Maxima Function
test_variance_ratio (x1, x2)
test_variance_ratio(x1,x2,option_1,option_2,...)
This is the variance ratio F-test for two normal populations. Arguments x1 and x2 are lists or column matrices containing two independent samples.
Options:
'alternative, default 'twosided, is the alternative hypothesis;
valid values are: 'twosided, 'greater and 'less.
'mean1, default 'unknown, when it is known, this is the mean of
the population from which x1 was taken.
'mean2, default 'unknown, when it is known, this is the mean of
the population from which x2 was taken.
'conflevel, default 95/100, confidence level for the confidence interval of the
ratio; it must be an expression which takes a value in (0,1).
The output of function test_variance_ratio is an inference_result Maxima object
showing the following results:
'ratio_estimate: the sample variance ratio.
'conf_level: confidence level selected by the user.
'conf_interval: confidence interval for the variance ratio.
'method: inference procedure.
'hypotheses: null and alternative hypotheses to be tested.
'statistic: value of the sample statistic used for testing the null hypothesis.
'distribution: distribution of the sample statistic, together with its parameters.
'p_value: p-value of the test.
Examples:
The equality of the variances of two normal populations is checked against the alternative that the first is greater than the second.
(%i1) load("stats")$ (%i2) x: [20.4,62.5,61.3,44.2,11.1,23.7]$ (%i3) y: [1.2,6.9,38.7,20.4,17.2]$ (%i4) test_variance_ratio(x,y,'alternative='greater); | VARIANCE RATIO TEST | | ratio_estimate = 2.316933391522034 | | conf_level = 0.95 | | conf_interval = [.3703504689507268, inf] | (%o4) | method = Variance ratio F-test. Unknown means. | | hypotheses = H0: var1 = var2 , H1: var1 > var2 | | statistic = 2.316933391522034 | | distribution = [f, 5, 4] | | p_value = .2179269692254457