Understanding type I and type II errors, statistical power and sample size

2016 ◽  
Vol 105 (6) ◽  
pp. 605-609 ◽  
Author(s):  
Anthony K. Akobeng
Keyword(s):  
Sample Size ◽  
Statistical Power ◽  
Type I ◽  
Type Ii ◽  
Type Ii Errors

scholarly journals Statistical Power in Plant Pathology Research

2018 ◽  
Vol 108 (1) ◽  
pp. 15-22 ◽  
Author(s):  
David H. Gent ◽  
Paul D. Esker ◽  
Alissa B. Kriss
Keyword(s):  
Plant Pathology ◽  
Treatment Effect ◽  
Effect Size ◽  
Null Hypothesis ◽  
Power Analysis ◽  
Statistical Power ◽  
Statistical Test ◽  
Type I ◽  
Type Ii ◽  
Type Ii Errors

In null hypothesis testing, failure to reject a null hypothesis may have two potential interpretations. One interpretation is that the treatments being evaluated do not have a significant effect, and a correct conclusion was reached in the analysis. Alternatively, a treatment effect may have existed but the conclusion of the study was that there was none. This is termed a Type II error, which is most likely to occur when studies lack sufficient statistical power to detect a treatment effect. In basic terms, the power of a study is the ability to identify a true effect through a statistical test. The power of a statistical test is 1 – (the probability of Type II errors), and depends on the size of treatment effect (termed the effect size), variance, sample size, and significance criterion (the probability of a Type I error, α). Low statistical power is prevalent in scientific literature in general, including plant pathology. However, power is rarely reported, creating uncertainty in the interpretation of nonsignificant results and potentially underestimating small, yet biologically significant relationships. The appropriate level of power for a study depends on the impact of Type I versus Type II errors and no single level of power is acceptable for all purposes. Nonetheless, by convention 0.8 is often considered an acceptable threshold and studies with power less than 0.5 generally should not be conducted if the results are to be conclusive. The emphasis on power analysis should be in the planning stages of an experiment. Commonly employed strategies to increase power include increasing sample sizes, selecting a less stringent threshold probability for Type I errors, increasing the hypothesized or detectable effect size, including as few treatment groups as possible, reducing measurement variability, and including relevant covariates in analyses. Power analysis will lead to more efficient use of resources and more precisely structured hypotheses, and may even indicate some studies should not be undertaken. However, the conclusions of adequately powered studies are less prone to erroneous conclusions and inflated estimates of treatment effectiveness, especially when effect sizes are small.

An Analysis of Statistical Power in Behavioral Accounting Research

2001 ◽  
Vol 13 (1) ◽  
pp. 63-84 ◽  
Author(s):  
Susan C. Borkowski ◽  
Mary Jeanne Welsh ◽  
Qinke (Michael) Zhang
Keyword(s):  
Statistical Power ◽  
Type I Error ◽  
Significance Testing ◽  
Type I ◽  
Type Ii ◽  
Behavioral Accounting ◽  
Significance Tests ◽  
Accounting Research ◽  
Sufficient Power ◽  
Type Ii Errors

Attention to statistical power and effect size can improve the design and the reporting of behavioral accounting research. Three accounting journals representative of current empirical behavioral accounting research are analyzed for their power (1−β), or control of Type II errors (β), and compared to research in other disciplines. Given this study's findings, additional attention should be directed to adequacy of sample sizes and study design to ensure sufficient power when Type I error is controlled at α = .05 as a baseline. We do not suggest replacing traditional significance testing, but rather augmenting it with the reporting of β to complement and interpret the relevance of a reported α in any given study. In addition, the presentation of results in alternative formats, such as those suggested in this study, will enhance the current reporting of significance tests. In turn, this will allow the reader a richer understanding of, and an increased trust in, a study's results and implications.

