The difference and connection between f test and t test

The origin of T test and F test

## Generally speaking, in order to determine the sample ) The probability of making a mistake when the statistical results are extrapolated to the population. We will use some statistical methods developed by statisticians to conduct statistical tests.

By comparing the obtained statistical test value with the probability distribution of some random variables established by statisticians, we can know what % of chances we will get the current value. result. (Recommended study:

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If it is found after comparison that the chance of this result occurring is very small, that is to say, it is under a very rare and rare situation. only appeared; then we can confidently say that this is not a coincidence, but is statistically significant (in statistical terms, it means that the null hypothesis can be rejected, Ho). On the contrary, if after comparison it is found that the probability of occurrence is very high and it is not uncommon, then we cannot say with high confidence that this is not a coincidence. Maybe it is a coincidence, maybe not, but we cannot be sure.

F value and t value are these statistical test values, and the probability distributions corresponding to them are F distribution and t distribution. Statistical significance (sig) is the probability of this result occurring in the current sample.

You want to test whether the difference in means of two independent samples can be inferred to the population, and perform the t test.

As for F-test, analysis of variance (or translation analysis of variance, Analysis of Variance), its principle is roughly the same as mentioned above, but it is carried out by examining the variance of variables. It is mainly used for: significance testing of mean differences, separation of relevant factors and estimating their effects on the total variation, analysis of interactions between factors, Equality of Variances testing, etc.

The relationship between T test and F test

The t test process is to test the significance of the difference between the means of two samples. However, the t-test requires knowing whether the variances of the two populations are equal; the calculation of the t-test value will be different depending on whether the variances are equal. In other words, the t-test depends on the equality of variances (Equality of Variances) result. Therefore, while SPSS performs t-test for Equality of Means, it also performs Levene's Test for Equality of Variances.

What you are doing is a T test, why is there an F value?

It is because you need to evaluate whether the variances of the two populations are equal, and you need to do Levene's Test for Equality of Variances. To test the variance, there is an F value.

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