Table of Contents

Which correlation method to use?¶

Pearson's correlation is the most popular for continuous data. However, if data has outliers or does not meet the normality assumption, Pearson's correlation is inappropriate. Instead, one should use robust correlation methods, for example, Spearman skipped or percentage-bend correlation. On the other hand, if data is normally distributed and has no outliers, Pearson's correlation gives more power. Here I provide an R-script that first inspects the data for outliers (boxplot/bagplot method) and normality (Henze-Zirkler test) and then chooses the most appropriate of the three correlation methods. Based on Pernet et al. (2013), I follow three simple rules for selecting the correlation method:

• Pearson's correlation: Data is normally distributed and has no outliers
• Spearman skipped correlation: Data has bi-variate outliers
  • Using the minimum covariance determinant (MCD) estimator
• (20%) Percentage-bend correlation: Data has no bi-variate outliers but is not normally distributed or has univariate outliers

The 'Flexible Correlation' script is available from my GitHub repository.

Function description¶

flexible_correlations.r script contains three functions.

1. check_data¶

check_data function checks data outliers and normality. It uses the boxplot method to check for univariate outliers, bagplot method for bi-variate outliers, and Henze-Zirkler test for bi-variate normality.

Input

check_data(var1, var2, var1name = "var1", var2name = "var2", var1ylab = "", var2ylab = "", disp = FALSE)

• Required
  • var1 and var2 are numerical vectors; the two continuous variables you want to correlate.
• Optional
  • var1name and var2name are strings; names of the variables to be displayed on boxplots. The default is "var1" and "var2".
  • var1ylab and var2ylab are strings; y-axis labels for the two variables to be displayed on boxplots. The defaults are empty strings.
  • disp is logical. Whether you want to display the assumption check results (boxplots, bagplot,q-q plot). The default is FALSE.

Output

A 4-item list:

1. outliers_all: All outlier cases; a numeric vector
2. outliers_uni: Univariate outlier cases; a numeric vector
3. outliers_bi: Bi-variate outlier cases; a numeric vector
4. normality: Whether data is bi-variat normal; TRUE/FALSE

If attribute disp = TRUE then summary text will be outputed and 4 plots displayed: 2 boxplots, a bagplot, and q-qplot.

The output is used by the other two functions, do_correlation and plot_correlation.

2. do_correlation¶

do_correlation function performs one of the three correlation methods. It uses the number of univariate and bi-variate outliers obtained from the check_data function. It performs the Henze-Zirkler test to determine whether the data meet bi-variate normal distribution.

Input

do_correlation(var1, var2, data_check = NULL)

• Required
  • var1 and var2 are numerical vectors; the two continuous variables you want to correlate.
• Optional
  • data_check is the list of data check results. If not provided, then check_data function will be executed to get the outlier list.

Output

A 3-item list:

1. txt: Correlation results in the form to be displayed on the correlation plot.
2. p: A p-value of the correlation.
3. datainfo: Information whether data has otliers and is normally distributed.

The output is used by the plot_correlation function.

3. plot_correlation¶

plot_correlation function displays a scatterplot, trend line with shaded 95%CI, and correlation results in a text form at the top.

Input

plot_correlation(var1, var2, var1name = "var1", var2name = "var2", corr_results = NULL, data_check = NULL, pointsize = 1.8, txtsize = 11, plotoutliers = FALSE, pthreshold = NULL, datainfo = TRUE)

• Required
  • var1 and var2 are numerical vectors; the two continuous variables you want to correlate.
• Optional
  • var1name and var2name are strings; names of the variables to be displayed on boxplots. The default is "var1" and "var2".
  • corr_results is the correlation results from the function do_correlation. If not provided, the do_correlation function will be executed to get the results.
  • data_check is the list of data check results. If not provided, then check_data function will be executed to get the outlier list.
  • pointsizeis numeric; the size of the scatterplot points. The default is 1.8.
  • txtsize is numeric; the font size of the scatterplot labels. The default is 11. The title size would be 2 points larger.
  • plotoutliers is logical. Whether to plot outlier cases on the scatterplot. The default is FALSE.
  • pthreshold is numeric; a p-value threshold for statistically significant correlation. If provided, a red box will be displayed around the scaterplot and the result text will be displayed in bold.
  • datainfo is logical. Whether to display data summary information about outliers and normality. The information would be displayed in the plot camption. The default is TRUE.

Output

A correlation scatterplot with result text at the top.

Examples¶

Load the 'flexible correlations' script¶

A standart correlation plot¶

Let's use the R built-in dataset mtcars and look at the correlation between automobile weight and fuel consumption.

We see that Spareman skipped correlation was performed, and it was significant. We also see that there were two outliers in the data, and data did not meet bi-variate normality.

A plot with outliers displayed¶

You can also display the outlier cases on the scatterplot if you like. And you can also remove the data assumption summary from the bottom.

Inspecting outliers and normality¶

You might want to inspect the data outliers and normality distribution more closely. For that, you can run the check_data function with disp = TRUE setting.

We see that there were two outliers in the 'weight' variable, no outliers in the 'fuel consumption' variable, and one bi-variate outlier. The robust Spearman skipped correlation is most appropriate because of the bi-variate outlier in the data.

Multiple correlation plots¶

I have found this 'flexible correlation' script particularly handy for explorations, looking at several correlations together.

As an example, let's look at another R built-in dataset iris and correlate the petal length and petal width for each species of Iris flower.