Kvantilkvantilplott

Kvantilkvantilplott, often abbreviated as Q-Q plot, is a graphical method for comparing two probability distributions. It is typically used to assess whether a sample of data comes from a specific theoretical distribution, such as a normal distribution. The plot displays the quantiles of the sample data against the theoretical quantiles of the chosen distribution.

To construct a Q-Q plot, the data points are first sorted in ascending order. Then, the quantiles of the sample data are calculated. For each sample quantile, the corresponding theoretical quantile is determined from the chosen distribution. These pairs of sample and theoretical quantiles are then plotted on a scatterplot. If the two distributions are similar, the plotted points will lie approximately along a straight line. Deviations from this line indicate differences between the distributions.

Commonly, Q-Q plots are used to check for normality. In this case, the quantiles of the observed data are plotted against the quantiles of a standard normal distribution. If the data is normally distributed, the points should follow a straight line with a slope of 1 and an intercept of 0. However, the exact slope and intercept are not as critical as the linearity of the points. Significant deviations, such as S-shaped curves or U-shapes, suggest departures from normality.

Q-Q plots are a valuable tool in exploratory data analysis and statistical modeling. They provide a visual assessment that can complement or even precede formal statistical tests of distribution fit. While they are subjective to some degree, experienced users can discern subtle patterns and deviations that might be missed by other methods. Beyond normality testing, Q-Q plots can also be used to compare two independent samples or to compare a sample against any specified theoretical distribution for which quantiles can be calculated.