Inverse Sampling for McNemar's Test

Inverse sampling for McNemars test is studied. Sampling is conducted until a pre-specified number of discordant pairs is observed instead of sampling until a pre-specified total number of pairs is observed. The joint likelihood is decomposed into a product of a negative binomial distribution for the number of pairs required to observe r discordant pairs, a binomial distribution for the number of successes in the concordant observations, and a binomial distribution for the number of successes in the discordant observations. Since inference in this problem is based on the discordant observations, inverse sampling controls the type II error when small numbers of discordant observations are observed and the exact binomial test is required. The control results from fixing the sample size for the exact binomial test. Standard sampling instead lets the sample size for the exact binomial test vary and then performs the test conditionally on the observed number of discordant pairs.

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The Importance of Beta, the Type II Error, and Sample Size in the Design and Interpretation of the Randomized Controlled Trial

Medical Uses of Statistics ◽

10.1201/9780429187445-19 ◽

2019 ◽

pp. 357-389

Author(s):

Jennie A. Freiman ◽

Thomas C. Chalmers ◽

Harry A. Smith ◽

Roy R. Kuebler

Keyword(s):

Randomized Controlled Trial ◽

Sample Size ◽

Controlled Trial ◽

Type Ii ◽

Type Ii Error ◽

Randomized Controlled

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Fuzzy U control chart based on fuzzy rules and evaluating its performance using fuzzy OC curve

The TQM Journal ◽

10.1108/tqm-10-2017-0118 ◽

2018 ◽

Vol 30 (3) ◽

pp. 232-247 ◽

Cited By ~ 9

Author(s):

Somayeh Fadaei ◽

Alireza Pooya

Keyword(s):

Fuzzy Control ◽

Sample Size ◽

Control Chart ◽

Control Charts ◽

Operating Characteristic ◽

Fuzzy Rules ◽

Type Ii ◽

Type Ii Error ◽

Content Type ◽

Variable Sample Size

Purpose The purpose of this paper is to apply fuzzy spectrum in order to collect the vague and imprecise data and to employ the fuzzy U control chart in variable sample size using fuzzy rules. This approach is improved and developed by providing some new rules. Design/methodology/approach The fuzzy operating characteristic (FOC) curve is applied to investigate the performance of the fuzzy U control chart. The application of FOC presents fuzzy bounds of operating characteristic (OC) curve whose width depends on the ambiguity parameter in control charts. Findings To illustrate the efficiency of the proposed approach, a practical example is provided. Comparing performances of control charts indicates that OC curve of the crisp chart has been located between the FOC bounds, near the upper bound; as a result, for the crisp control chart, the probability of the type II error is of significant level. Also, a comparison of the crisp OC curve with OCavg curve and FOCα curve approved that the probability of the type II error for the crisp chart is more than the same amount for the fuzzy chart. Finally, the efficiency of the fuzzy chart is more than the crisp chart, and also it timely gives essential alerts by means of linguistic terms. Consequently, it is more capable of detecting process shifts. Originality/value This research develops the fuzzy U control chart with variable sample size whose output is fuzzy. After creating control charts, performance evaluation in the industry is important. The main contribution of this paper is to employs the FOC curve for evaluating the performance of the fuzzy control chart, while in prior studies in this area, the performance of fuzzy control chart has not been evaluated.

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How Large Should the Sample Be? Part II—The One-Sample Case for Survey Research

Educational and Psychological Measurement ◽

10.1177/001316448504500210 ◽

1985 ◽

Vol 45 (2) ◽

pp. 271-280 ◽

Cited By ~ 7

Author(s):

Dennis E. Hinkle ◽

J. Dale Oliver ◽

Charles A. Hinkle

Keyword(s):

Sample Size ◽

Survey Research ◽

Effect Size ◽

Previous Article ◽

Type Ii ◽

Type Ii Error ◽

The One ◽

Sample Case

In a previous article, the authors discuss the importance of the effect size and the Type II error as factors in determining the sample size (Hinkle and Oliver, 1983). Tables were developed and presented for one-factor designs with k levels (2 ≤ k ≤ 8). However, between the time the article was submitted and its publication, the authors presented these tables at several national and regional meetings. A recurring question from colleagues attending these meetings was how these tables could be used for the one-sample case ( k = 1). Since they could not be, we were encouraged to develop comparable tables for the one-sample case. Thus, the purpose of this paper is to readdress the sample size question and to present these tables.

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Sampling Hazelnuts for Aflatoxin: Effect of Sample Size and Accept/Reject Limit on Reducing the Risk of Misclassifying Lots

Journal of AOAC International ◽

10.1093/jaoac/90.4.1028 ◽

2007 ◽

Vol 90 (4) ◽

pp. 1028-1035 ◽

Cited By ~ 7

Author(s):

Guner Ozay ◽

Ferda Seyhan ◽

Aysun Yilmaz ◽

Thomas B Whitaker ◽

Andrew B Slate ◽

...

Keyword(s):

Sample Size ◽

Negative Binomial Distribution ◽

Binomial Distribution ◽

Negative Binomial ◽

Food Additives ◽

Sampling Plan ◽

Test Results ◽

Sampling Plans ◽

Wide Range ◽

Sample Test

Abstract About 100 countries have established regulatory limits for aflatoxin in food and feeds. Because these limits vary widely among regulating countries, the Codex Committee on Food Additives and Contaminants began work in 2004 to harmonize aflatoxin limits and sampling plans for aflatoxin in almonds, pistachios, hazelnuts, and Brazil nuts. Studies were developed to measure the uncertainty and distribution among replicated sample aflatoxin test results taken from aflatoxin-contaminated treenut lots. The uncertainty and distribution information is used to develop a model that can evaluate the performance (risk of misclassifying lots) of aflatoxin sampling plan designs for treenuts. Once the performance of aflatoxin sampling plans can be predicted, they can be designed to reduce the risks of misclassifying lots traded in either the domestic or export markets. A method was developed to evaluate the performance of sampling plans designed to detect aflatoxin in hazelnuts lots. Twenty hazelnut lots with varying levels of contamination were sampled according to an experimental protocol where 16 test samples were taken from each lot. The observed aflatoxin distribution among the 16 aflatoxin sample test results was compared to lognormal, compound gamma, and negative binomial distributions. The negative binomial distribution was selected to model aflatoxin distribution among sample test results because it gave acceptable fits to observed distributions among sample test results taken from a wide range of lot concentrations. Using the negative binomial distribution, computer models were developed to calculate operating characteristic curves for specific aflatoxin sampling plan designs. The effect of sample size and accept/reject limits on the chances of rejecting good lots (sellers' risk) and accepting bad lots (buyers' risk) was demonstrated for various sampling plan designs.

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Sample Size in the Planning and Interpretation of Clinical Trials

Thrombosis and Haemostasis ◽

10.1055/s-0038-1646033 ◽

1987 ◽

Vol 58 (04) ◽

pp. 953-956 ◽

Cited By ~ 7

Author(s):

Mark N levine ◽

Jack Hirsh

Keyword(s):

Clinical Trials ◽

Sample Size ◽

False Negative ◽

Sample Size Determination ◽

Type Ii ◽

Size Determination ◽

Type Ii Error ◽

Treatment Groups ◽

Negative Conclusion

AbstractAn understanding of sample size determination is important in both planning and interpreting the results of clinical trials. A Type II error occurs when it is concluded that there is no difference between treatment groups, when in truth there is a difference. Such a false negative conclusion results from too few patients in a trial. In this review the principles of estimating sample size before a trial is commenced and evaluating the results of a negative completed trial are reviewed. Clinically relevant examples are used to illustrate these concepts.

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