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    A Different Statistical Perspective on the Evaluation of Ecological Data Sets
    (Mdpi, 2025) Yigit, Soner
    Statistical significance varies depending on the sample size. Therefore, when the sample size is sufficient, even differences that affect the total variation very little may be statistically significant. For this reason, it is very important to report effect size measures that estimate the share of the difference between groups of samples in the total variation. This study aims to determine the most reliable effect size measures that can be used when evaluating data obtained from ecological studies. The three most popular effect size measures used in practice were compared in terms of their performance in 2700 different experimental conditions. For this purpose, random numbers generated from the multivariate Poisson distribution were used with the Monte Carlo simulation technique. As a result of the simulations, it was determined that Epsilon-squared and Omega-squared were quite unbiased estimators. Therefore, it was concluded that one of these two effect size measures should be reported in addition to the p-value when evaluating ecological studies.
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    Comparison of ANOVA-F and ANOM tests with regard to type I error rate and test power
    (Taylor & Francis Ltd, 2013) Mendes, Mehmet; Yigit, Soner
    A Monte Carlo simulation was conducted to compare the type I error rate and test power of the analysis of means (ANOM) test to the one-way analysis of variance F-test (ANOVA-F). Simulation results showed that as long as the homogeneity of the variance assumption was satisfied, regardless of the shape of the distribution, number of group and the combination of observations, both ANOVA-F and ANOM test have displayed similar type I error rates. However, both tests have been negatively affected from the heterogeneity of the variances. This case became more obvious when the variance ratios increased. The test power values of both tests changed with respect to the effect size (), variance ratio and sample size combinations. As long as the variances are homogeneous, ANOVA-F and ANOM test have similar powers except unbalanced cases. Under unbalanced conditions, the ANOVA-F was observed to be powerful than the ANOM-test. On the other hand, an increase in total number of observations caused the power values of ANOVA-F and ANOM test approach to each other. The relations between effect size () and the variance ratios affected the test power, especially when the sample sizes are not equal. As ANOVA-F has become to be superior in some of the experimental conditions being considered, ANOM is superior in the others. However, generally, when the populations with large mean have larger variances as well, ANOM test has been seen to be superior. On the other hand, when the populations with large mean have small variances, generally, ANOVA-F has observed to be superior. The situation became clearer when the number of the groups is 4 or 5.
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    Reevaluating the reliability of common multiple comparison tests
    (Wiley, 2025) Yigit, Soner
    Many comparison tests are available to determine treatment differences. The validity of these tests is commonly assessed using the Type I error rate. Type I error is obtaining a false positive result. It is known that Fisher's Least Significant Difference (LSD) and Duncan tests have high Type I error rates because even a single false positive is sufficient to constitute a Type I error. For multiple comparison tests, the number of correct decisions (true positives and true negatives) is more important than the Type I error rate. Therefore, in this study, specificity and sensitivity were considered alongside the Type I error rate. Specificity refers to the true negative rate, while sensitivity refers to the true positive rate. A Monte Carlo simulation showed that the LSD and Duncan tests had relatively high Type I error rates; however, when specificity was considered, the LSD and Duncan tests correctly predicted statistically similar groups (true negative) with a mean of 97.00%, while other tests achieved 99.00%. Regarding sensitivity, the LSD and Duncan tests correctly identified statistically different groups (true positive) with a mean of 15.00%, while other tests achieved 3.00%. The true negative rate of the other tests is 1.02 times (99.00/97.00) that of LSD and Duncan. In contrast, the true positive rate of LSD and Duncan is 5.00 times (15.00/3.00) that of the other tests. Therefore, considering both specificity and sensitivity, the LSD and Duncan tests were found to be superior to others. In conclusion, these tests were shown to be more reliable.
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    Type I error and test power of different tests for testing interaction effects in factorial experiments
    (Wiley, 2013) Mendes, Mehmet; Yigit, Soner
    A simulation study was conducted to investigate the effect of non normality and unequal variances on Type I error rates and test power of the classical factorial anova F-test and different alternatives, namely rank transformation procedure (FR), winsorized mean (FW), modified mean (FM) and permutation test (FP) for testing interaction effects. Simulation results showed that as long as no significant deviation from normality and homogeneity of the variances exists, generally all of the tests displayed similar results. However, if there is significant deviation from the assumptions, the other tests are observed to be affected at considerably high levels except FR and FP tests. As a result, when the assumptions of factorial anova F-test are not met or, in the case those assumptions are not tested whether met, it can be concluded that using FR and FP tests is more suitable than the classical factorial anova F-test.
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    TYPE I ERROR RATES AND TEST POWER FOR SOME OUTLIER DETECTING TESTS
    (Pushpa Publishing House, 2011) Yigit, Soner; Mendes, Mehmet; Mirtagioglu, Hamit
    This study is conducted to compare some outlier detection tests such as Grubbs, Dixon, Chauvenet criterion and Weisberg t-test with respect to Type I error rate and test power. For this purpose, random numbers from normal population are generated by Monte Carlo simulation technique. Results of 50,000 simulation trials showed that the Weisberg t-test gave the most reliable results with respect to the others. Chauvenet criterion has followed this test. Dixon and Grubbs tests have not displayed reliable results except for studying with small sample sizes. As a result, regardless of the sample size being studied, Weisberg t-test should be used as detecting whether there is an outlier in the data set or not.
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    WHICH EFFECT SIZE MEASURE IS APPROPRIATE FOR ONE-WAY AND TWO-WAY ANOVA MODELS? A MONTE CARLO SIMULATION STUDY
    (Inst Nacional Estatistica-Ine, 2018) Yigit, Soner; Mendes, Mehmet
    It is very important to report some effect size measures that will show if the observed differences among the groups are also of practical significance along with statistical significance while reporting statistical analysis results. Performances of four commonly used effect size measures (Eta-Squared, Partial Eta Squared, Omega Squared and Epsilon Squared) were compared for one and two-way ANOVA models under 3000 different conditions. Results of simulation runs showed that the Epsilon and Omega-Squared estimates were quite unbiased when compared to Eta and Partial Eta-Squared which are directly reported by commonly used statistical packages while reporting ANOVA results. Thus, it could be concluded that reporting Epsilon or Omega-Squared is more appropriate to evaluate the practical significance of observed differences along with P-values.
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    Which effect size measure isappropriate for one-way andtwo-way anovamodels? A Monte Carlo simulation study
    (National Statistical Institute, 2018) Yigit, Soner; Mendes, Mehmet
    It is very important to report some effect size measures that will show if the observed differences among the groups are also of practical significance along with statistical significance while reporting statistical analysis results. Performances of four com- monly used effect size measures (Eta-Squared, Partial Eta Squared, Omega Squared and Epsilon Squared) were compared for one and two-way ANOVA models under 3000 different conditions. Results of simulation runs showed that the Epsilon and Omega-Squared estimates were quite unbiased when compared to Eta and Partial Eta-Squared which are directly reported by commonly used statistical packages while reporting ANOVA results. Thus, it could be concluded that reporting Epsilon or Omega-Squared is more appropriate to evaluate the practical significance of observed differences along with P-values. © 2018, National Statistical Institute. All rights reserved.