What is a test statistic?

What is a test statistic?

• A. A statistic for which we know how frequently different values occur.
• B. A measure of central tendency.
• C. A parameter estimated from the sample.
• D. A value that must always be nonnegative.

Answer: (A)

A test statistic is a value computed from the sample data that, under the null hypothesis, has a known sampling distribution. This means we know how often different values of the statistic would occur if the null were true, which lets us judge how extreme our observed value is. That comparison yields a p-value or a critical region to decide whether to reject the null. For example, in a t-test the statistic t = (observed difference) divided by its standard error follows a t distribution with a certain degrees of freedom under the null. In an ANOVA, the F statistic follows an F distribution under the null. In a chi-square test, the chi-square statistic follows a chi-square distribution. These known distributions are what let us quantify the rarity of the observed value. This is not a measure of central tendency or a population parameter estimate. And while some test statistics (like chi-square) are nonnegative, others (like t or z) can be negative, so nonnegativity is not a defining trait of a test statistic.

A test statistic is a value computed from the sample data that, under the null hypothesis, has a known sampling distribution. This means we know how often different values of the statistic would occur if the null were true, which lets us judge how extreme our observed value is. That comparison yields a p-value or a critical region to decide whether to reject the null.

For example, in a t-test the statistic t = (observed difference) divided by its standard error follows a t distribution with a certain degrees of freedom under the null. In an ANOVA, the F statistic follows an F distribution under the null. In a chi-square test, the chi-square statistic follows a chi-square distribution. These known distributions are what let us quantify the rarity of the observed value.

This is not a measure of central tendency or a population parameter estimate. And while some test statistics (like chi-square) are nonnegative, others (like t or z) can be negative, so nonnegativity is not a defining trait of a test statistic.