Lecture 21: Correlation and normality

December 1st, 2022 (12th week of classes)

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Correlation, assessing normality and non-parametric statistical hypothesis testing

In this lecture I cover we cover Pearson’s correlation, which is a statistic to measure the amount of covariation between two continuous variables. I then cover a visual assessment for normality. This is assessment is called QQ plot and the video below is an excellent resource to understand theses plots and how they help assessment normality. Finally, I cover one example of a non-parametric test for when the assumption of normality doesn’t hold. Non-parametric tests are diverse and have an in-depth treatment would take about half of a semester. Traditional parametric tests that assume normality are the most widely used and hence the decision to concentrate on them. However, it is important to know that alternatives exist. In Lecture 22 we will continue on these alternatives.

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Normal Quantile-Quantile Plots, by JBStatistics.

“An introduction to normal quantile-quantile (QQ) plots (a graphical method for assessing whether a set of observations is approximately normally distributed). The author discusses the motivation for the plot, the construction of the plot, then look at several examples. In the examples they look at what a normal quantile-quantile plot looks like when sampling from various other distributions. They then illustrate what normal QQ plots look like when sampling from a normal distribution by simulating several samples, for two different sample sizes.”

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Lecture

Slides:

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Slides above contain parts 1 and 2 of the lecture.

part 1
Correlation

part 2
QQ plots and the Kruskal-Wallis for testing (non-parametrically) the difference among samples. It’s akin to ANOVA but based on a rank transformation.