Univariate Statistics

This summary provides descriptive statistics to characterize the univariate distribution of selected numeric variables. In addition, three tests of normality and two estimates of the number of outliers are shown for each variable.

The dialog for displaying descriptive statistics for selected variables

The univariate statistics dialog prompts for:

  • Whether to use all data in the data table or or just the subset that has been selected (e.g., by clicking on the table or map).

  • One or more numeric variables.

  • An optional grouping variable, which must be a categorical variable.

The dialog then displays a table of univariate statistics for all of the variables, as illustrated above. Statistics for untransformed and log10-transformed data are shown on separate tabs on the right side of the dialog. The table of statistics is immediately updated if any changes are made to the user’s selections on this dialog or, if only selected data are being used, changes are made to the selected data.

If a grouping variable is specified, the value of the grouping variable will be listed as the first item on each row of the output tables.

If a selected variable does not have a value in any of the selected rows of the data table, it will not appear in the output.

The complete set of univariate statistics is:

  • Number of observations

  • Minimum

  • Maximum

  • Mean

  • Median

  • Mode

  • Geometric mean, for untransformed data only

  • Sample standard deviation

  • Coefficient of Variation (C.V.)

  • Sum

  • 5th percentile

  • 95th percentile

  • The p value for the Anderson-Darling test of normality (Anderson and Darling 1952). This is calculated only when there are five or more cases. Low p values (e.g., less than 0.05) indicate that the distribution is non-normal.

  • The p value for the Lilliefors test of normality (Lilliefors 1967). This is calculated only when there are five or more cases. Low p values (e.g., less than 0.05) indicate that the distribution is non-normal.

  • The p value for the omnibus test of normality (D’Agostino 1971). This is calculated only when there are 20 or more cases. Low p values (e.g., less than 0.05) indicate that the distribution is non-normal.

  • The number of outliers found by Rosner’s test (or the Generalized Extreme Studentized Deviate test) (Rosner 1983). This test is only carried out when there are at least 15 observations, and it tests for a maximum of 5 outliers for 15-99 observations, and a maximum of 10 outliers for 100 or more observations. This test assumes that the distribution is approximately normal, so if the distribution is not normal the results of this test are not reliable. An alpha value of 0.05 is used for the t distribution to calculate the critical values for the test.

  • The number of values (outliers) greater or less than Tukey’s fences, or 1.5 times the interquartile range. This value should match the number of outliers shown on the box plot. This is calculated only when there are at least 5 observations.

The table of statistics for untransformed data can be exported to a file using the keystroke Ctrl-S, and the table of statistics for log10-transformed data can be exported using the keystroke Ctrl-Z.