Statistical power and design requirements for environmental monitoring

1991 ◽  
Vol 42 (5) ◽  
pp. 555 ◽  
Author(s):  
PG Fairweather
Keyword(s):  
Low Power ◽  
Environmental Monitoring ◽  
Null Hypothesis ◽  
Power Analysis ◽  
Statistical Power ◽  
Type I ◽  
Type Ii ◽  
Type Ii Error ◽  
Type I Errors ◽  
Type Ii Errors

This paper discusses, from a philosophical perspective, the reasons for considering the power of any statistical test used in environmental biomonitoring. Power is inversely related to the probability of making a Type II error (i.e. low power indicates a high probability of Type II error). In the context of environmental monitoring, a Type II error is made when it is concluded that no environmental impact has occurred even though one has. Type II errors have been ignored relative to Type I errors (the mistake of concluding that there is an impact when one has not occurred), the rates of which are stipulated by the a values of the test. In contrast, power depends on the value of α, the sample size used in the test, the effect size to be detected, and the variability inherent in the data. Although power ideas have been known for years, only recently have these issues attracted the attention of ecologists and have methods been available for calculating power easily. Understanding statistical power gives three ways to improve environmental monitoring and to inform decisions about actions arising from monitoring. First, it allows the most sensitive tests to be chosen from among those applicable to the data. Second, preliminary power analysis can be used to indicate the sample sizes necessary to detect an environmental change. Third, power analysis should be used after any nonsignificant result is obtained in order to judge whether that result can be interpreted with confidence or the test was too weak to examine the null hypothesis properly. Power procedures are concerned with the statistical significance of tests of the null hypothesis, and they lend little insight, on their own, into the workings of nature. Power analyses are, however, essential to designing sensitive tests and correctly interpreting their results. The biological or environmental significance of any result, including whether the impact is beneficial or harmful, is a separate issue. The most compelling reason for considering power is that Type II errors can be more costly than Type I errors for environmental management. This is because the commitment of time, energy and people to fighting a false alarm (a Type I error) may continue only in the short term until the mistake is discovered. In contrast, the cost of not doing something when in fact it should be done (a Type II error) will have both short- and long-term costs (e.g. ensuing environmental degradation and the eventual cost of its rectification). Low power can be disastrous for environmental monitoring programmes.

An Analysis of the Ability to Detect Reductions in Year-class Strength of the Hudson River White Perch (Morone americana) Population

1981 ◽  
Vol 38 (6) ◽  
pp. 627-632 ◽  
Author(s):  
W. Van Winkle ◽  
D. S. Vaughan ◽  
L. W. Barnthouse ◽  
B. L. Kirk
Keyword(s):  
Statistical Power ◽  
White Perch ◽  
Hudson River ◽  
Type I ◽  
Type Ii ◽  
Morone Americana ◽  
Fish Stocks ◽  
Class Strength ◽  
Fractional Reduction ◽  
Type Ii Errors

Impingement rates for young-of-the-year white perch (Morone americana) in the Hudson River were analyzed to address two questions: (1) assuming a specified number of years of additional data, what is the minimum fractional reduction in mean year-class strength that could be detected, and (2) assuming a specified fractional reduction in mean year-class strength, how many additional years of impingement data would be required to detect the reduction. Our results indicate that the variability in the baseline data is so great that 10 more years of data are not adequate for detecting even substantial (>50%) reductions in mean year-class strength and that more than 50 years of data would be required to detect an actual 50% reduction in mean year-class strength, given a Type II error of 50%. Our methodology offers a generic tool for establishing bounds on reductions in fish stocks and for estimating the number of additional years of data required to detect such reductions.Key words: fractional reduction, impingement, power plant, statistical power, Type I and Type II errors, white perch, year-class strength

scholarly journals REQUIRED SAMPLE SIZE FOR COMPARING PROPORTIONS IN TWO INDEPENDENT SAMPLES

2020 ◽  
Vol 6 (3) ◽  
pp. 76-83
Author(s):  
A. M. Grjibovski ◽  
M. A. Gorbatova ◽  
A. N. Narkevich ◽  
K. A. Vinogradov
Keyword(s):  
Sample Size ◽  
Statistical Power ◽  
Statistical Tests ◽  
Simple Algorithm ◽  
Statistical Test ◽  
Type Ii ◽  
Sample Size Calculations ◽  
Chi Squared ◽  
Type Ii Errors ◽  
False Null Hypothesis

This paper continues our series of articles on required sample size for the most common basic statistical tests used in biomedical research. Sample size calculations are rarely performed in research planning in Russia often resulting in Type II errors, i.e. on acceptance on false null hypothesis due to insufficient sample size. The most common statistical test for analyzing proportions in independent samples is Pearson’s chi-squared test. In this paper we present a simple algorithm for calculating required sample size for comparing two independent proportions. In addition to manual calculations we present a step-by-step guide on how to use WinPepi and Stata software for calculating sample size for independent proportions. In addition, we present a table for junior researchers with already calculated sample sizes for comparing proportions from 0,1 to 0,9 by 0,1 with 95% confidence level and 80% statistical power.

