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Difference Between Z-test and T-test

statistics_bookZ-test Vs T-test

Sometimes, measuring every single piece of item is just not practical. That is why we developed and use statistical methods to solve problems. The most practical way to do it is to measure just a sample of the population. Some methods test hypotheses by comparison. The two of the more known statistical hypothesis test are the T-test and the Z-test. Let us try to breakdown the two.

A T-test is a statistical hypothesis test. In such test, the test statistic follows a Student’s T-distribution if the null hypothesis is true. The T-statistic was introduced by W.S. Gossett under the pen name “Student”. The T-test is also referred as the “Student T-test”. It is very likely that the T-test is most commonly used Statistical Data Analysis procedure for hypothesis testing since it is straightforward and easy to use. Additionally, it is flexible and adaptable to a broad range of circumstances.

There are various T-tests and two most commonly applied tests are the one-sample and paired-sample T-tests. One-sample T-tests are used to compare a sample mean with the known population mean. Two-sample T-tests, the other hand, are used to compare either independent samples or dependent samples.

T-test is best applied, at least in theory, if you have a limited sample size (n < 30) as long as the variables are approximately normally distributed and the variation of scores in the two groups is not reliably different. It is also great if you do not know the populations’ standard deviation. If the standard deviation is known, then, it would be best to use another type of statistical test, the Z-test. The Z-test is also applied to compare sample and population means to know if there’s a significant difference between them. Z-tests always use normal distribution and also ideally applied if the standard deviation is known. Z-tests are often applied if the certain conditions are met; otherwise, other statistical tests like T-tests are applied in substitute. Z-tests are often applied in large samples (n > 30). When T-test is used in large samples, the t-test becomes very similar to the Z-test. There are fluctuations that may occur in T-tests sample variances that do not exist in Z-tests. Because of this, there are differences in both test results.

Summary:

1. Z-test is a statistical hypothesis test that follows a normal distribution while T-test follows a Student’s T-distribution.
2. A T-test is appropriate when you are handling small samples (n < 30) while a Z-test is appropriate when you are handling moderate to large samples (n > 30).
3. T-test is more adaptable than Z-test since Z-test will often require certain conditions to be reliable. Additionally, T-test has many methods that will suit any need.
4. T-tests are more commonly used than Z-tests.
5. Z-tests are preferred than T-tests when standard deviations are known.


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8 Comments

  1. NOT QUITE ACCURATE!

    There are books written about the two concepts and the misuse of the two tests
    More important, the main idea behind this is the standard deviation:
    - if the standard deviation is known sample size does not matter – ALWAYS USE Z-TEST
    - if the standard deviation is unknown then you have a choice
    – z-test if sample is large
    – t-test if sample is small and normally distributed

    DO NOT USE T-TEST FOR SMALL SAMPLE THAT ARE NOT NORMALLY DISTRIBUTED
    The statistically correct answer in such cases: cannot be solved — not enough information

    • When you say standard deviation does it mean the standard deviation of the population or sample?

      If you are given a question with samples from two populations, sample size is six and you are given samples standard deviations and sample mean you are required to compare the two means what test will you use.

  2. So, when would you need to use a t-distribution and z-distribution?? Is this based solely on the given standard deviation? Or, would the sample size be a factor as well?

  3. thanks heaps! helped a lot :)
    but yes Jodi, sample size is also a factor, we have to take everything into account

  4. How can I solved the the problem if there is no

  5. How can I solved the the problem if there is no STANDARD DEVIATION?

  6. I understand that a t-test result will have the same sign (positive/ negative) as the underlying value.

    Is this also the case for the z-test?

    Many thanks,

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