![]() Qqnorm(data, main = 'Q-Q Plot for Normality', xlab = 'Theoretical Dist', The following code modifies the titles, axis labels, and color of the points in the plot: #make this example reproducible We can modify some of the aesthetics of the Q-Q plot in R including the title, axis labels, data point colors, line color, and line width. Modifying the Aesthetics of a Q-Q Plot in R Once again we can see that this dataset does not appear to follow a normal distribution, especially near the tails. #generate vector of 100 values that follows a Chi-Square distribution We can see the clear departure from the straight line in this Q-Q plot, indicating that this dataset likely does not follow a normal distribution.Ĭonsider another chunk of code that generates a vector of 100 random values that follow a Chi-Square distribution with 5 degrees of freedom and creates a Q-Q plot for this data to check if it follows a normal distribution: #make this example reproducible #generate vector of 100 values that follows a gamma distribution We can see that the data points near the tails don’t fall exactly along the straight line, but for the most part this sample data appears to be normally distributed (as it should be since we told R to generate the data from a normal distribution).Ĭonsider instead the following code that generates a vector of 100 random values that follow a gamma distribution and creates a Q-Q plot for this data to check if it follows a normal distribution: #make this example reproducible To make it even easier to see if the data falls along a straight line, we can use the qqline() function: #create Q-Q plot #create Q-Q plot to compare this dataset to a theoretical normal distribution #generate vector of 100 values that follows a normal distribution ![]() We can easily create a Q-Q plot to check if a dataset follows a normal distribution by using the built-in qqnorm() function.įor example, the following code generates a vector of 100 random values that follow a normal distribution and creates a Q-Q plot for this dataset to verify that it does indeed follow a normal distribution: #make this example reproducible If the data points fall along a straight diagonal line in a Q-Q plot, then the dataset likely follows a normal distribution. In most cases the normal distribution is used, but a Q-Q plot can actually be created for any theoretical distribution. Q-Q plots identify the quantiles in your sample data and plot them against the quantiles of a theoretical distribution. The 0.5 quantile represents the point below which 50% of the data fall below, and so on. For example, the 0.9 quantile represents the point below which 90% of the data fall below. Quantiles represent points in a dataset below which a certain portion of the data fall. If both sets of quantiles came from the same distribution, then the points on the plot should roughly form a straight diagonal line. We can create a Q-Q plot by plotting two sets of quantiles against one another. Many statistical tests make the assumption that a set of data follows a normal distribution, and a Q-Q plot is often used to assess whether or not this assumption is met.Īlthough a Q-Q plot isn’t a formal statistical test, it does provide an easy way to visually check whether a dataset follows a normal distribution, and if not, how this assumption is violated and which data points potentially cause this violation. A Q-Q plot, short for “quantile-quantile” plot, is a type of plot that we can use to determine whether or not a set of data potentially came from some theoretical distribution.
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