![]() Here $n_1$ is the sample size of group 1, and $n_2$ is the sample size of group 2. Two sample $t$ test/$CI$ - equal variances assumed Here $s^2_1$ is the sample variance in group 1, and $s^2_2$ is the sample variance in group 2. Here $n_1$ is the sample size of group 1, and $n_2$ is the sample size of group 2.Ĭomputer programs use the following formula for the degrees of freedom: Two sample $t$ test/$CI$ - equal variances not assumedįor hand calculations, it is common to use the smaller of $n_1 - 1$ and $n_2 - 1$ as an approximation for the degrees of freedom. Here $N$ is the number of difference scores. If the sample sizes in the two groups being compared are equal, Student's original t-test is highly robust to the presence of unequal variances.Degrees of freedom t test or confidence intervalįind the degrees of freedom for a particular t test or confidence interval ($CI$) below: If using Student's original definition of the t-test, the two populations being compared should have the same variance (testable using F-test, Levene's test, Bartlett's test, or the Brown–Forsythe test or assessable graphically using a Q–Q plot).Under weak assumptions, this follows in large samples from the central limit theorem, even when the distribution of observations in each group is non-normal. The means of the two populations being compared should follow normal distributions.In the t-test comparing the means of two independent samples, the following assumptions should be met: This assumption is met when the observations used for estimating s 2 come from a normal distribution (and i.i.d. s 2( n − 1)/ σ 2 follows a χ 2 distribution with n − 1 degrees of freedom. ![]()
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