Option computes Satterthwaite's approximation instead of the usualĭegree of freedom. The unequal option above indicates that variances of Two Sample t-test data: log10 (untreated) and log10 (treated) t 2.984, df 14, p-value 0.009858 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.05634678 0. If there no information about the equality of the population variance is given, then apply the two independent sample t test with unequal variances.

This makes a t-test valid even in a case of In the case of independent samples where the variances are assumed to be equal, a two-sample pooled t-test is used.

Option, which produces Satterthwaite's or Welch's approximation for By default, the R t.test() function makes the assumption that the variances of the two groups of samples, being compared, are different. When theĮqual variance assumption is not satisfied, a pooled variance is no Information here may no longer be accurate, and links may no longer be available or reliable.Ĭomparing the means of two independent samples requires threeĪssumptions: independence, normality, and equal variance. And it’s also easy to show that the lower bound on the number of degrees freedom you can get is $n-1$, which is what you would get if the sample standard deviation in one of the samples is very much larger than the sample standard deviation in the other sample ($n-1$ is the limit as $s_1/s_2$ tends to infinity).This content has been archived, and is no longer maintained by Indiana University. Note that for the equal sample size case, $2n-2$ is the largest number of degrees of freedom you can get. ttest command also has the unequal option, which produces Satterthwaite's or Welch's approximation for the degree of freedom. When the equal variance assumption is not satisfied, a pooled variance is no longer valid. So I would guess that your two standard deviations are very similar. Comparing the means of two independent samples requires three assumptions: independence, normality, and equal variance. the same number of degrees of freedom you would have with an equal variance t-test.įor your example $n=11$, so you would get 20 degrees of freedom, similar to your 19 degrees. t-test intended for two samples having possibly unequal variances. The test statistic is t x y s x 2 n + s y 2 m, where x and y are the sample means, sx and sy are the sample standard deviations, and n and m are the sample sizes. Welch t-test is the parametric test for comparing means between two independent. Where $n_i$ is the number of observations in the $i$th sample and $s_i$ is the standard deviation in this sample. The two-sample t -test is a parametric test that compares the location parameter of two independent data samples. The formula for the number of degrees of freedom is

Two sample unequal variance t test