Using the Student's t-Test With Small Sample Sizes
This paper examines J.C.F. de Winter's (2013) article on using the Student's t-test with extremely small sample sizes (N ≤ 5). It walks through an independent samples t-test example comparing two groups on a continuous variable, explains the rationale for choosing this statistical approach, and summarizes de Winter's conclusions regarding Type I error rates, statistical power, and the conditions under which small-sample t-tests remain valid. The paper also highlights the importance of interpreting results cautiously when sample sizes are minimal.
- Introduction to the T-Test Example: Presents the t-test example from de Winter
- Interpreting the T-Test Results: Explains t-value, degrees of freedom, p-value
- Rationale for Using the Independent Samples T-Test: Justifies choice of independent samples t-test
- Conclusions on Small Sample T-Tests: Summarizes findings on small-sample validity
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What makes this paper effective
- Grounds the discussion in a specific, cited example from a published academic article, giving the analysis concrete data to work from.
- Clearly explains each component of the t-test output — t-value, degrees of freedom, and p-value — in accessible language appropriate for introductory statistics students.
- Connects the statistical example back to the broader argument of the source article, linking methodology to research conclusions.
Key academic technique demonstrated
The paper demonstrates source-anchored analysis: it extracts a specific statistical result from a peer-reviewed article, explains what each element means, and then situates that example within the article's larger research question. This technique shows how to move from a narrow quantitative output to a broader interpretive claim.
Structure breakdown
The paper opens by presenting the t-test example verbatim from de Winter (2013), then unpacks the numerical components of the result, explains the author's methodological choices, and closes with the article's overarching conclusions about the validity and limitations of small-sample t-tests. The structure moves from specific to general throughout.
Introduction to the T-Test Example
The t-test statistic discussed below draws from the article Using the Student's t-test with Extremely Small Sample Sizes by J.C.F. de Winter (2013). The article presents the following example of an independent samples t-test:
"An independent samples t-test was conducted to compare the mean scores of Group A (M = 3.2, SD = 0.6, N = 3) and Group B (M = 2.8, SD = 0.5, N = 3) on the variable X. The t-test revealed no significant difference between the groups, t(4) = 1.08, p > .05."
Interpreting the T-Test Results
In this example, the author used an independent samples t-test to compare the means of two groups (Group A and Group B) on a continuous variable (X), with sample sizes of N = 3 in each group. The t-value is 1.08 and the degrees of freedom are 4. The p-value is greater than .05, indicating that the difference between the groups is not statistically significant.
References
De Winter, J. C. (2013). Using the Student's t-test with extremely small sample sizes. Practical Assessment, Research, and Evaluation, 18(1), 10. https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1307&context=pare
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