Answer to Question #225573 in Economics for Ota

Question

 What is the difference between t-test f-test and r squared, explain?

Answer 1

Student's test (t-test) is a statistical method that allows you to compare the mean values ​​of two samples and, based on the test results, make a conclusion about whether they differ statistically from each other or not.

F-test or Fisher's test (F-test, φ * -criterion) is a statistical test, the test statistics of which, when the null hypothesis is fulfilled, has the Fisher distribution (F-distribution).

One way or another, test statistics are reduced to the ratio of sample variances (sums of squares divided by "degrees of freedom"). For a statistic to have a Fisher distribution, the numerator and denominator must be independent random variables and the corresponding sums of squares must have a Chi-square distribution. This requires the data to be normally distributed. In addition, it is assumed that the variance of the random variables whose squares are added is the same.

The coefficient of determination (R-squared) is the proportion of the variance of the dependent variable explained by the considered dependence model, that is, the explanatory variables. More precisely, it is one minus the proportion of unexplained variance (variance of the random error of the model, or conditional variance of the dependent variable by factors) in the variance of the dependent variable. It is considered a universal measure of the dependence of one random variable on many others. In the particular case of a linear relationship, it is the square of the so-called multiple correlation coefficient between the dependent variable and the explanatory variables.