two.sided", conf.level = 0.95, 
    sigma.squared = 1, data.name = NULL)

Arguments

x

numeric vector of observations. Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are allowed but will be removed.

alternative

character string indicating the kind of alternative hypothesis. The possible values are "two.sided" (the default), "greater", and "less".

conf.level

numeric scalar between 0 and 1 indicating the confidence level associated with the confidence interval for the population variance. The default value is conf.level=0.95.

sigma.squared

a numeric scalar indicating the hypothesized value of the variance. The default value is sigma.squared=1.

data.name

character string indicating the name of the data used for the test of variance.

Value

• A list of class "htest" containing the results of the hypothesis test. See the help file for htest.object for details.

Details

The function varTest performs the one-sample chi-squared test of the hypothesis that the population variance is equal to the user specified value given by the argument sigma.squared, and it also returns a confidence interval for the population variance. The Rfunction var.test performs the F-test for comparing two variances.

References

van Belle, G., L.D. Fisher, Heagerty, P.J., and Lumley, T. (2004). Biostatistics: A Methodology for the Health Sciences, 2nd Edition. John Wiley & Sons, New York. Millard, S.P., and N.K. Neerchal. (2001). Environmental Statistics with S-PLUS. CRC Press, Boca Raton, FL. Zar, J.H. (2010). Biostatistical Analysis. Fifth Edition. Prentice-Hall, Upper Saddle River, NJ.

See Also

var.test, varGroupTest.

Examples

# Generate 20 observations from a normal distribution with parameters 
  # mean=2 and sd=1.  Test the null hypothesis that the true variance is 
  # equal to 0.5 against the alternative that the true variance is not 
  # equal to 0.5.  
  # (Note: the call to set.seed allows you to reproduce this example).

  set.seed(23) 
  dat <- rnorm(20, mean = 2, sd = 1) 
  varTest(dat, sigma.squared = 0.5) 

  #Results of Hypothesis Test
  #--------------------------
  #
  #Null Hypothesis:                 variance = 0.5
  #
  #Alternative Hypothesis:          True variance is not equal to 0.5
  #
  #Test Name:                       Chi-Squared Test on Variance
  #
  #Estimated Parameter(s):          variance = 0.753708
  #
  #Data:                            dat
  #
  #Test Statistic:                  Chi-Squared = 28.64090
  #
  #Test Statistic Parameter:        df = 19
  #
  #P-value:                         0.1436947
  #
  #95% Confidence Interval:         LCL = 0.4359037
  #                                 UCL = 1.6078623

  # Note that in this case we would not reject the 
  # null hypothesis at the 5% or even the 10% level.

  # Clean up
  rm(dat)