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Single Sample T-test

Single Sample T-test

The single sample t-test is used to compare the sample mean from one sample to a given population mean. The purpose of this test is to determine if the sample is drawn from (or different from) the given population.

Basic Hypotheses

Null: The sample mean is not significantly different from the population mean.
Alternative: The sample mean is significantly different from the population mean.

Real-World Examples
  • Determining if a treatment is effective at reducing symptoms or improving scores based on population parameters (not control group comparison)
    • Does CBT increase the proportion of patients that successfully complete therapy?
    • Does the Read with Me program improve reading scores?
    • Is the new facility able to produce more products than previous ones?
  • Determining if there's been a change in some dynamic (i.e. IQ) since the time that the parameter was generated
    • Has the average IQ increased since 2000?
    • Does the current class perform better on exams than previous students?
Reporting Results in APA Style

When reporting the results of the single-sample t-test, APA Style has very specific requirements on what information should be included. Below is the key information required for reporting the results of the. You want to replace the red text with the appropriate values from your output.

t(degrees of freedom) = the t statistic, p = p value.

A single-sample t-test was run to determine if the current freshman class's performance on the exam was different than previous students' performance. The results showed that the current freshmen's performance (= 83, SD = 4.2) was not significantly different from the existing average (t(34) = 1.03, p = .231).


  • When reporting the p-value, there are two ways to approach it. One is when the results are not significant. In that case, you want to report the p-value exactly: p = .24. The other is when the results are significant. In this case, you can report the p-value as being less than the level of significance: p < .05.
  • The t statistic should be reported to two decimal places without a 0 before the decimal point: .36
  • Degrees of freedom for this test are N - 1, where "N" represents the number of people in the sample. N can be found in the SPSS output.
Additional Resources

Laerd Statistics - One-Sample T-Test guide
Khan Academy - Testing hypotheses about a mean
Statistics Solutions - One Sample T-Test

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