(R) Q-Q Plots (SPSS)

The topic of Q-Q Plots was originally covered in an a prior article pertaining to the identification of normally distributed data. In this article, we will again review the concept of the Q-Q plot, which is a graphical methodology for identifying normally distributed data.

I will illustrate this concept with examples generated both within the SPSS platform, and the R platform.

Example (SPSS):

Our data vector within the R platform.

SDSample <- c(7.00, 5.10, 4.80, 2.90, 4.80, 5.80, 6.40, 6.10, 4.30, 7.20, 5.30, 4.00, 5.50, 5.40, 4.70, 4.50, 5.00, 4.70, 6.10, 5.10, 5.20, 5.00, 4.20, 5.10, 4.90, 5.30, 2.90, 5.80, 3.50, 4.90, 5.80, 6.10, 3.00, 5.90, 4.30, 5.30, 4.70, 6.40, 4.60, 3.50, 5.00, 3.50, 4.10, 5.70, 4.90, 6.10, 5.30, 6.90, 4.60, 4.90, 4.00, 3.90, 4.50, 5.90, 5.20, 7.20, 4.60, 4.40, 5.40, 5.90, 3.10, 5.60, 5.10, 4.40, 4.50, 3.10, 4.50, 6.00, 6.00, 5.10, 7.30, 4.60, 3.20, 4.10, 5.10, 4.90, 5.10, 5.60, 4.10, 5.70, 4.70, 5.70, 5.50, 4.50, 5.20, 5.00, 5.40, 5.10, 3.90, 4.30, 4.10, 4.30, 4.40, 2.40, 5.40, 6.30, 5.50, 4.30, 4.90, 2.90)

Within the SPSS platform, though partially visible, our data variable would resemble:

To begin our analysis, we will first select “Descriptive Statistics”, followed by “Q-Q Plots”.

This should cause the following menu to appear:

Through the utilization of the center arrow, designate “SDSample” as a variable. Once this has been completed, click “OK”. This should cause the following output to be generate.

Ideally, if the data is normally distributed, the dotted points should follow the solid trend line as closely as possible.

This particular Q-Q plot is reasonably consistent with normality.

To generate the same output within R, we would utilize the following code:

Example (R):

# Define the data vector #

SDSample <- c(7.00, 5.10, 4.80, 2.90, 4.80, 5.80, 6.40, 6.10, 4.30, 7.20, 5.30, 4.00, 5.50, 5.40, 4.70, 4.50, 5.00, 4.70, 6.10, 5.10, 5.20, 5.00, 4.20, 5.10, 4.90, 5.30, 2.90, 5.80, 3.50, 4.90, 5.80, 6.10, 3.00, 5.90, 4.30, 5.30, 4.70, 6.40, 4.60, 3.50, 5.00, 3.50, 4.10, 5.70, 4.90, 6.10, 5.30, 6.90, 4.60, 4.90, 4.00, 3.90, 4.50, 5.90, 5.20, 7.20, 4.60, 4.40, 5.40, 5.90, 3.10, 5.60, 5.10, 4.40, 4.50, 3.10, 4.50, 6.00, 6.00, 5.10, 7.30, 4.60, 3.20, 4.10, 5.10, 4.90, 5.10, 5.60, 4.10, 5.70, 4.70, 5.70, 5.50, 4.50, 5.20, 5.00, 5.40, 5.10, 3.90, 4.30, 4.10, 4.30, 4.40, 2.40, 5.40, 6.30, 5.50, 4.30, 4.90, 2.90)

# Create the Q-Q plot #

qqnorm(SDSample, main="")
qqline(SDSample)

This should produce the following visual output:

For more information on how to interpret the Q-Q plot, please click on the link below:

http://data.library.virginia.edu/understanding-q-q-plots/