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Statistics Resources

This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

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.

Assumptions

  1. The dependent variable is continuous (interval or ratio) - based on operationalization of the variable
  2. Each observation is independent of other observations - evaluated through the study's design
  3. No significant outliers for the dependent variable - can be assessed using boxplots, scatterplots, and other methods
  4. The dependent variable should be approximately normally distributed - can be assessed using a histogram, Q-Q plot, skewness, kurtosis, K-S test and/or Shapiro Wilks

Running a Single Sample t-test using SPSS

  1. Analyze > Compare Means and Proportions > One Sample T Test
  2. Move the dependent variable into the Test Variable(s) box
  3. Enter the comparison mean in the Test Value box.
    Note: keeping the "Estimate effect sizes" box checked will provide a measure of effect size in the output that is useful in reporting significant results
  4. Review Options for missing values and confidence interval options.
  5. Select OK to run the analysis.

Interpreting the Output

  • Descriptives
    • provides summary statistics about the dependent variable including sample size, mean, standard deviation, and standard error of the mean
  • One-Sample Test
    • provides the results of the statistical test
      • test statistic = t
      • associated probability (p-value) = Significance
        • one-tail and two-tail probabilities are provided - use the alternative hypothesis to determine which is appropriate to interpret for your study
      • confidence interval of the difference (if elected to include)

Reporting Results in APA Style

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

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

Example:
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 (M = 83, SD = 4.2) was not significantly different from the existing average (t(34) = 1.03, p = .231).

Notes:

  • 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 = .247. 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. If SPSS reports the p-value as < .001, you would report it the same way: p < .001.
  • The t statistic should be reported to two decimal places with a 0 before the decimal point if needed: t = 0.36 or t = 2.71.
  • 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.