# Power Analysis Response

According to Gray and Grove (2021). Power is the probability that a statistical test will detect an effect when it actually exists. Power is the inverse of type II error and it is the probability of retaining the null (Gray & Grove, 2021, p.636). Greenland et al. (2016) explains that every method of statistical inference depends on a complex web of assumptions about how data were collected and analyzed. And how the analysis results were selected for presentation. The full set of assumptions is embodied in a statistical model that underpins the method.

This model is a mathematical representation of data variability, and thus ideally would capture accurately all sources of such variability. The power of a test to detect a correct alternative hypothesis is the pre-study probability. That the test will reject the test hypothesis (e.g., the probability that P will not exceed a pre-specified cut-off such as 0.05). The corresponding pre-study probability of failing to reject the test hypothesis when the alternative is correct is one minus the power. Also known as the Type-II or beta error rate (Greenland et al., 2016)

## null hypothesis

According to Shreffler (2021), a type I error occurs when in research when we reject the null hypothesis. And erroneously state that the study found significant differences when there indeed was no difference. In other words. It is equivalent to saying that the groups or variables differ when, in fact, they do not or having false positives. A concept closely aligned to type II error is statistical power. Statistical power is a crucial part of the research process that is most valuable in the design and planning phases of studies. Though it requires assessment when interpreting results. Power is the ability to correctly reject a null hypothesis that is indeed false. Unfortunately, many studies lack sufficient power and should be presented as having inconclusive findings (Shreffler, 2021).

Shreffler (2021) also mentions that Power is the probability of a study to make correct decisions or detect an effect when one exists. The power of a statistical test is dependent on the level of significance set by the researcher, the sample size, and the effect size or the extent to which the groups differ based on treatment. Statistical power is critical for healthcare providers to decide how many patients to enroll in clinical studies. Power is strongly associated with sample size; when the sample size is large, power will generally not be an issue. Thus, when conducting a study with a low sample size, and ultimately low power, researchers should be aware of the likelihood of a type II error. By limiting type I and type II errors, healthcare providers can ensure that decisions based on research outputs are safe for patients (Shreffler, 2021).

## References

Gray, J., & Grove, S. K. (2021). *Burns and Grove’s the practice of nursing research: appraisal, synthesis, and generation of evidence* (9th ed.). Elsevier.

Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, p values, confidence intervals, and power: A guide to misinterpretations. *European Journal of Epidemiology*, *31*(4), 337–350. https://doi.org/10.1007/s10654-016-0149-3

Shreffler, J. (2021). *Type i and type ii errors and statistical power*. StatPearls [Internet]. https://www.ncbi.nlm.nih.gov/books/NBK557530/.