IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF APPLIED SCIENCES AND MATHEMATICAL THEORY (IJASMT )

E- ISSN 2489-009X
P- ISSN 2695-1908
VOL. 9 NO. 3 2023
DOI: https://doi.org/10.56201/ijasmt.v9.no3.2023.pg19.30

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Median based Fisher’s Test: An alternative to Fishers’ Least Significant Difference in the presence of outlier

Ozoh, Nonye Chinwendu, Onu, Obineke Henry, Nelson, Maxwell

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Abstract

The study considered Median based Fisher’s Test: An alternative to Fishers’ Least Significant Difference in the presence of outlier for interval data. It started with running outlier test by using Grubbs method and analysis of variance for three population samples were carried out. In the general sense, in problems like this, the hypothesis is tested, if the null hypothesis is rejected, and the alternative hypothesis accepted, that is to say, there is significant difference in the means of the samples, one will usually conduct multiple comparison test, to know the pair that contributed to the significant difference. For the purpose of this study, only Fisher’s test was considered, because it centered their operations on the difference in means of the data. This research, introduced difference in median for Fisher’s test as a result, proposed M-Fisher’s method of knowing if a pair of median differs or not. These method used median in place of mean in Sum of Squares, Mean Squares, F-value, t-test and Fisher’s test. This is because of the fact that the mean is always affected by outliers and extreme values. So, method that are not sensitive to outliers is proposed. Three data sets were used. Data 1 without outlier was the data of advertisement on new product of orange juice focused on three cities 1, 2, 3. city 1 centered on convenience, city 2 centered on quality and city 3 centered on price for 20 sample size, data 2 has the introduction of outliers for 20 sample size and data 3 is 100 sample size and it is a simulated data. The results showed that the Fisher’s method alongside M-Fisher’s had similar results for data 1. For data 2, the M-Fisher’s showed robustness, when outliers were introduced. While Fishers was heavily affected by the presence of the outliers.

keywords:

Mean, Median, Fisher’s test, Median Fisher;s test, ANOVA, Sum of Squares.

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References:

Fisher, R. A.(1918). The correlation between relatives on the supposition of Mendelian
inheritance. Transactions of the Royal Society of Edinburgh, 52, 399-433.

Harter, H. L.(1980). Early history of multiple comparison tests. In: Vinod H, Rao C, eds. Hand
Book of Statistics, Elsevier. 1, 617-622.

Iwundu, M. P. (2017). Principles of Experimental Design.CHADIK printing press, No 9 East
West road, Port Harcourt, Nigeria.

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