Abstract
In the case of comparison between samples with unequal replications [n1 # n2 # n3 # ... # nk], the statistician should use LSD (Least Significant Difference) many times to achieve these comparisons, this method consumes more time and effort. The purpose of this research is to find out a new method to do easy and reliable comparison between population means when the experiment or data involving different numbers of replications. In order to do this, a new formula was designed; the aim of this new formula is to develop the multiple comparisons into one step instead of doing it with many steps that consume more effort and time. In this work, the researcher used the mean of the replication number in the LDS formula instead of doing the calculation many times for each two means. The results of this study found that the new formula give similar results for multiple comparisons with minimal effort. It was concluded that the new formula (named Al-fahham’s Formula) achieves the same results with less time and efforts. It was recommended that Al-fahham’s Formula can be approved in the statistical textbooks and procedures.
Highlights
In order to do this, a new formula was designed; the aim of this new formula is to develop the multiple comparisons into one step instead of doing it with many steps that consume more effort and time
The results of this study found that the new formula give similar results for multiple comparisons with minimal effort
It was concluded that the new formula achieves the same results with less time and efforts
Summary
The analysis of variance ANOVA is the parametric method for identify whether differences occur significantly in an experiment including more than conditions. It is an example of simultaneous inference in which multiple comparisons are achieved and investigate only two-tailed hypotheses. The first pairwise comparison method was invented by Ronald Aylmer Fisher (1890-1962), who tried to indicate which treatments had a significant different effect in the ANOVA test, he establish his work on the least squares of the standard deviations of the treatment means with equal replications [5].
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