Pearson parametric

Here you can still use the Pearson chi-square test as shown in the 2x2 table example as long as your response variable is nominal and merely descriptive. If your response variable is ordinal, meaning that it is an ordered sequence, and you can use a parametric test, then you should use the Mantel-Haenszel test statistic for parametric tests of association. For instance, if in our previous example the variable called headache was coded as a 2 when the patient experienced extreme headache, a 1 if mild headache, and a 0 if no headache, then headache would be an ordinal variable. You can get the Mantel-Haenszel /pvalue by running the following SAS code ... 

The Spearman s Rank Correlation is the non-parametric alternative to the Pearson s and Cosine Correlation Distances. No assumption is made concerning the data distribution or the center of the data... 

Describe the requirement for normally distributed data when using parametric tests (t-tests, ANOVAs and Pearson correlation)... 

Technically, Pearson correlation (Chapter 14) does have an assumption that the two sets of data are normally distributed, but it is pretty rare to see anybody bothering to check whether they actually are and there is precious little evidence of anything going radically wrong if they are not. However, non-parametric Spearman correlation is quite frequently resorted to with ordinal data. 

Tests, analyses of variance and Pearson correlation are referred to as parametric methods and they all make an assumption that data will be normally distributed. These (especially the first two) can be very misleading if applied to severely nonnormal data. 

With respect to the normality condition of the composite T-scores in Table 1, skewness and kurtosis values confirm that the distributions are close to a normal curve so the data may be analyzed through parametric analyses such as f-test and Pearson correlation. Mean comparisons are performed to investigate if gender-based differences exist. 

This means that important descriptors can be identified by simply calculating correlation coefficients. It is worth noting that the distribution of descriptor values was far from a normal distribution, so the use of the non-parametric Spearman s correlation coefficient (p) was preferred over the more commonly used Pearson s correlation coefficient (r). ... 

For the reason, that the null hypothesis of normally distributed samples can t be rejected only by the half of the measurements, the use of parametric tests is not possible. Therefore, nonparametric tests such as Mann-Whitney U or Levene s (Hartung 1998) for the comparison of the samples shall be applied. Also the Pearson product-moment correlation assumes the norm distribution of the samples. Hence, the use of Spearman s rank correlation, which is independent on the distribution model, is more adequate. 

Nevertheless, what currently passes for frequentist parametric statistics includes a collection of techniques, concepts, and methods from each of these two schools, despite the disagreements between the founders. Perhaps this is because, for the very important cases of the normal distribution and the binomial distribution, the MLE and the UMVUE coincided. Efron (1986) suggested that the emotionally loaded terms (unbiased, most powerful, admissible, etc.) contributed by Neyman, Pearson, and Wald reinforced the view that inference should be based on likelihood and this reinforced the frequentist dominance. Frequentist methods work well in the situations for which they were developed, namely for exponential families where there are minimal sufficient statistics. Nevertheless, they have fundamental drawbacks including ... 

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