Précis of Statistical significance: Rationale, validity, and utility

1998 ◽  
Vol 21 (2) ◽  
pp. 169-194 ◽  
Author(s):  
Siu L. Chow
Keyword(s):  
Effect Size ◽  
Null Hypothesis ◽  
Statistical Power ◽  
Statistical Significance ◽  
Research Result ◽  
Practical Importance ◽  
Test Procedure ◽  
Statistical Hypothesis ◽  
Interval Estimate ◽  
Test Statistic

The null-hypothesis significance-test procedure (NHSTP) is defended in the context of the theory-corroboration experiment, as well as the following contrasts: (a) substantive hypotheses versus statistical hypotheses, (b) theory corroboration versus statistical hypothesis testing, (c) theoretical inference versus statistical decision, (d) experiments versus nonexperimental studies, and (e) theory corroboration versus treatment assessment. The null hypothesis can be true because it is the hypothesis that errors are randomly distributed in data. Moreover, the null hypothesis is never used as a categorical proposition. Statistical significance means only that chance influences can be excluded as an explanation of data; it does not identify the nonchance factor responsible. The experimental conclusion is drawn with the inductive principle underlying the experimental design. A chain of deductive arguments gives rise to the theoretical conclusion via the experimental conclusion. The anomalous relationship between statistical significance and the effect size often used to criticize NHSTP is more apparent than real. The absolute size of the effect is not an index of evidential support for the substantive hypothesis. Nor is the effect size, by itself, informative as to the practical importance of the research result. Being a conditional probability, statistical power cannot be the a priori probability of statistical significance. The validity of statistical power is debatable because statistical significance is determined with a single sampling distribution of the test statistic based on H0, whereas it takes two distributions to represent statistical power or effect size. Sample size should not be determined in the mechanical manner envisaged in power analysis. It is inappropriate to criticize NHSTP for nonstatistical reasons. At the same time, neither effect size, nor confidence interval estimate, nor posterior probability can be used to exclude chance as an explanation of data. Neither can any of them fulfill the nonstatistical functions expected of them by critics.

scholarly journals The earth is flat (p > 0.05): significance thresholds and the crisis of unreplicable research

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e3544 ◽  
Author(s):  
Valentin Amrhein ◽  
Fränzi Korner-Nievergelt ◽  
Tobias Roth
Keyword(s):  
Publication Bias ◽  
Null Hypothesis ◽  
Statistical Power ◽  
Statistical Significance ◽  
Practical Importance ◽  
Effect Sizes ◽  
Point Estimate ◽  
Selective Reporting ◽  
Interval Estimate ◽  
True Effect

The widespread use of ‘statistical significance’ as a license for making a claim of a scientific finding leads to considerable distortion of the scientific process (according to the American Statistical Association). We review why degradingp-values into ‘significant’ and ‘nonsignificant’ contributes to making studies irreproducible, or to making them seem irreproducible. A major problem is that we tend to take smallp-values at face value, but mistrust results with largerp-values. In either case,p-values tell little about reliability of research, because they are hardly replicable even if an alternative hypothesis is true. Also significance (p ≤ 0.05) is hardly replicable: at a good statistical power of 80%, two studies will be ‘conflicting’, meaning that one is significant and the other is not, in one third of the cases if there is a true effect. A replication can therefore not be interpreted as having failed only because it is nonsignificant. Many apparent replication failures may thus reflect faulty judgment based on significance thresholds rather than a crisis of unreplicable research. Reliable conclusions on replicability and practical importance of a finding can only be drawn using cumulative evidence from multiple independent studies. However, applying significance thresholds makes cumulative knowledge unreliable. One reason is that with anything but ideal statistical power, significant effect sizes will be biased upwards. Interpreting inflated significant results while ignoring nonsignificant results will thus lead to wrong conclusions. But current incentives to hunt for significance lead to selective reporting and to publication bias against nonsignificant findings. Data dredging,p-hacking, and publication bias should be addressed by removing fixed significance thresholds. Consistent with the recommendations of the late Ronald Fisher,p-values should be interpreted as graded measures of the strength of evidence against the null hypothesis. Also largerp-values offer some evidence against the null hypothesis, and they cannot be interpreted as supporting the null hypothesis, falsely concluding that ‘there is no effect’. Information on possible true effect sizes that are compatible with the data must be obtained from the point estimate, e.g., from a sample average, and from the interval estimate, such as a confidence interval. We review how confusion about interpretation of largerp-values can be traced back to historical disputes among the founders of modern statistics. We further discuss potential arguments against removing significance thresholds, for example that decision rules should rather be more stringent, that sample sizes could decrease, or thatp-values should better be completely abandoned. We conclude that whatever method of statistical inference we use, dichotomous threshold thinking must give way to non-automated informed judgment.

