# SAGE Journal Articles

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**Summary/Abstract: **The power of a statistical test of a null hypothesis (H_{o}) is the probability that the H_{o} will be rejected when it is false, that is, the probability of obtaining a statistically significant result. Statistical power depends on the significance criterion (α), the sample size (*N*), and the population effect size (ES). The importance of power analysis arises from the fact that most empirical research in the social and behavioral sciences proceeds by formulating and testing H_{o}s that the investigators hope to reject as a means of establishing facts about the phenomena under study. Statistical power analysis exploits the mathematical relationship among these four variables in statistical inference: power, α, *N*, and ES*.* The relationship is such that when any three of them are fixed, the fourth is determined. Two forms of power analysis are most useful: One is the determination of the *N* that is necessary to attain a specified degree of power to detect as significant (at specified α) a hypothesized ES. This form of power analysis is used in research planning. The second is the determination of power to detect a hypothesized ES (for specified *N* and α), the form used in meta-analytic power reviews of research areas or journals.

**Questions to Consider**

1. According to Cohen, statistical power analysis exploits the mathematical relationship among what four variables in statistical inference?

2. The conventional risk standard for mistakenly rejecting the H0 is:

- 0.01.
- 0.05.
- 0.10.
- 0.15.

3. To determine sample size one needs to posit the __________.

- effect size and desired power
- effect size and skewness of the distribution
- desired power and variance
- desired power

**Summary/Abstract: **Bayesian and classical statistical approaches are based on different types of logical principles. In order to avoid mistaken inferences and misguided interpretations, the practitioner must respect the inference rules embedded into each statistical method. Ignoring these principles leads to the paradoxical conclusions that the hypothesis μ1 = μ2 could be less supported by the data than a more restrictive hypothesis such as μ1 = μ2 = 0, where μ1 and μ2 are two population means. This article intends to discuss and explicit some important assumptions inherent to classical statistical models and null statistical hypotheses. Furthermore, the definition of the p-value and its limitations are analyzed. An alternative measure of evidence, the s-value, is discussed. This article presents the steps to compute s-values and, in order to illustrate the methods, some standard examples are analyzed and compared with p-values. The examples denunciate that p-values, as opposed to s-values, fail to hold some logical relations.

#### Questions to Consider

1. According to the author, what is a limitation of a p-value and how do they suggest to correct for it?

2. Which of the following is not one of the steps for choosing a statistical model?

- Define the objectives of the study
- Define the population of interest
- Define the desired effect size
- Define an adequate experiment to collect the sample

3. The statistical hypotheses H0 and H1 are _____________.

- not necessarily exhaustive
- exhaustive
- mutually exclusive
- mutually exhaustive