# How to Calculate T-Tests

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A T-test is a statistical test to determine whether the means of two groups are equal. For example, you may test whether men and women weigh the same amount. Or you could test whether people's legs are the same length.

There are two types of T-test: independent and paired. An independent T-test is used when the two samples are independent - that is, when information on one sample tells you nothing about the other. If you sample a random group of men and a random group of women, then the first example is independent. The second example is paired, because the length of one leg does tell you something about the length of the other.

### Things You'll Need

• Scientific calculator with mean and variance functions.

## Calculating an Independent Sample T-test

• Find the mean of the first group. The mean is the total of the sample divided by the number of items.

• Find the mean of the second group.

• Subtract the result in step 2 from the result in step 1.

• Find the variance of the first group. The variance is a measure of the spread of a sample. It is calculated as the sum of the squared difference between the individual scores and the mean.

• Divide the variance by the number of subjects in the first group.

• Find the variance of the second group, and divide it by the number of subjects in the second group.

• Add the results of step 5 and step 6.

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• Take the square root of the result in step 7.

• Divide the result in step 3 by the result in step 8. This is the T-statistic.

## Calculating a Paired Sample T-test

• Calculate the difference between each pair. For example, the difference between right leg and left leg length.

• Find the mean of the difference from step 1.

• Find the variance of the difference from step 1.

• Take the square root of the variance of the difference; This is the standard deviation of the difference.

• Calculate the square root of the number of subjects.

• Divide the standard deviation of the difference, by the result in step 5

• Divide the mean difference by the result in step 6. This is the T-statistic.

## References

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