scholarly journals The earth is flat (p>0.05): Significance thresholds and the crisis of unreplicable research

2017 ◽  
Author(s):  
Valentin Amrhein ◽  
Fränzi Korner-Nievergelt ◽  
Tobias Roth
Keyword(s):  
Publication Bias ◽  
Null Hypothesis ◽  
Statistical Power ◽  
Statistical Significance ◽  
Practical Importance ◽  
Effect Sizes ◽  
Selective Reporting ◽  
Interval Estimate ◽  
P Values ◽  
True Effect

The widespread use of 'statistical significance' as a license for making a claim of a scientific finding leads to considerable distortion of the scientific process (according to the American Statistical Association). We review why degrading p-values into 'significant' and 'nonsignificant' contributes to making studies irreproducible, or to making them seem irreproducible. A major problem is that we tend to take small p-values at face value, but mistrust results with larger p-values. In either case, p-values tell little about reliability of research, because they are hardly replicable even if an alternative hypothesis is true. Also significance (p≤0.05) is hardly replicable: at a good statistical power of 80%, two studies will be 'conflicting', meaning that one is significant and the other is not, in one third of the cases if there is a true effect. A replication can therefore not be interpreted as having failed only because it is nonsignificant. Many apparent replication failures may thus reflect faulty judgment based on significance thresholds rather than a crisis of unreplicable research. Reliable conclusions on replicability and practical importance of a finding can only be drawn using cumulative evidence from multiple independent studies. However, applying significance thresholds makes cumulative knowledge unreliable. One reason is that with anything but ideal statistical power, significant effect sizes will be biased upwards. Interpreting inflated significant results while ignoring nonsignificant results will thus lead to wrong conclusions. But current incentives to hunt for significance lead to selective reporting and to publication bias against nonsignificant findings. Data dredging, p-hacking, and publication bias should be addressed by removing fixed significance thresholds. Consistent with the recommendations of the late Ronald Fisher, p-values should be interpreted as graded measures of the strength of evidence against the null hypothesis. Also larger p-values offer some evidence against the null hypothesis, and they cannot be interpreted as supporting the null hypothesis, falsely concluding that 'there is no effect'. Information on possible true effect sizes that are compatible with the data must be obtained from the point estimate, e.g., from a sample average, and from the interval estimate, such as a confidence interval. We review how confusion about interpretation of larger p-values can be traced back to historical disputes among the founders of modern statistics. We further discuss potential arguments against removing significance thresholds, for example that decision rules should rather be more stringent, that sample sizes could decrease, or that p-values should better be completely abandoned. We conclude that whatever method of statistical inference we use, dichotomous threshold thinking must give way to non-automated informed judgment.

scholarly journals The earth is flat (p>0.05): Significance thresholds and the crisis of unreplicable research

2017 ◽  
Author(s):  
Valentin Amrhein ◽  
Fränzi Korner-Nievergelt ◽  
Tobias Roth
Keyword(s):  
Publication Bias ◽  
Null Hypothesis ◽  
Statistical Power ◽  
Statistical Significance ◽  
Practical Importance ◽  
Effect Sizes ◽  
Selective Reporting ◽  
Interval Estimate ◽  
P Values ◽  
True Effect

