How to Calculate a T-Score

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A T-score is a form of a standardized test statistic, which allows you to take an individual score and transform it into a standardized form to make comparison easier. The T-test is similar to the Z-test, but generally T-tests are most helpful with a smaller sample size (typically under 30) and when the standard deviation is unknown, whereas Z-tests work with a large sample size when the variances are known.

  1. Record the Values

  2. Write down the values for a T-score calculation. For example, say you believe your classmates spend more time on social media than the rest of the school does. You need to show, statistically, that your classmates spend a lot of time on social media. Write down the sample mean, the population mean, the sample standard deviation and the sample size.

  3. Apply the Values

  4. Apply values to the T-score formula, which is:

    t = (sample mean - population mean) ÷ (sample standard deviation ÷ √sample size).

    For example, say you believe your classmates spend an average of three hours per day on social media. You select a sample of 10 classmates and the mean time on social media is four hours per day, with a sample standard deviation of 30 minutes (0.5 hours).

    (Assuming your belief is true, you can work out the probability that the mean time spent on social media will be no more than four hours per day.) In this case:

    t = (4 - 3) ÷ (0.5 ÷ √10), which is -1 ÷ 0.158114, which is -6.325.

  5. Work out Degrees of Freedom

  6. Subtract 1 from your sample size to get the degrees of freedom (df), which is 9.

  7. Calculate the Probability

  8. Use a scientific calculator or an online calculator to find the probability by inputting the df and t values. In this case, the probability is 0.99, or 9.9 percent.

    Tips

    • Use the T-score formula to solve probability questions. Usually, you should only use the T-test if your distribution is normal; In other words, that a graph of your data would make a bell-shaped curve. Generally, the bigger the T-score, the bigger the difference is between the groups tested. This is influenced by many factors, including the number of items in your sample, the means of your sample, the mean of the population from which you draw your sample and the standard deviation of your sample.

References

About the Author

Claire is a writer and editor with 18 years' experience. She writes about science and health for a range of digital publications, including Reader's Digest, HealthCentral, Vice and Zocdoc.

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