# Sample Size Impact on Error Probability

The traditional approach to statistics declares that every experiment requires a sample size that would produce statistical significance for the effect. The Type I error is a chance that a null effect will be declared significant, and this error is usually chosen manually and fixed so that any modifications to sample size would not influence it. On the other hand, the Type II error is a chance that the smallest important effect will be unnoticed or declared insignificant. When the sample size is the lowest possible to get the significance, the Type II error rate is 20% (Hopkins & Batterham, 2018). However, it is possible to reduce the Type II error down to 5-10% if the sample size increases (Hopkins & Batterham, 2018). This modification allows for clustering, considers drop-outs, and generally endures what is defined as the smallest significant effect. Overall, this modification can raise the accuracy of an experiment since it will more precisely indicate even the smallest significance. The possibility of a null effect, as was mentioned above, will stay the same as long as it is constant and defined by the given alpha.

Hello, thank you for sharing the results of your research and your thoughts on it. You were right to mention that the Type I error is fixed and impossible to influence through modifying the sample size. Indeed, it is unfortunate that both types of error could not be reduced simultaneously within one research. Although the Type I error appears to be a constant, you mention Freiman et al.’s (2019) statement that trying to reduce one error exposes the researcher to committing the other. With that said, I found it interesting that you emphasize the risk factor of the Type I error and call it «the nightmare» for researchers but do not mention the dangers of the Type II error. I see your point about researchers wishing to reduce the Type I error, but I think you should consider explaining in more detail why curbing each type of error is essential. The threats and limitations that the Type II error creates in research are certainly something to contemplate since the discussion aims to reduce its probability.

## References

Freiman, J. A., Chalmers, T. C., Smith, H. A., & Kuebler, R. R. (2019). The importance of beta, the type II error, and sample size in the design and interpretation of the randomized controlled trial: survey of two sets of “negative” trials. In Medical uses of statistics (pp. 357-389). CRC Press.

Hopkins, W. G., & Batterham, A. (2018). Estimating sample size for magnitude-based inferences. Sportscience, 21, 63-72. Web.

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1. ApeGrade. "Sample Size Impact on Error Probability." October 31, 2022. https://apegrade.com/sample-size-impact-on-error-probability/.

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