Looking this up in a t-table (or calculating it in your favorite stats program) you find a p-value < 0.001. The degrees of freedom is 38 (nвЂ“1 for each group). This means that the difference in group means is 12.79 standard deviations away from the mean of the distribution of the null hypothesis. Example of a p-valueThe two-tailed t-test of the difference in test scores generates a t-value of 12.79. The t-score which generates a p-value below your threshold for statistical significance is known as the critical value of t, or t*. While most statistical programs will automatically calculate the corresponding p-value for the t-score, you can also look up the values in a t-table, using your degrees of freedom and t-score to find the p-value. The test statistic for t-tests and regression tests is the t-score. They then calculate a p-value that describes the likelihood of your data occurring if the null hypothesis were true. Statistical tests generate a test statistic showing how far from the null hypothesis of the statistical test your data is. From the t-test you find the difference in average score between class 1 and class 2 is 4.61, with a 95% confidence interval of 5.31 to 3.88.Д«ecause the confidence interval does not cross zero, and is in fact quite far from zero, it is unlikely that this difference in test scores could have occurred under the null hypothesis of no difference between groups. Using a two-tailed t-test, you generate an estimate of the difference between the two classes and a confidence interval around that estimate. Example of a confidence intervalYou have sampled 20 students from two different classes to estimate the mean standardized test scores and want to know if there is a difference between the two groups. The t-score used to generate the upper and lower bounds is also known as the critical value of t, or t*. The p-value of the test statistic for t-tests and regression tests.Д¬onfidence intervals use t-scores to calculate the upper and lower bounds of the prediction interval.The upper and lower bounds of a confidence interval when the data are approximately normally distributed.In statistics, t-scores are primarily used to find two things: You can typically look up a t-score in a t-table, or by using an online t-score calculator. It can make more precise estimates than the t-distribution, whose variance is approximated using the degrees of freedom of the data.ДЄ t-score is the number of standard deviations from the mean in a t-distribution. The z-distribution is preferable over the t-distribution when it comes to making statistical estimates because it has a known variance. Therefore, the z-distribution can be used in place of the t-distribution with large sample sizes. the z-distribution, until they are almost identical.ДЄbove 30 degrees of freedom, the t-distribution roughly matches the z-distribution. T-distribution and the standard normal distributionДЄs the degrees of freedom (total number of observations minus 1) increases, the t-distribution will get closer and closer to matching the standard normal distribution, a.k.a. If you use the z-distribution, your confidence interval will be artificially precise. Example: t-distribution vs z-distributionIf you measure the average test score from a sample of only 20 students, you should use the t-distribution to estimate the confidence interval around the mean. This means that it gives a lower probability to the center and a higher probability to the tails than the standard normal distribution. It is a more conservative form of the standard normal distribution, also known as the z-distribution. The variance in a t-distribution is estimated based on the degrees of freedom of the data set (total number of observations minus 1). The t-distribution is used when data are approximately normally distributed, which means the data follow a bell shape but the population variance is unknown. Normally-distributed data form a bell shape when plotted on a graph, with more observations near the mean and fewer observations in the tails. The t-distribution is a type of normal distribution that is used for smaller sample sizes. Frequently asked questions about the t-distribution.T-distribution and the standard normal distribution.

T standard normal table