Then, as you read each statement, A.

Tweet T-tests are handy hypothesis tests in statistics when you want to compare means. You can compare a sample mean to a hypothesized or target value using a one-sample t-test.

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You can compare the means of two groups with a two-sample t-test. If you have two groups with paired observations e.

How do t-tests work? How do t-values fit in? In this post, I will explain t-values, t-distributions, and how t-tests use them to calculate probabilities and assess hypotheses.

T-tests are called t-tests because the test results are all based on t-values. T-values are an example of what statisticians call test statistics.

A test statistic is a standardized value that is calculated from sample data during a hypothesis test. The procedure that calculates the test statistic compares your data to what is expected under the null hypothesis.

Each type of t-test uses a specific procedure to boil all of your sample data down to one value, the t-value. The calculations behind t-values compare your sample mean s to the null hypothesis and incorporates both the sample size and the variability in the data. A t-value of 0 indicates that the sample results exactly equal the null hypothesis.

As the difference between the sample data and the null hypothesis increases, the absolute value of the t-value increases. Assume that we perform a t-test and it calculates a t-value of 2 for our sample data.

What does that even mean? I might as well have told you that our data equal 2 fizbins! We need a larger context in which we can place individual t-values before we can interpret them.

This is where t-distributions come in. When you perform a t-test for a single study, you obtain a single t-value.

However, if we drew multiple random samples of the same size from the same population and performed the same t-test, we would obtain many t-values and we could plot a distribution of all of them. This type of distribution is known as a sampling distribution.

Fortunately, the properties of t-distributions are well understood in statistics, so we can plot them without having to collect many samples! A specific t-distribution is defined by its degrees of freedom DFa value closely related to sample size.

Therefore, different t-distributions exist for every sample size.The t-test, and any statistical test of this sort, consists of three steps. Define the null and alternate hyptheses, Calculate the t-statistic for the data, Compare t calc to the tabulated t-value, for the appropriate significance level and degree of freedom.

If t calc > t tab, we reject the null hypothesis and accept the alternate hypothesis. The values in the table are the areas critical values for the given areas in the right tail or in both tails.

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