Tukey s quick test

A further convenient method with some interesting features is Tukey s quick test. Its use can be shown using the same example. 

Tukey s quick test involves counting the total number of measurements in the two independent samples that are not included in the overlap region of the two data sets. 

Apply Tukey s quick test to the data of the previous example. 

If ties occur in Tukey s quick test (i.e. if one of the values in the hypothetically higher sample is equal to the highest value in the other sample, or if one of the values in the lower sample is equal to the lowest value in the higher sample) then each tie counts 0.5 towards the value of T. 

Mann-Whitney U-test beer values are expected to be larger than lager values. Number of lager values greater than the individual values = 4.5 (one tie). Critical value for a one-sided test is 5, so we can just reject the null hypothesis (P = 0.05). Tukey s Quick Test coimt is 5.5, just below the critical value of 6. So tests disagree more data needed. 

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