INFERENTIAL STATISTICS PARAMETRIC TESTS Inferential Statistics is not a straight forward task. Because we can never know for sure the true underlying state of the population (i.e. reality), we have to always make some assumptions. These assumptions are not just lucky guesses; but very specific and calculated steps that help us move forward with our data analysis in the most efficient way (inferential statistics is all about looking beyond the data). One of the main uses of these assumptions is to help us differentiate between two very different procedures in inferential statistics: Parametric and Nonparametric tests.
Parametric Tests Parametric Tests are the conservative version of inferential statistics, in which researchers assume numerous strict assumptions about the variables. Some of the common assumptions for the parametric tests include: Normality, Randomness, Absence of Outliers, Homogeneity of Variances and Independence of Observations. We will only talk about the most important three assumptions due to the scope of this introductory manual.
Parametric Tests Assumptions Normality The most important distinction that helps you with choosing the type of test you will use is whether the results for the variable you are measuring are normally distributed. This can be done either Graphically, by plotting the data and looking at the graph; or Analytically, using one of the common tests (e.g. Shapiro–Wilk Test or Kolmogorov–Smirnov Test).
Absence of Outliers After checking for normality, researchers review their dataset for the presence of Outliers. An Outlier is a datapoint that just does not fit with the rest of the dataset (significantly away from the rest of the observations). These datapoints primarily exist for one of two reasons:
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