The widespread use of 'statistical significance' as a license for making a claim of a scientific finding leads to considerable distortion of the scientific process (according to the American Statistical Association). We review why degrading p-values into 'significant' and 'nonsignificant' contributes to making studies irreproducible, or to making them seem irreproducible. A major problem is that we tend to take small p-values at face value, but mistrust results with larger p-values. In either case, p-values tell little about reliability of research, because they are hardly replicable even if an alternative hypothesis is true. Also significance (p≤0.05) is hardly replicable: at a good statistical power of 80%, two studies will be 'conflicting', meaning that one is significant and the other is not, in one third of the cases if there is a true effect. A replication can therefore not be interpreted as having failed only because it is nonsignificant. Many apparent replication failures may thus reflect faulty judgment based on significance thresholds rather than a crisis of unreplicable research. Reliable conclusions on replicability and practical importance of a finding can only be drawn using cumulative evidence from multiple independent studies. However, applying significance thresholds makes cumulative knowledge unreliable. One reason is that with anything but ideal statistical power, significant effect sizes will be biased upwards. Interpreting inflated significant results while ignoring nonsignificant results will thus lead to wrong conclusions. But current incentives to hunt for significance lead to selective reporting and to publication bias against nonsignificant findings. Data dredging, p-hacking, and publication bias should be addressed by removing fixed significance thresholds. Consistent with the recommendations of the late Ronald Fisher, p-values should be interpreted as graded measures of the strength of evidence against the null hypothesis. Also larger p-values offer some evidence against the null hypothesis, and they cannot be interpreted as supporting the null hypothesis, falsely concluding that 'there is no effect'. Information on possible true effect sizes that are compatible with the data must be obtained from the point estimate, e.g., from a sample average, and from the interval estimate, such as a confidence interval. We review how confusion about interpretation of larger p-values can be traced back to historical disputes among the founders of modern statistics. We further discuss potential arguments against removing significance thresholds, for example that decision rules should rather be more stringent, that sample sizes could decrease, or that p-values should better be completely abandoned. We conclude that whatever method of statistical inference we use, dichotomous threshold thinking must give way to non-automated informed judgment.

scholarly journals The earth is flat (p>0.05): Significance thresholds and the crisis of unreplicable research

2017 ◽  
Author(s):  
Valentin Amrhein ◽  
Fränzi Korner-Nievergelt ◽  
Tobias Roth
Keyword(s):  
Publication Bias ◽  
Null Hypothesis ◽  
Statistical Power ◽  
Alternative Hypothesis ◽  
Statistical Significance ◽  
Practical Importance ◽  
Decision Rules ◽  
Effect Sizes ◽  
P Values ◽  
True Effect

The widespread use of 'statistical significance' as a license for making a claim of a scientific finding leads to considerable distortion of the scientific process (American Statistical Association, Wasserstein & Lazar 2016). We review why degrading p-values into 'significant' and 'nonsignificant' contributes to making studies irreproducible, or to making them seem irreproducible. A major problem is that we tend to take small p-values at face value, but mistrust results with larger p-values. In either case, p-values can tell little about reliability of research, because they are hardly replicable even if an alternative hypothesis is true. Also significance (p≤0.05) is hardly replicable: at a realistic statistical power of 40%, given that there is a true effect, only one in six studies will significantly replicate the significant result of another study. Even at a good power of 80%, results from two studies will be conflicting, in terms of significance, in one third of the cases if there is a true effect. This means that a replication cannot be interpreted as having failed only because it is nonsignificant. Many apparent replication failures may thus reflect faulty judgement based on significance thresholds rather than a crisis of unreplicable research. Reliable conclusions on replicability and practical importance of a finding can only be drawn using cumulative evidence from multiple independent studies. However, applying significance thresholds makes cumulative knowledge unreliable. One reason is that with anything but ideal statistical power, significant effect sizes will be biased upwards. Interpreting inflated significant results while ignoring nonsignificant results will thus lead to wrong conclusions. But current incentives to hunt for significance lead to publication bias against nonsignificant findings. Data dredging, p-hacking and publication bias should be addressed by removing fixed significance thresholds. Consistent with the recommendations of the late Ronald Fisher, p-values should be interpreted as graded measures of the strength of evidence against the null hypothesis. Also larger p-values offer some evidence against the null hypothesis, and they cannot be interpreted as supporting the null hypothesis, falsely concluding that 'there is no effect'. Information on possible true effect sizes that are compatible with the data must be obtained from the observed effect size, e.g., from a sample average, and from a measure of uncertainty, such as a confidence interval. We review how confusion about interpretation of larger p-values can be traced back to historical disputes among the founders of modern statistics. We further discuss potential arguments against removing significance thresholds, such as 'we need more stringent decision rules', 'sample sizes will decrease' or 'we need to get rid of p-values'.

