Handling violations of assumptions 13.1 ... amazonaws com

Handling violations of assumptions 13.1 detecting deviations from normality  Normal quantile plot: compares each observation in the sample with its quantile expected from the standard normal distribution. Points should fall roughly along a straight line if the data come from a normal distribution.  Shapiro-wilk test: evaluates the goodness of fit of a normal distribution to a set of data randomly sampled from a population 13.2 when to ignore violations of assumptions  Robust: a statistical procedure is robust if the answer it gives is not sensitive to violations of the assumptions of the method 13.3 data transformations  Data transformation: changes each measurement by the same mathematical formula  Log transformation: most common data transformation, natural ln  Arcsine transformation: only on data that are proportions  Square-root transformation: used when the data are counts  Square transformation: when frequency distribution of the data is skewed left but if it doesn’t work, use the antilog transformation  Reciprocal transformation: when data is skewed right 13.4 Nonparametric alternatives to one-sample and paired t-tests  Nonparametric method: makes fewer assumptions than standard parametric methods about the distribution of the variable  Sign test: compares the median of a sample to a constant specified in the null hypothesis. It makes no assumptions about the distribution of the measurement in the population  Wilcoxon signed-rank test: improvement to the sign test 13.5 Comparing two groups: the Mann-Whitney U-test  The mann-whitney u-test: compares the distribution of two groups. It does not require as many assumptions as the two-sample t-test

13.7 type I and type II error rates of nonparmetric methods  Nonparametric tests are typically less powerful than parametric tests