Determination of the Sample Size on Different Independent K Group Comparisons by Power Analysis

The purpose of this study was to determine the number of samples that should be used in independent treatment comparisons with different effect sizes (0.25-3.0), the number of treatments (2-5), and the power of the test (70% -95%) in single and multi-factor treatments. The material of the study was the random numbers drawn from the population that shows a normal distribution with N (0, 1) parameter. The power of the test was calculated by sampling with replacement from the population and after the differences between the treatments in terms of standard deviation were established, 10000 simulations were performed. This setup was carried out for experiments with one, two, and three factors. In the comparison of single factor independent treatment means, when the effect size was larger than Δ = 2 and the test power was between 70% and 95%, the sample sizes varied between 3 and 7. In the comparison of two-factor independent treatment means, when the effect size was larger than Δ = 2 and the test power was between 70% and 95%, the sample sizes varied between 2 and 3. In the comparison of three-factor independent treatment means, when the effect size was larger than Δ= 1.5 and the test power was between 70% and 95%, the sample size was 2. If all treatment comparisons were generalized; it was observed that when the effect size increased, and the power of the test decreased, the sample size decreased In the t-test and F tests used in independent treatment comparisons, a power analysis was performed under different situations, and the number of experimental units for each 5% power increment between 70% and 95% were presented in tables. These tables, may help researchers to determine the number of samples without power analysis in independent group comparisons.

Anahtar Kelimeler:

Independent treatment comparisons, power analysis, effect size, sample size, F-t test, simulation

Determination of the Sample Size on Different Independent K Group Comparisons by Power Analysis

Keywords:

Independent treatment comparisons, Power analysis, Effect size, Sample size, Simulation, F-t test,

PDF

___

Akkartal, E., Mendes, M., Mendes, E., 2010. Determination of suitable permutation numbers in comparing independent group means: a monte carlo simulation study. Journal of Scienctific & Industrial Research, 69(6): 22-425.
Arıcı, Y.K., 2012. The effect of transformations on type I. error and test power in balanced factorial experiments. PhD Thesis, Ankara University Institute of Science and Technology, Ankara, Turkey. (In Turkish).
Aslan, E., 2018. Power analysis for different test statistics. Master Thesis, Süleyman Demirel University Institute of Science and Technology, Isparta, Turkey. (In Turkish).
Başpınar, E., 2001. Type I error and power of tests when applying the student's-t, welch and trimmed-t tests to two samples of various sizes from normal populations having various variance ratios. Journal of Agricultural Sciences, 7(1): 151-157. (In Turkish).
Başpınar, E., Çamdeviren, H., Gürbüz, F., 1999. Determination of the power of the test and the appropriate sample size in Student t-test and variance analysis technique. Journal of Agricultural Sciences, 5(3): 116-123. (In Turkish).
Başpınar, E., Gürbüz, F., 2000. The Power of the test in the samples of various sample sizes were taken from the binary combinations of the Normal, Beta, Gamma and Weibull Distributions. Journal of Agricultural Sciences, 6(1): 116-127. (In Turkish).
Bossi, A., 2009. Power Calculation Tool For t-Tests, ANOVA and DOE 2k. Quantide.
Boyar, S., 2019. Comparison of testsused in comparing independent two groups in terms of type 1 error and power of test. Master Thesis, Isparta Applied Sciences University Graduate Education Institute, Isparta, Turkey. (In Turkish).
Cozby, P., Bates, S., 2012. Methods in Behavioral Research. McGraw-Hill, Newyork.
Ellis, P.D., 2010. The Essential Guide to Effect Size, Statistical Power, Meta-Analysis and Interpretation Research Results. Cambridge University Press, New York.
Fairweather, P.G., 1991. Statistical power and design requirements for environmental monitoring. Australian Journal of Marine and Freshwater Research, 42(5): 555-567.
Keskin, S., Özsoy, A.N., 2004. Canonical correlation analysis and its an application. Journal of Agricultural Sciences, 10(1): 57-71. (In Turkish).
Koşkan, Ö., Gürbüz, F., 2008. Resampling approach and comparison of t-test for type I error rate and test power. Journal of Animal Production, 49(1): 29-37. (In Turkish).
Kul, S., 2011. Sample size determination for clinical research. Ekstraplevral, 2(2): 129-132.
Lenth, R.V., 2007. Statistical power calculations. Journal of Animal Science, 85(13): 24-29.
Lewis, K.P., 2006. Statistical power, sample sizes, and the software to calculate them easily. BioScience, 56(7): 607-612.
MacCallum, R.C., Browne, M.W., Sugawara, H.M., 1996. Power analysis and determination of sample sizze covariance structure modeling. American Psychological Association, 1(2): 130-149.
Mendeş, M., 2002. The Comparison of some alternative parametric tests to one - way analysis of variance about Type I error rates and power of test under non - normality and heterogeneity of variance. PhD Thesis, Ankara University Institute of Science and Technology, Ankara, Turkey. (In Turkish).
Mendeş, M., 2004. ANOVA comparisons of ANOVA and F and K tests in terms of type III. Journal of Agricultural Sciences, 10(2): 121-126. (In Turkish).
Mendeş, M., Yiğit, S., 2013. Comparison of ANOVA-F and ANOM tests with regard to type I error rate and test power. Journal of Statistical Computation and Simulation, 83(11): 2093-2104.
Moder, K., 2010. Alternatives to F-test in one way ANOVA in case of heterogeneity of variances a simulation study). Psychological Test and Assessment Modeling, 52(4): 343-353.
Muller, K.E., Benignus, V.A., 1992. Increasing scientific power with statistical power. Neurotoxicology and Teratology, 14(3): 211-219.
Murphy,, K.R., Myors, B., 2004. Statistical Power Analysis, A Simple and General Model for Traditional and Modern Hypothesis Test. Routledge, London.
Peterman, R.M., 1990. Statistical power analysis can improve fisheries research and analysis can improve fisheries research and management. Canadian Journal of Fish and Aquatic Sciences, 47(1): 2-15.
Searcy-Bernal, R., 1994. Statistical power and aquacultural research. Aquaculture, 127(4): 371-388.
Taylor, B.L., Gerrodette, T., 1993. The uses of statistical power in conservation biology: The vaquita and Northern Spotted Owl. Conservation Biology, 7(3): 489-500.
Thomas, L., 1997. Retrospective power analysis. Conservation Biology, 11(1): 276-280.
Thomas, L., Juanes, F., 1996. The importance of statistical power analysis: an example from animal behaviour. Animal Behaviour, 52(4): 856-859.
Welch, B.L., 1951. On the comparison of several mean values: An alternative approach. Biometrica, 38(3/4): 330-336.
Wilcox, R.R., 1989. Adjusting for unequal variances when comparing means in oneway and two-way effects ANOVA models. Journal of Educational Statistics, 14(3): 269-278.
Yiğit, S., 2012. Type I error rate and test power for different approaches to factorial designs when normality and homogeneity of variances assumptions are not satisfied. Master Thesis, Çanakkale Onsekiz Mart University Institute of Science and Technology, Çanakkale, Turkey. (In Turkish).
Zar, J.H., 2013. Biostatistical Analysis: Pearson New İnternational Edition. Pearson, New Jersey.