In statistics, probability plots, scatter plots, and quantile plots serve different purposes and provide unique visual insights into data.
Probability Plot
A probability plot is a graphical technique used to assess if a dataset follows a given distribution. It plots the empirical cumulative distribution function (CDF) of the data against the theoretical CDF of a specified distribution. For example, if we suspect our data follows a normal distribution, we would use a normal probability plot. If the points in the plot closely follow a straight line, it indicates that the data is likely from that distribution.
Scatter Plot
A scatter plot is used to display the relationship between two continuous variables. Each point represents an observation in the dataset with one variable plotted on the x-axis and the other on the y-axis. This plot helps in identifying trends, patterns, and potential correlations between the variables, such as whether an increase in one variable leads to an increase or decrease in another.
Quantile Plot
A quantile plot, also known as a quantile-quantile (Q-Q) plot, is similar to a probability plot but focuses on comparing the quantiles of the dataset against the quantiles of a theoretical distribution. In a Q-Q plot, the quantiles of the data are plotted on the y-axis and the quantiles of the theoretical distribution on the x-axis. If the data follows the theoretical distribution, the points will fall approximately along the line y = x.
Summary
In summary, while all three plots are used for data analysis, a probability plot is about assessing distribution fit, a scatter plot examines relationships between two variables, and a quantile plot compares the distribution of the dataset with a theoretical distribution. Each serves its unique purpose in the analysis and interpretation of data.