There are times when a statistician finds that there are several means to compare. The reason that a researcher needs to compare the mean differences is; first, to find out if all the means are equal; and second; to find out which means are unequal and by how much. The method that is commonly used is ANOVA or the Analysis Of Variance. However, certain requirements must first be met if a researcher is to compare the mean differences. The first requirement is that the researcher needs to have simple random samples for the r treatment, which should be independent samples. The second requirement is that the underlying population should be normally distributed ; and lastly, the samples should have the same standard deviation for the ANOVA test to be robust. After these requirements are satisfied, there are many ways that a researcher can compare different means, and each way gives different answers. However, the most commonly preferred method is the Tukey’s HSD, which stands for Honestly Significant Difference.
The Tukey HSD is used to determine which means are different based on the level of significance. This method the most suitable since for all the series of tests that a researcher can perform, they all increase the likelihood of getting a Type 1 error. This error is called the rejection of a true null hypothesis. So, to avoid incurring that error, the Tukey’s HSD answers this question by performing at score for each pair of means, only this time the researcher uses a new distribution that is called q distribution. Since the researcher wants to find out which means differ and by how much, the first step that should be implemented is calculating the confidence interval, and using it to interpret the significant differences in means.
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The first results of the test can be: if the endpoints of the confidence interval both have positive or a negative sign, it would be an indication that the means are different. If the endpoints have opposite signs, it indicates that the means are equal or different.