Corrected Analysis of the Ability to Detect Reductions in Year-Class Strength of the Hudson River White Perch (Morone americana) Population

1982 ◽  
Vol 39 (5) ◽  
pp. 782-785 ◽  
Author(s):  
Douglas S. Vaughan ◽  
Webster Van Winkle
Keyword(s):  
Statistical Power ◽  
White Perch ◽  
Hudson River ◽  
Type I ◽  
Type Ii ◽  
Class Strength ◽  
Fractional Reduction ◽  
Incorrect Solution ◽  
Type Ii Errors ◽  
T Distribution

This analysis presents a correction of that presented in Van Winkle et al. (1981; Can. J. Fish. Aquat. Sci. 38: 627–632). An exact solution is obtained based on the noncentral t-distribution to replace the incorrect solution based on the central t-distribution used in our earlier analysis. Our new results, although less pessimistic than before, still are not encouraging. They indicate that variability in baseline data is so great that data from 10 additional years are not adequate for detecting even substantial (> 50%) reductions in mean year-class strength, and that at least 20 years of data collection would be required to detect an actual 50% reduction in mean year-class strength, given a Type II error of 50%.Key words: fractional reduction, impingement, power plant, statistical power, Type I and Type II errors, white perch, year-class strength

An old friend is better than two new ones? Approaches to market research in the context of digital transformation for the antitrust laws enforcement

2020 ◽  
pp. 37-55 ◽  
Author(s):  
A. E. Shastitko ◽  
O. A. Markova
Keyword(s):  
Business Models ◽  
Rapid Development ◽  
Digital Transformation ◽  
Market Definition ◽  
Type I ◽  
Type Ii ◽  
Digital Platforms ◽  
Advantages And Disadvantages ◽  
Pass Through ◽  
Type Ii Errors

Digital transformation has led to changes in business models of traditional players in the existing markets. What is more, new entrants and new markets appeared, in particular platforms and multisided markets. The emergence and rapid development of platforms are caused primarily by the existence of so called indirect network externalities. Regarding to this, a question arises of whether the existing instruments of competition law enforcement and market analysis are still relevant when analyzing markets with digital platforms? This paper aims at discussing advantages and disadvantages of using various tools to define markets with platforms. In particular, we define the features of the SSNIP test when being applyed to markets with platforms. Furthermore, we analyze adjustment in tests for platform market definition in terms of possible type I and type II errors. All in all, it turns out that to reduce the likelihood of type I and type II errors while applying market definition technique to markets with platforms one should consider the type of platform analyzed: transaction platforms without pass-through and non-transaction matching platforms should be tackled as players in a multisided market, whereas non-transaction platforms should be analyzed as players in several interrelated markets. However, if the platform is allowed to adjust prices, there emerges additional challenge that the regulator and companies may manipulate the results of SSNIP test by applying different models of competition.

The Potential of Tax Surprises to Affect Measures of Tax Avoidance and Researchers' Inferences

2018 ◽  
Vol 41 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Chelsea Rae Austin
Keyword(s):  
Stock Options ◽  
Tax Avoidance ◽  
Type I ◽  
Type Ii ◽  
Effective Tax Rate ◽  
Tax Rate ◽  
Tax Savings ◽  
Type Ii Errors

ABSTRACT While not explicitly stated, many tax avoidance studies seek to investigate tax avoidance that is the result of firms' deliberate actions. However, measures of firms' tax avoidance can also be affected by factors outside the firms' control—tax surprises. This study examines potential complications caused by tax surprises when measuring tax avoidance by focusing on one specific type of surprise tax savings—the unanticipated tax benefit from employees' exercise of stock options. Because the cash effective tax rate (ETR) includes the benefits of this tax surprise, the cash ETR mismeasures firms' deliberate tax avoidance. The analyses conducted show this mismeasurement is material and can lead to both Type I and Type II errors in studies of deliberate tax avoidance. Suggestions to aid researchers in mitigating these concerns are also provided.

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