The Modification and Evaluation of the Alexander-Govern Test in Terms of Power

Ochuko, Tobi Kingsley; Abdullah, Shahrum; Zain, Zakiyah; Yahaya, Sharipah Soaad Syed

doi:10.5539/mas.v9n13p1

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…Consequently, any decision based on the abused tests will not provide the supposedly needed solution. According to Ochuko et al (2015b), non-normality and variance heterogeneity are obstacles to ANOVA. This increases the likelihood of Type I errors while decreasing power (Ochuko et al, 2015a).…”

Section: Introductionmentioning

confidence: 99%

The Implementation of the Alexander-Govern Test in Factorial Design Analysis

Ishak Latfi,

Abdullah

2024

JCIA

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This study proposed to evaluate the performance of the Alexander-Govern test (AG test), Analysis of Variance (ANOVA), and t-test by analyzing the Type I error rate. The AG test is regarded as a reliablecontrol Type I error rate. This technique is insensitive in the presence of heteroscedasticity under a normal distribution. Simulation research was carried out using Statistical Analysis Software (SAS) to assess the effectiveness of the tests that are based on the rate of Type I error. By creating the conditions that could highlight the strengths and weaknesses of each test, three variables are being manipulated: sample size, variance heterogeneity, and type of pairings. The performance of the AG tests is convincing when it is able to control the Type I error rates better compared to ANOVA under all conditions of heterogeneous variances. Meanwhile, the ANOVA performs best only when the variances are homogenous. A real data experiment was applied to validate the result. In the battery life design experiment, the p-value using the AG test and ANOVA are computed and compared. The AG test provides valid results when it can test the main effect and the interaction effect, as well as the ANOVA. With good performance in the simulation study, the AG test can be considered a good alternativeto the ANOVA when the assumptions of the homogeneity of variances are violated in the case of factorial design.

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Section: Introductionmentioning

confidence: 99%

The Implementation of the Alexander-Govern Test in Factorial Design Analysis

Ishak Latfi,

Abdullah

2024

JCIA

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“…Cribbie et al (2012) proposed the modified PB test based on the trimmed mean. Ochuko et al (2015) modified the AG test using the one-step m-estimator as central tendency measure to obtain a more powerful test under non-normality. Karagoz and Saracbasi (2016) proposed the robust Brown-Forsythe tests based on median/MAD and median/Q n to test the equality of Weibull distributed group means in the presence of outliers.…”

Section: Introductionmentioning

confidence: 99%

A revised generalized F-test for testing the equality of group means under non-normality caused by skewness

Çavuş¹,

Yazıcı²,

Sezer³

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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The non-normality may occur in the data due to several reasons such as the presence of the outlier or skewness. It leads to lose the power and fail control Type I error probability of the tests which are used to test the equality of the group means under heteroscedasticity. To overcome this problem, a revised generalized F-test (RGF) is proposed to test the equality of group means under heteroscedasticity in which non-normality is caused by skewness in this study. An extensive Monte-Carlo simulation study is conducted to investigate and compare the performance of the proposed test with non-parametric alternatives under several values of skewness, and different number of groups. The proposed RGF is the best choice in the high level of skewness for k = 3, 4, 5. The Kruskal-Wallis test shows better performance than the others in small and moderate sample sizes for k = 6, and 7. It is shown that the proposed RGF test is superior than the non-parametric alternatives in the most of the conditions.

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The Power of the Test for the Winsorized Modified Alexander-Govern Test

Ochuko

Abdullah

Zain

et al. 2016

ComTech

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This research examined the usage of the parametric method in comparing two or more means as independent group test, for instance, the Alexander-Govern (AG) test. The utilization of mean as the determinant for the center of distribution of variance diversity takes place in testing, and the test provides excellence in maintaining the amount of Type I error and giving immense sensitivity for a regular data. Unfortunately, it isineffective on irregular data, leading to the application of trimmed mean upon testing as the determinant for the center of distribution under irregular data for two group condition. However, as the group quantity is more than two, the estimator unsuccessfully provides excellence in maintaining the amount of Type I error. Therefore, an estimator high in effectiveness called the MOM estimator was introduced for the testing as the determinant for the center of distribution. Group quantity in a test does not affect the estimator, but it unsuccessfully providesexcellence in maintaining the amount of Type I error under intense asymmetry and unevenness. The application of Winsorized modified one-step M-estimator (WMOM) upon the Alexander-Govern testing takes place so that it can prevail against its drawbacks under irregular data in the presence of variance diversity, can eliminate the presence of the outside observation and can provide effectiveness for the testing on irregular data. Statistical Analysis Software (SAS) was used for the analysis of the tests. The results show that the AGWMOM test gave the most intense sensitivity under g = 0,5 and h = 0,5, for four group case and g = 0 and h = 0, under six group case, differing from three remaining tests and the sensitivity of the AG testing is said suffices and intense enough.

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The Modification and Evaluation of the Alexander-Govern Test in Terms of Power

Cited by 3 publications

References 25 publications

The Implementation of the Alexander-Govern Test in Factorial Design Analysis

The Implementation of the Alexander-Govern Test in Factorial Design Analysis

A revised generalized F-test for testing the equality of group means under non-normality caused by skewness

The Power of the Test for the Winsorized Modified Alexander-Govern Test

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