Student S Test

Student S Test is a statistical criterion used to test statistical hypotheses about the equality of the means of two samples in the case where the distribution of a characteristic in the population is unknown.

The Student's test is used when the samples are small (the size of each sample is less than 30 observations) and the distribution of the characteristic in the population differs from normal.

The essence of the test is to compare the actual value of the Student's test with the critical value determined from a special table.

If the actual value of the criterion is greater than the critical value, then the null hypothesis of no differences between the means is rejected and the alternative hypothesis is accepted.

Thus, the Student's test allows us to assess the significance of differences in the average values ​​of two samples when the distribution law of the general population is unknown. This criterion is widely used in applied statistical research.

The Student's t test is a statistical test that is used to test the hypothesis that the means of two samples are equal. This test was developed by American statistician William Gossett in 1908.

The Student t test is based on the Student distribution, which is used to evaluate the differences between two means. The Student distribution is bell-shaped and symmetrical about the mean.

To conduct a Student's t test, you must complete the following steps:

1. Determine the number of degrees of freedom (df). df is defined as the difference between the number of observations in each sample and the number of parameters we want to estimate (usually one parameter - the mean).

2. Calculate the test criterion (t-statistic). The t-statistic is calculated using the formula: t = (mean of the first sample - mean of the second sample) / (standard deviation of both samples).

3. Compare the resulting t-statistic value with the critical values ​​of the Student distribution. The critical values ​​depend on the chosen significance level (usually 5% or 1%) and the number of degrees of freedom.

4. If the resulting t-statistic value is greater than the critical value for the selected significance level and number of degrees of freedom, then we can reject the null hypothesis that the means of the two samples are equal at the given significance level.

5. If the obtained t-statistic value is less than the critical value, then the null hypothesis cannot be rejected.

In general, the Student's t test can determine whether the differences between two groups are statistically significant, which can help decide whether more research is needed or whether data analysis methods need to be changed.