BIOM301 Chapter 14 Nonparametric Tests Previously Parametric Tests All previous tests have been parametric tests this includes Chapter 11 Chi Square Tests on Qualitative data why THEY ASSUME THE DATA FOLLOWS SOME UNDERLYING DISTRIBUTION o t distribution o z distribution o Chi Square distribution To use Parametric Tests o Your data must meet the assumptions for that test o This is usually normality and perhaps homogeneity of variance Ch 11 all expected values 5 How decide if data meet assumptions o Most Parametric Tests are ROBUST It often takes a strong deviation from normality and homogeneity to violate the assumptions But we need to check for strong trends in our data and for outliers Need justification to remove an outlier Transforming data e g log transformation may help with trends o But if assumptions not met you then need to use a Nonparametric Test No underlying distribution assumed Nonparametric Tests Distribution Free Advantages o Doesn t require normality o Can deal with outliers better than parametric tests o Easy to do and easy to understand Major Disadvantages o Less statistically powerful less likely to reject the Ho when it is really false in population o Not all parametric tests have a nonparametric counterpart Many Nonparametric Test Out There We will only cover 4 conceptually You will NOT be asked to analyze a data set statistically or calculate values Statistical Power Nonparametric tests have less statistical power but some are better than others It s all about the relative position of observations Some nonparametric tests focus on the rank of the observations relative to each other o E g Mann Whitney U Test to compare 2 independent populations If samples come from populations with means that ARE really different then the population with the mean should also produce samples that have a rank 2 Population Mann Whitney U Test You sample 2 lakes to look at the mean length of fish but because your sample size was small and you had outliers you can t assume normality and run a 2 sample t test o Instead 2 population Mann Whitney U Test Same process slight different wording o Ho Lake A and Lake B have fish lengths that have identical distributions o Ha Lake A and Lake B have fish lengths that are not the same Conceptually o If you change the sample values into ranks from smallest to largest regardless of lake and there is NO difference in populations then you should see Lots of Overlap in sample ranks Lake A ranks 1 3 4 6 9 10 Lake B ranks 2 5 7 8 11 12 o If instead there IS a difference in the populations then you should see Little Overlap in sample ranks Lake A ranks 1 2 3 4 5 7 Lake B ranks 6 8 9 10 11 12 1 Population Spearman s Rank Test Same idea for a nonparametric correlation analysis There is a trend to your bivariate data but it s not linear can still ask if there is a trend to the ranks o We are looking for a trend in the bivariate data o Same idea as covariance but we are using ranks Example Paired T test Alternative 2 Population Sign Test Paired observations so can calculate the DIFFERENCE Then look at the SIGN of the difference not the actual value 1 Population Sign Test Will ask if the differences are all positive or negative as before Same idea but now comparing you sample values to Some Value What Should You Do You ONLY have to know what is discussed in this lecture Textbook focuses on how to actually run the statistical tests which you do now need to know so practice questions not helpful
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