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Method : <br />I use the" Wilcoxon rank sum test" to determine whether or not there is significant difference <br />between the distribution of the "Substitute Soil "and the distribution of each of the other three <br />types of soil. The null hypothesis for this test is that the distributions for two groups are the <br />same ,which means that the two groups are not the same kind of population. The alternative <br />hypothesis is that the distributions for two groups are not the same. Note that this test is not <br />about the difference between group means, which is the object to be compared by the "Tukey's <br />method" and some other t- tests. <br />I give up using the " Tukey's method ", and t -tests for the reason that such methods assume a <br />normal distribution for the sample. However, it is not necessarily true that the underlying <br />distribution in this case is normal. Moreover, the sample size for each group is small, which <br />means we are not able to use the normal distribution to approximate the true distribution for <br />each group. <br />Conclusion: <br />Based on the analysis by the "Wilcoxon rank sum test ", I got the following results. For each test, <br />I set the a level to be 0.05, which is the confidence coefficient fora hypothesis test. If the p -value <br />of a test is smaller than 0.05, then I conclude that the two distributions are not the same. <br />1. Results based on the first data set: <br />There is no significant difference between the distributions for "Substitute Soil" and "Soil <br />Barxprofile ". <br />There is significant difference between the distributions for "Substitute Soil" and "Soil <br />$arx IiftA" <br />There is no significant difference betw een the distributions for "Substitute Soil" and "Soil <br />Bars IiftB ". <br />2. Results based on the second data set: <br />There is no significant difference between the distributions for "Substitute Soil" and "Soil <br />Barxprofile ". <br />There is significant difference between the distributions for "Substitute Soil" and "Solt <br />Bari liftA". <br />There is no significant difference between the distributions for "Substitute Soil" and "Soil <br />Barx liftB ". <br />PLTF 002495 <br />