2. Independent sample T test (double sample): Its null hypothesis is that the difference between the mean values of two normally distributed populations is a real number, for example, to test whether the average height of two groups is equal. If the variance of two populations is equal (homogeneous variance), the degree of freedom is the sum of two samples and then MINUS two; If it is heteroscedasticity (population variance is not equal), the degree of freedom is Welch degree of freedom, sometimes called Welch test.
3. Paired sample T-test: Check whether the difference between paired samples extracted from the same population is zero. For example, detect the tumor size of patients before and after treatment. If the treatment is effective, we can infer that the tumor size will shrink after most patients receive treatment.
4. To test whether the partial regression coefficient of a regression model is significantly different from zero, that is, to test whether the explanatory variable X has explanatory power to the explained variable Y, and its test statistic is called t-ratio.
origin
Student T-test is a method of observing brewing quality proposed by William Goss in 1908, and "student" is his pen name.
Based on Claude Guinness's innovative policy of employing the best graduates from Oxford University and Cambridge University to apply biochemistry and statistics to Guinness's industrial process, Goss was hired as a statistician by Guinness Brewery in Dublin. Gosse suggested using T-test to reduce the cost of beer weight monitoring.
Gosse published the T-test in Biometrika on 1908, but was forced to use a pseudonym because his boss thought it was a trade secret and the content of the statistical paper had nothing to do with wine making. In fact, other statisticians know Goss's true identity.