Null hypothesis significance testing: a short tutorial

Abstract

Although thoroughly criticized, null hypothesis significance testing (NHST) remains the statistical method of choice used to provide evidence for an effect, in biological, biomedical and social sciences. In this short tutorial, I first summarize the concepts behind the method, distinguishing test of significance (Fisher) and test of acceptance (Newman-Pearson) and point to common interpretation errors regarding the p-value. I then present the related concepts of confidence intervals and again point to common interpretation errors. Finally, I discuss what should be reported in which context. The goal is to clarify concepts to avoid interpretation errors and propose reporting practices. Referee Status:Invited Referees Creative Commons Attribution Licence permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The author(s) declared that no grants were involved in supporting this work. The Null Hypothesis Significance Testing frameworkNHST is a method of statistical inference by which an experimental factor is tested against a hypothesis of no effect or no relationship based on a given observation. The method is a combination of the concepts of significance testing developed by Fisher in 1925 and of acceptance based on critical rejection regions developed by Neyman & Pearson in 1928. In the following I am first presenting each approach, highlighting the key differences and common misconceptions that result from their combination into the NHST framework (for a more mathematical comparison, along with the Bayesian method, see Christensen, 2005). I next present the related concept of confidence intervals. I finish by discussing practical aspects in using NHST and reporting practice. Fisher, significance testing, and the p-valueThe method developed by (Fisher, 1934; Fisher, 1955; Fisher, 1959) allows to compute the probability of observing a result at least as extreme as a test statistic (e.g. t value), assuming the null hypothesis of no effect is true. This probability or p-value reflects (1) the conditional probability of achieving the observed outcome or larger: p(Obs≥t|H0), and (2) is therefore a cumulative probability rather than a point estimate. It is equal to the area under the null probability distribution curve from the observed test statistic to the tail of the null distribution (Turkheimer et al., 2004). The approach proposed is of 'proof by contradiction ' (Christensen, 2005), we pose the null model and test if data conform to it.In practice, it is recommended to set a level of significance (a theoretical p-value) that acts as a reference point to identify significant results, that is to identify results that differ from the null-hypothesis of no effect. Fisher recommended using p=0.05 to judge whether an effect is significant or not as it is roughly two standard deviations away from the mean for the normal distribution (Fisher, 1934 page 45: 'The value for which p=.05, or 1 in 20, is 1.96 or nearly 2; it is convenient to take this...

Statistical Hypothesis Testing: Overview and Application

“…3,15 Thus, in the above example, if the headache frequency distributions of men and women were tested and resulted in a P value = .035, the null hypothesis would be rejected, as the P value is less than .05, the predefined level of significance. 3,15 Thus, in the above example, if the headache frequency distributions of men and women were tested and resulted in a P value = .035, the null hypothesis would be rejected, as the P value is less than .05, the predefined level of significance.…”

“…7 3. Stated differently, a statistically significant finding is a statement about the improbability of the null hypothesis, 15 but it is not a statement about the clinical or practical significance of an effect. 27 Though often assumed, a P value is not the probability that the null hypothesis is true.…”

“…The significance level is often set at P < .05, probably because Fisher thought that this threshold was "convenient," as it corresponded with a 1 in 20 chance, or approximately 2 standard deviations away from the mean of a normal distribution. 3,15 Thus, in the above example, if the headache frequency distributions of men and women were tested and resulted in a P value = .035, the null hypothesis would be rejected, as the P value is less than .05, the predefined level of significance. In this case, the observed data have yielded a low P value indicating that the data seem unlikely to be consistent with the null hypothesis, and the groups would be stated to differ from one another.…”

“…Because simply rejecting the null hypothesis does not necessarily imply that the findings are important, the interpretation of NHST must be made in conjunction with the size of the group differences or size of the effect under study. Stated differently, a statistically significant finding is a statement about the improbability of the null hypothesis, 15 but it is not a statement about the clinical or practical significance of an effect. 30 For example, an investigator is interested in examining if a new treatment for head lice is effective at eliminating this extremely bothersome problem.…”

Hybrid data‐model method to improve generation estimation and performance assessment of grid‐tied PV: a case study

“…The low p-values in the table, considered in conjunction with the patterns observed in boxplots and correlation matrix, could provide suitable grounds for the rejection of null hypothesis and conclude that there is a significant likelihood for irradiance, module temperature, and ambient temperature to impact PV generation This is further observed from the R 2 and adjusted R 2 values that provide information on how much of the variations in PV generation values are captured by the linear model. They are calculated by [43] , MST = MST (n − 1) ,…”