QQ-plots: Quantile-Quantile plots - R Base Graphs - Easy Guides - Wiki (2024)

FAQs

What is QQ quantile-quantile plots? ›

The quantile-quantile (q-q) plot is a graphical technique for determining if two data sets come from populations with a common distribution. A q-q plot is a plot of the quantiles of the first data set against the quantiles of the second data set.

A QQ plot is a scatterplot created by plotting two sets of quantiles against one another. If both sets of quantiles came from the same distribution, we should see the points forming a line that's roughly straight. Here's an example of a normal QQ plot when both sets of quantiles truly come from normal distributions.

QQ plots can be made in R using a function called qqnorm(). Simply give the vector of data as input and it will draw a QQ plot for you. (qqline() will draw a line through that Q-Q plot to make the linear relationship easier to see.)

QQ plot (or quantile-quantile plot) draws the correlation between a given sample and the normal distribution. A 45-degree reference line is also plotted. QQ plots are used to visually check the normality of the data.

Examining data distributions using QQ plots

Points on the Normal QQ plot provide an indication of univariate normality of the dataset. If the data is normally distributed, the points will fall on the 45-degree reference line. If the data is not normally distributed, the points will deviate from the reference line.

A chi square quantile-quantile plots show the relationship between data-based values which should be distributed as χ2 and corresponding quantiles from the χ2 distribution.

Q-Q plots are used to find the type of distribution for a random variable whether it be a Gaussian distribution, uniform distribution, exponential distribution or even a Pareto distribution. You can tell the type of distribution using the power of the Q-Q plot just by looking at it.

The theoretical Q-Q plot is the graph of the quantiles of a the CDF F, xp = F−1(p), versus the corresponding quantiles of the CDF G, yp = G−1(p), that is the graph [F−1(p), G−1(p)] for p ∈ (0, 1). If the two CDFs are identical, the theoretical Q-Q plot will be the line y = x. , t-distribution with n degrees of freedom.

The whiskers in the boxplot show only the extent of the tails for most of the data (with outside values denoted separately); more detailed information about the shape of the tails, such as skewness and “weight” relative to a standard reference distribution, is much better displayed via quantile–quantile (q-q) plots.

Quantile plots directly display the quantiles of a set of values. The sample quantiles are plotted against the fraction of the sample they correspond to. There is no built-in quantile plot in R, but it is relatively simple to produce one. Quantile-quantile plots allow us to compare the quantiles of two sets of numbers.

What is the use of quantile in R? ›

Note: The quantile function divides the data into equal halves, in which the median acts as middle and over that the remaining lower part is lower quartile and upper part is upper quartile.

A P-P plot compares the empirical cumulative distribution function of a data set with a specified theoretical cumulative distribution function F(·). A Q-Q plot compares the quantiles of a data distribution with the quantiles of a standardized theoretical distribution from a specified family of distributions.

A Q–Q plot is used to compare the shapes of distributions, providing a graphical view of how properties such as location, scale, and skewness are similar or different in the two distributions. Q–Q plots can be used to compare collections of data, or theoretical distributions.

Histograms show the distribution of data, while Q-Q plots compare observed data points to what would be expected in a normal distribution. Statistical tests, such as those mentioned (skewness, kurtosis), can quantitatively assess whether the data deviates significantly from a normal distribution.

To search for evidence of systematic bias (from unrecognized population structure, analytical approach, genotyping artifacts, etc.), a quantile-quantile (Q-Q) plot can be used to characterize the extent to which the observed distribution of the test statistic follows the expected (null) distribution.

A normal quantile-quantile (QQ) plot can be useful in meta-analyses to check various aspects and assumptions of the data. Ideally, the points in the plot should fall on a diagonal line with slope of 1, going through the (0,0) point.

A Q-Q (quantile-quantile) plot shows how two distributions' quantiles line up, with our theoretical distribution (e.g., the normal distribution) as the x variable and our model residuals as the y variable.

The q-q plot compares two distributions by plotting the quantiles of one distribution against those of the other. Data can be compared with a theoretical or empirical “reference distribution” and substantial deviations from a straight line indicate differences in the shapes of the two distributions.