When would you use a t-test vs a z-test?
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You use a t-test or a z-test to determine if there’s a significant difference between sample data and a population or between two samples, but the choice depends mainly on sample size and knowledge of population variance.
When to Use a Z-test:
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Sample size is large (usually n > 30)
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The population standard deviation (σ) is known
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Data is approximately normally distributed or the sample is large enough for the Central Limit Theorem to apply
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Used for testing means or proportions with known variance
Example: Comparing the average test score of a large sample to a known population mean with a known population standard deviation.
When to Use a T-test:
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Sample size is small (usually n < 30)
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The population standard deviation is unknown (which is common in practice)
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Data is approximately normally distributed
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The test uses the sample standard deviation (s) instead of σ
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Comes with different types: one-sample t-test, independent two-sample t-test, paired t-test
Example: Comparing the average weight loss in a group of 20 participants to a target value when the population variance is unknown.
Summary:
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Use a z-test when you know the population variance and have a large sample.
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Use a t-test when the population variance is unknown and/or your sample size is small.
The t-distribution accounts for the added uncertainty in estimating variance from small samples.
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