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When should you use a t-test vs a z-test in hypothesis testing?

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Hypothesis testing is a common method in product R&D to compare the performance of different features, designs, or strategies. However, choosing the right statistical test for your data can be tricky. In this article, you will learn when to use a t-test vs a z-test, and what are the advantages and disadvantages of each one.

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1 What are t-tests and z-tests?

A t-test and a z-test are both types of parametric tests that compare the means of two groups or samples. A parametric test assumes that the data follows a normal distribution, and that the variance and standard deviation are known or estimated. The main difference between a t-test and a z-test is that a t-test uses the sample standard deviation to calculate the test statistic, while a z-test uses the population standard deviation.

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2 When to use a t-test?

A t-test is appropriate when you have a small sample size (usually less than 30), or when you do not know the population standard deviation. A t-test is more flexible and robust than a z-test, as it can adjust for the uncertainty and variability in the sample. There are different types of t-tests, such as one-sample, two-sample, or paired, depending on the number and nature of the samples you are comparing.

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3 When to use a z-test?

A z-test is appropriate when you have a large sample size (usually more than 30), and when you know the population standard deviation. A z-test is more accurate and precise than a t-test, as it uses the true measure of dispersion in the population. A z-test can also be used to test proportions, such as the percentage of users who prefer a certain feature or design.

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4 Advantages and disadvantages of t-tests

T-tests offer several advantages, such as the ability to handle small sample sizes and unknown population parameters, as well as the capability to test various hypotheses, like one-tailed, two-tailed, or non-directional. They also take into account the variability and uncertainty in the sample. However, there are some drawbacks to t-tests. These include the need for assuming normality, which may not be feasible for all data sets, and possibly lower power and higher error rates than z-tests for large sample sizes. Additionally, t-tests may not be suitable for testing proportions or categorical data.

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5 Advantages and disadvantages of z-tests

Z-tests offer several advantages, such as the ability to handle large sample sizes and known population parameters, as well as providing more accurate and precise results than t-tests. Additionally, z-tests can test proportions and categorical data, as well as means. However, there are some drawbacks to using z-tests, such as the need for the assumption of normality, which may not hold for some data sets. Furthermore, z-tests require knowledge of the population standard deviation, which may not be available or reliable. Lastly, z-tests may not be suitable for small sample sizes or unknown population parameters.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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When should you use a t-test vs a z-test in hypothesis testing?

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1 What are t-tests and z-tests?

2 When to use a t-test?

3 When to use a z-test?

4 Advantages and disadvantages of t-tests

5 Advantages and disadvantages of z-tests

6 Here’s what else to consider

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When should you use a t-test vs a z-test in hypothesis testing?

1

2

3

4

5

6

1 What are t-tests and z-tests?

2 When to use a t-test?

3 When to use a z-test?

4 Advantages and disadvantages of t-tests

5 Advantages and disadvantages of z-tests

6 Here’s what else to consider

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