two sample degrees of freedom calculator

The first thing to try in this situation is a transformation of the data. If population variances cannot be assumed equal (following for example an F-ratio test), then we cannot use the standard t-test. Where the sample size and variance are expected to be very similar, the variance of the difference between observations is about double the variance of the observations themselves. v 1 and v 2 are the two sample variances.t is the estimated t-statistic under the null hypothesis it is a random quantile of the t-distribution with (n 1 + n 2 − 2) degrees of freedom,.The equal-variance t-test The general formula The standard version which we give first assumes that the two population variances are equal. There are two versions of the two-sample t-test. The t-distribution diverges from the normal distribution for small samples as it allows for the random error in estimating the variance. If the standard normal distribution is used to obtain critical values, the test is sometimes known as the z-test or occasionally the d-test. The standard error of the difference is usually estimated from the weighted variance about the means of the samples being compared.įor large sample sizes the t-distribution becomes equivalent to a 'standard' normal distribution with a mean of zero and a standard deviation of one.

For a null hypothesis of no difference, the difference between the true population means is zero. The t-statistic is estimated as the difference between the two sample means, minus the difference between the true population means, divided by the estimated standard error of the difference between the sample means. These can be obtained either by random sampling from two populations (an observational design) or by random allocation to two treatment groups (an experimental design) - although that assumes the experimental group represents the wider population, that is seldom the case in reality. The purpose of the two sample t-test is to compare the means of two independent samples.

Two sample degrees of freedom calculator