![]() ![]() 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.Ī 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.Ībove 30 degrees of freedom, the t-distribution roughly matches the z-distribution. T-distribution and the standard normal distributionĪs 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. ![]()
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