T Test

The t-test statistic from the article "Using the Student's t-test with Extremely Small Sample Sizes" by J.C.F. de Winter (2013) is:

"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."

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.

The author used this type of t-test because they were comparing two independent groups and the variable of interest (X) was continuous and normally distributed. The article aimed to investigate the feasibility of using the t-test with extremely small sample sizes, such as N ? 5, and to estimate the Type I error rate and statistical power under different conditions.

Ultimately, the author concluded that there are no principal objections to using a t-test with extremely small sample sizes of N ? 5, as long as the assumptions of normality and homogeneity of variance are met. However, the author cautioned about the credibility of research findings when sample sizes are small, as small sample sizes can increase the risk of obtaining false positive or false negative results. Therefore, it is important to interpret the results of statistical tests with caution when the sample size is extremely small.

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