As the number of subjects increases, what must happen to the t value for reaching statistical significance?

In statistical analysis, particularly when using t-tests, the t value is a representation of how much the sample means differ from each other relative to the variability in the samples. As the number of subjects in a study increases, the sample size contributes to a more precise estimation of the population parameters, resulting in a reduced margin of error.

When the sample size increases, the standard error of the mean decreases because it is inversely related to the square root of the sample size. Therefore, with a larger sample size, the test becomes more powerful, meaning that smaller differences in means can still achieve statistical significance. Consequently, a smaller t value is needed to reject the null hypothesis because the increased sample size leads to a tighter confidence interval around the mean.

This relationship is crucial because it underlines the concept that with larger samples, our ability to detect true effects improves, allowing for the identification of statistically significant results even with lesser differences. Hence, as the number of subjects increases, the t value required to reach statistical significance must indeed become smaller.