Econometrics For Dummies
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The t distribution is used quite a bit in econometrics. You probably used the t distribution extensively when dealing with means in your statistics class, but in econometrics you also use it for regression coefficients. Before you find out how that works, you should know how the t distribution is derived and its basic properties.

The t distribution is derived from a ratio of a standard normal random variable and the square root of a chi-squared random variable. It’s bell-shaped, symmetrical around zero, and approaches a normal distribution, as the degrees of freedom (number of observations) increases.

The figure shows how the t distribution changes with degrees of freedom. The df1, df2, and df3 indicate increasing degrees of freedom (or observations). As the sample size approaches the population size, the t distribution approaches the standard normal.

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If you have a normally distributed sample mean, such as

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then you can convert it to a standard normal by

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Similarly, if you have a squared normal, such as the sample variance

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you can convert it to a chi-squared by

image4.png

When you take the ratio of the standard normal to the square root of your chi-squared distribution, you end up with a t distribution:

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About This Article

This article is from the book:

About the book author:

Roberto Pedace, PhD, is an associate professor in the Department of Economics at Scripps College. His published work has appeared in Economic Inquiry, Industrial Relations, the Southern Economic Journal, Contemporary Economic Policy, the Journal of Sports Economics, and other outlets.

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