Data considerations for Paired t

To ensure that your results are valid, consider the following guidelines when you collect data, perform the analysis, and interpret your results.

The data must be continuous, such as the weights of packages

Continuous data has an infinite number of values between any two values.

The sample data should not be severely skewed, and the sample sizes should be greater than 20

If your sample sizes are greater than 20 and the underlying distribution is unimodal and continuous, the hypothesis test performs appropriately even if data are mildly skewed. If your sample sizes are less than 20, you should graph the data to check for skewness and unusual observations. If the data is severely skewed or has many unusual observations, use caution when you interpret the results.

You should have a set of paired (dependent) observations, such as measurements made on the same item under different conditions

If you have two samples of independent observations, use 2-Sample t instead. For more information, go to How are dependent and independent samples different?.

The sample data should be selected randomly

In statistics, random samples are used to make generalizations, or inferences, about a population. If your data are not collected randomly, your results may not represent the population. For more information, go to Randomness in samples of data.

Determine an appropriate sample size
Your sample should be large enough so that the following are true:
  • The estimates have enough precision.
  • The confidence intervals are narrow enough to be useful.
  • You have adequate protection against type I and type II errors.
To determine the appropriate sample size for your hypothesis test, go to Power and Sample Size for Paired t.