The t-test, also known as the student t-test (student'S t test), which is mainly used for normal distribution data with small sample content (e.g., n < 30) and a population standard deviation unknown. The t-test is a comparison method of mean values, which uses the t-distribution theory to infer the probability of the difference, so as to determine whether the difference between the two averages is significant. Applicable conditions for t-test: normally distributed data. The t-test is divided into one-sample t-test, independent t-test, and dependent t-test.
The calculation of the degrees of freedom of the t-test depends on the specific test type and the sample data.
For the independent samples t-test, the degrees of freedom are calculated as: df = n1 + n2 - 2, where n1 and n2 are the sample sizes of the two samples, respectively.
For the paired samples t-test, the degrees of freedom are calculated as: df = n-1, where n is the total sample size of the paired samples. If there is a correlation between the paired samples, then the degrees of freedom need to use the modified formula: df = (n-1)*r, where r is the correlation coefficient between each pair of observations.
In the probabilistic t-test, the degrees of freedom are calculated as: degrees of freedom = (number of groups - 1) * number of variables - 1).
For a single-sample t-test, the degrees of freedom are n-1, where n is the sample size.
For an independent t-test, the degrees of freedom are n-2, where n is the total sample size.
For the Welch test, the degrees of freedom are 5.
For the chi-square fit test, the degrees of freedom are n-1, where n is the number of groups.
For the chi-square four-grid table test, the degree of freedom is 1.
For the chi-square contingency table test, the degrees of freedom are (r-1)*(c-1), where r is the number of rows and c is the number of columns.
For the Kraskal-Wallis test, there are no degrees of freedom when the sample size is less than 15; When the sample size is greater than 15, the degrees of freedom are n-1, where n is the number of groups.
The above are some of the calculation methods of degrees of freedom in the t-test, which may need to be determined according to specific statistical theories and data conditions.