The null-hypothesis significance-test procedure is still warranted

1998 ◽  
Vol 21 (2) ◽  
pp. 228-235 ◽  
Author(s):  
Siu L. Chow
Keyword(s):  
Null Hypothesis ◽  
Statistical Power ◽  
Meta Analysis ◽  
Statistical Significance ◽  
Test Procedure ◽  
Significance Test ◽  
Null Hypothesis Significance Test ◽  
Wide Range ◽  
Statistical Hypotheses ◽  
Alternative Hypotheses

Entertaining diverse assumptions about empirical research, commentators give a wide range of verdicts on the NHSTP defence in Statistical significance. The null-hypothesis significance-test procedure (NHSTP) is defended in a framework in which deductive and inductive rules are deployed in theory corroboration in the spirit of Popper's Conjectures and refutations (1968b). The defensible hypothetico-deductive structure of the framework is used to make explicit the distinctions between (1) substantive and statistical hypotheses, (2) statistical alternative and conceptual alternative hypotheses, and (3) making statistical decisions and drawing theoretical conclusions. These distinctions make it easier to show that (1) H0 can be true, (2) the effect size is irrelevant to theory corroboration, and (3) “strong” hypotheses make no difference to NHSTP. Reservations about statistical power, meta-analysis, and the Bayesian approach are still warranted.

Using confidence intervals to estimate the response of salmon populations (Oncorhynchus spp.) to experimental habitat alterations

2005 ◽  
Vol 62 (12) ◽  
pp. 2716-2726 ◽  
Author(s):  
Michael J Bradford ◽  
Josh Korman ◽  
Paul S Higgins
Keyword(s):  
Confidence Intervals ◽  
Effect Size ◽  
Null Hypothesis ◽  
Statistical Power ◽  
Habitat Restoration ◽  
Coho Salmon ◽  
Fish Habitat ◽  
Monitoring Program ◽  
Considerable Uncertainty ◽  
Monitoring Programs

There is considerable uncertainty about the effectiveness of fish habitat restoration programs, and reliable monitoring programs are needed to evaluate them. Statistical power analysis based on traditional hypothesis tests are usually used for monitoring program design, but here we argue that effect size estimates and their associated confidence intervals are more informative because results can be compared with both the null hypothesis of no effect and effect sizes of interest, such as restoration goals. We used a stochastic simulation model to compare alternative monitoring strategies for a habitat alteration that would change the productivity and capacity of a coho salmon (Oncorhynchus kisutch) producing stream. Estimates of the effect size using a freshwater stock–recruit model were more precise than those from monitoring the abundance of either spawners or smolts. Less than ideal monitoring programs can produce ambiguous results, which are cases in which the confidence interval includes both the null hypothesis and the effect size of interest. Our model is a useful planning tool because it allows the evaluation of the utility of different types of monitoring data, which should stimulate discussion on how the results will ultimately inform decision-making.

On “Field Significance” and the False Discovery Rate

2006 ◽  
Vol 45 (9) ◽  
pp. 1181-1189 ◽  
Author(s):  
D. S. Wilks
Keyword(s):  
False Discovery Rate ◽  
Statistical Power ◽  
Statistical Significance ◽  
Significance Test ◽  
P Value ◽  
Test Statistic ◽  
Global Test ◽  
Additional Advantage ◽  
Counting Procedure ◽  
False Discovery

