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

1985 ◽  
Vol 45 (2) ◽  
pp. 271-280 ◽  
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.

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

2018 ◽  
Vol 30 (3) ◽  
pp. 232-247 ◽  
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.

Sample Size in the Planning and Interpretation of Clinical Trials

1987 ◽  
Vol 58 (04) ◽  
pp. 953-956 ◽  
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.

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

1978 ◽  
Vol 299 (13) ◽  
pp. 690-694 ◽  
Author(s):  
Jennie A. Freiman ◽  
Thomas C. Chalmers ◽  
Harry Smith ◽  
Roy R. Kuebler
Keyword(s):  
Sample Size ◽  
Randomized Control Trial ◽  
Type Ii ◽  
Type Ii Error ◽  
Randomized Control

THE EFFECT OF INTRASPECIFIC SAMPLE SIZE ON TYPE I AND TYPE II ERROR RATES IN COMPARATIVE STUDIES

Evolution ◽  
2005 ◽  
Vol 59 (12) ◽  
pp. 2705 ◽  
Author(s):  
Luke J. Harmon ◽  
Jonathan B. Losos
Keyword(s):  
Sample Size ◽  
Comparative Studies ◽  
Error Rates ◽  
Type I ◽  
Type Ii ◽  
Type Ii Error

scholarly journals Inverse Sampling for McNemar's Test

2016 ◽  
Vol 6 (1) ◽  
pp. 78
Author(s):  
Mark Von Tress
Keyword(s):  
Sample Size ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Binomial Test ◽  
Type Ii ◽  
Type Ii Error ◽  
Inverse Sampling ◽  
Exact Binomial Test ◽  
Joint Likelihood ◽  
Standard Sampling

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.

Optimal type I and type II error pairs when the available sample size is fixed

2013 ◽  
Vol 66 (8) ◽  
pp. 903-910.e2 ◽  
Author(s):  
John P.A. Ioannidis ◽  
Iztok Hozo ◽  
Benjamin Djulbegovic
Keyword(s):  
Sample Size ◽  
Type I ◽  
Type Ii ◽  
Type Ii Error ◽  
Optimal Type

The Power of Replicated Measures to Increase Statistical Power

2019 ◽  
Vol 2 (3) ◽  
pp. 199-213 ◽  
Author(s):  
Marc-André Goulet ◽  
Denis Cousineau
Keyword(s):  
Sample Size ◽  
Null Hypothesis ◽  
Statistical Power ◽  
Statistical Tests ◽  
Cognitive Tasks ◽  
Type Ii ◽  
Type Ii Error ◽  
Multiple Measures ◽  
Multiple Measurements ◽  
Sufficient Statistical Power

When running statistical tests, researchers can commit a Type II error, that is, fail to reject the null hypothesis when it is false. To diminish the probability of committing a Type II error (β), statistical power must be augmented. Typically, this is done by increasing sample size, as more participants provide more power. When the estimated effect size is small, however, the sample size required to achieve sufficient statistical power can be prohibitive. To alleviate this lack of power, a common practice is to measure participants multiple times under the same condition. Here, we show how to estimate statistical power by taking into account the benefit of such replicated measures. To that end, two additional parameters are required: the correlation between the multiple measures within a given condition and the number of times the measure is replicated. An analysis of a sample of 15 studies (total of 298 participants and 38,404 measurements) suggests that in simple cognitive tasks, the correlation between multiple measures is approximately .14. Although multiple measurements increase statistical power, this effect is not linear, but reaches a plateau past 20 to 50 replications (depending on the correlation). Hence, multiple measurements do not replace the added population representativeness provided by additional participants.

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