Variance test using values

This function performs the test for a single variance or two variances using values, not the vectors.

var_test(
  varx,
  nx,
  vary = NULL,
  ny = NULL,
  alternative = "two.sided",
  null.value = 1,
  conf.level = 0.95
)

Arguments

varx

sample variance for sample x.

nx

sample size for sample x.

vary

sample variance for sample y.

ny

sample size for sample y.

alternative

a character string specifying the alternative hypothesis, must be one of two.sided (default), greater or less. You can specify just the initial letter.

null.value

the hypothesized number (variance or ratio of the variances) in the null hypothesis.

conf.level

confidence level of the interval, by default its value is 0.95.

Value

A list with class htest containing the following components:

statistic

the value of the statistic.

p.value

the p-value for the test.

conf.int

a confidence interval for the variance.

estimate

the sample variance (or ratio of the sample variances)

null.value

the specified hypothesized value for alternative hypothesis.

alternative

a character string describing the alternative hypothesis.

method

a character string indicating the type of test performed.

Examples

# Examples with ONE sample

# Example 7.7.1 from Wayne (2013), http://tinyurl.com/y6z49hrw
var_test(varx=670.81, nx=16, null.value=600, alternative='two.sided')
#> 
#> 	X-squared test for variance
#> 
#> data:  varx = 670.81 and nx = 16
#> X-squared = 16.77, df = 15, p-value = 0.6656
#> alternative hypothesis: true variance is not equal to 600
#> 95 percent confidence interval:
#>   366.0509 1606.8235
#> sample estimates:
#> variance of x 
#>        670.81 
#> 

# Exercise 7.7.5 from Wayne (2013), http://tinyurl.com/y6z49hrw
var_test(varx=30, nx=25, null.value=25, alternative='greater')
#> 
#> 	X-squared test for variance
#> 
#> data:  varx = 30 and nx = 25
#> X-squared = 28.8, df = 24, p-value = 0.2277
#> alternative hypothesis: true variance is greater than 25
#> 95 percent confidence interval:
#>   0.00000 51.99147
#> sample estimates:
#> variance of x 
#>            30 
#> 

# Using the plot to illustrate Hypothesis Test
mytest1 <- var_test(varx=30, nx=25, null.value=25, alternative='greater')
mytest1
#> 
#> 	X-squared test for variance
#> 
#> data:  varx = 30 and nx = 25
#> X-squared = 28.8, df = 24, p-value = 0.2277
#> alternative hypothesis: true variance is greater than 25
#> 95 percent confidence interval:
#>   0.00000 51.99147
#> sample estimates:
#> variance of x 
#>            30 
#> 
plot(mytest1)


# Examples with TWO samples

# Example 7.8 from Montgomery (1996)
var_test(varx=5.1^2, nx=12, vary=4.7^2, ny=15, conf.level=0.90)
#> 
#> 	F test to compare two variances
#> 
#> data:  varx = 26.01 , nx = 12 , vary = 22.09 and ny = 15
#> F = 1.1775, num df = 11, denom df = 14, p-value = 0.7605
#> alternative hypothesis: true ratio of variances is not equal to 1
#> 90 percent confidence interval:
#>  0.4589581 3.2246374
#> sample estimates:
#> ratio of variances 
#>           1.177456 
#> 

# Example 8.17 from Montgomery (1996)
mytest2 <- var_test(varx=3.84, nx=20, vary=4.54, ny=20)
mytest2
#> 
#> 	F test to compare two variances
#> 
#> data:  varx = 3.84 , nx = 20 , vary = 4.54 and ny = 20
#> F = 0.84581, num df = 19, denom df = 19, p-value = 0.7189
#> alternative hypothesis: true ratio of variances is not equal to 1
#> 95 percent confidence interval:
#>  0.3347839 2.1369100
#> sample estimates:
#> ratio of variances 
#>           0.845815 
#> 
plot(mytest2)