Abstract The conventional approach to evaluating the joint statistical significance of multiple hypothesis tests (i.e., “field,” or “global,” significance) in meteorology and climatology is to count the number of individual (or “local”) tests yielding nominally significant results and then to judge the unusualness of this integer value in the context of the distribution of such counts that would occur if all local null hypotheses were true. The sensitivity (i.e., statistical power) of this approach is potentially compromised both by the discrete nature of the test statistic and by the fact that the approach ignores the confidence with which locally significant tests reject their null hypotheses. An alternative global test statistic that has neither of these problems is the minimum p value among all of the local tests. Evaluation of field significance using the minimum local p value as the global test statistic, which is also known as the Walker test, has strong connections to the joint evaluation of multiple tests in a way that controls the “false discovery rate” (FDR, or the expected fraction of local null hypothesis rejections that are incorrect). In particular, using the minimum local p value to evaluate field significance at a level αglobal is nearly equivalent to the slightly more powerful global test based on the FDR criterion. An additional advantage shared by Walker’s test and the FDR approach is that both are robust to spatial dependence within the field of tests. The FDR method not only provides a more broadly applicable and generally more powerful field significance test than the conventional counting procedure but also allows better identification of locations with significant differences, because fewer than αglobal × 100% (on average) of apparently significant local tests will have resulted from local null hypotheses that are true.

USING R FOR PSYCHOLOGICAL RESEARCH: A TUTORIAL OF BASIC METHODS

2020 ◽  
pp. 28-63
Author(s):  
A. G. Vinogradov
Keyword(s):  
Sample Size ◽  
Empirical Research ◽  
Effect Size ◽  
Statistical Power ◽  
Sample Size Calculation ◽  
Psychological Research ◽  
Research Data ◽  
Statistical Hypothesis ◽  
Categorical Variables ◽  
Measurement Scales

The article belongs to a special modern genre of scholar publications, so-called tutorials – articles devoted to the application of the latest methods of design, modeling or analysis in an accessible format in order to disseminate best practices. The article acquaints Ukrainian psychologists with the basics of using the R programming language to the analysis of empirical research data. The article discusses the current state of world psychology in connection with the Crisis of Confidence, which arose due to the low reproducibility of empirical research. This problem is caused by poor quality of psychological measurement tools, insufficient attention to adequate sample planning, typical statistical hypothesis testing practices, and so-called “questionable research practices.” The tutorial demonstrates methods for determining the sample size depending on the expected magnitude of the effect size and desired statistical power, performing basic variable transformations and statistical analysis of psychological research data using language and environment R. The tutorial presents minimal system of R functions required to carry out: modern analysis of reliability of measurement scales, sample size calculation, point and interval estimation of effect size for four the most widespread in psychology designs for the analysis of two variables’ interdependence. These typical problems include finding the differences between the means and variances in two or more samples, correlations between continuous and categorical variables. Practical information on data preparation, import, basic transformations, and application of basic statistical methods in the cloud version of RStudio is provided.

Statistical significance, effect size and statistical power

2017 ◽  
pp. 739-752 ◽  
Author(s):  
Louis Cohen ◽  
Lawrence Manion ◽  
Keith Morrison
Keyword(s):  
Effect Size ◽  
Statistical Power ◽  
Statistical Significance

When Studies are in Error: Basic Statistical Vocabulary Needed to Understand Clinical Studies

1996 ◽  
Vol 1 (1) ◽  
pp. 25-28 ◽  
Author(s):  
Martin A. Weinstock
Keyword(s):  
Null Hypothesis ◽  
Statistical Power ◽  
Critical Appraisal ◽  
Type I Error ◽  
Statistical Significance ◽  
P Value ◽  
Type I ◽  
Type Ii ◽  
Type Ii Error ◽  
Error Type

Background: Accurate understanding of certain basic statistical terms and principles is key to critical appraisal of published literature. Objective: This review describes type I error, type II error, null hypothesis, p value, statistical significance, a, two-tailed and one-tailed tests, effect size, alternate hypothesis, statistical power, β, publication bias, confidence interval, standard error, and standard deviation, while including examples from reports of dermatologic studies. Conclusion: The application of the results of published studies to individual patients should be informed by an understanding of certain basic statistical concepts.

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