Many nonparametric statistical methods use the ranks of observations to compute distribution-free statistics. In SAS, two procedures that use ranks are PROC NPAR1WAY and PROC CORR. Whereas the SPEARMAN option in PROC CORR (which computes rank correlation) uses only the "raw" tied ranks, PROC NPAR1WAY uses transformations of the ranks,
For many univariate statistics (mean, median, standard deviation, etc.), the order of the data is unimportant. If you sort univariate data, the mean and standard deviation do not change. However, you cannot sort an individual variable (independently) if you want to preserve its relationship with other variables. This statement is
It is well known that classical estimates of location and scale (for example, the mean and standard deviation) are influenced by outliers. In the 1960s, '70s, and '80s, researchers such as Tukey, Huber, Hampel, and Rousseeuw advocated analyzing data by using robust statistical estimates such as the median and the
When data contain outliers, medians estimate the center of the data better than means do. In general, robust estimates of location and sale are preferred over classical moment-based estimates when the data contain outliers or are from a heavy-tailed distribution. Thus, instead of using the mean and standard deviation of
You can standardize a numerical variable by subtracting a location parameter from each observation and then dividing by a scale parameter. Often, the parameters depend on the data that you are standardizing. For example, the most common way to standardize a variable is to subtract the sample mean and divide
A previous article discusses the definition of the Hoeffding D statistic and how to compute it in SAS. The letter D stands for "dependence." Unlike the Pearson correlation, which measures linear relationships, the Hoeffding D statistic tests whether two random variables are independent. Dependent variables have a Hoeffding D statistic
There are many statistics that measure whether two continuous random variables are independent or whether they are related to each other in some way. The most well-known statistic is Pearson's correlation, which is a parametric measure of the linear relationship between two variables. A related measure is Spearman's rank correlation,
Ranking is a fundamental concept in statistics. Ranks of univariate data are used by statisticians to estimate statistics such as percentiles (quantiles) and empirical distributions. A more advanced use is to compute various rank-based measures of correlation or association between pairs of variables. For example, ranks are used to compute
The ranks of a set of data values are used in many nonparametric statistics and statistical tests. When you request a statistic or nonparametric test in SAS, the procedure will automatically compute the ranks that are needed. However, sometimes it is useful to know how to compute the ranks yourself.
When you fit a regression model, it is useful to check diagnostic plots to assess the quality of the fit. SAS, like most statistical software, makes it easy to generate regression diagnostics plots. Most SAS regression procedures support the PLOTS= option, which you can use to generate a panel of
