Data considerations for 1-Sample t

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

The population standard deviation is not known

If you know the standard deviation of the population, use 1-Sample Z because the Z-test has more power than the t-test.

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

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

If your data contain counts, such as the number of defects per unit, use 1-Sample Poisson Rate. If your data classify each observation into one of two categories, such as pass/fail, use 1 Proportion. For more information on data types, go to Data types you can analyze with a hypothesis test.

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

If your sample size is greater than 20 and the underlying distribution is unimodal and continuous, the hypothesis test performs appropriately even if the data are mildly skewed. If your sample size is 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.

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.

Each observation should be independent from all other observations

If you have paired or dependent data, such as measurements of a bearing taken with two different calipers, use Paired t instead. For more information, go to How are dependent and independent samples different?.

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 1-Sample t.
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