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The OLAP (Online Analytical Processing) Cubes procedure calculates totals, means, and other univariate statistics for continuous summary variables within categories of one or more categorical grouping variables. A separate layer in the table is created for each category of each grouping variable. Example.Total and average sales for different regions and product lines within regions.

Statistics.Sum, number of cases, mean, median, grouped median, standard error of the mean, minimum, maximum, range, variable value of the first category of the grouping variable, variable value of the last category of the grouping variable, standard deviation, variance, kurtosis, standard error of kurtosis, skewness, standard error of skewness, percentage of total cases, percentage of total sum, percentage of total cases within grouping variables, percentage of total sum within grouping variables, geometric mean, and harmonic mean.

OLAP Cubes Data Considerations

Data.The summary variables are quantitative (continuous variables measured on an interval or ratio scale), and the grouping variables are categorical. The values of categorical variables can be numeric or string.

Assumptions.Some of the optional subgroup statistics, such as the mean and standard deviation, are based on normal theory and are appropriate for quantitative variables with symmetric distributions. Robust statistics, such as the median and range, are appropriate for quantitative variables that may or may not meet the assumption of normality.

To Obtain OLAP Cubes 1. From the menus choose:

Analyze>Reports>OLAP Cubes...

2. Select one or more continuous summary variables. 3. Select one or more categorical grouping variables. Optionally:

v _{Select different summary statistics (clickStatistics). You must select one or more grouping variables} before you can select summary statistics.

v _{Calculate differences between pairs of variables and pairs of groups that are defined by a grouping} variable (clickDifferences).

v _{Create custom table titles (clickTitle).}

v _{Hide counts that are less than a specified integer. Hidden values will be displayed as<N, whereN is} the specified integer. The specified integer must be greater than or equal to 2.

OLAP Cubes Statistics

You can choose one or more of the following subgroup statistics for the summary variables within each category of each grouping variable: sum, number of cases, mean, median, grouped median, standard error of the mean, minimum, maximum, range, variable value of the first category of the grouping variable, variable value of the last category of the grouping variable, standard deviation, variance, kurtosis, standard error of kurtosis, skewness, standard error of skewness, percentage of total cases, percentage of total sum, percentage of total cases within grouping variables, percentage of total sum within grouping variables, geometric mean, and harmonic mean.

You can change the order in which the subgroup statistics appear. The order in which the statistics appear in the Cell Statistics list is the order in which they are displayed in the output. Summary statistics are also displayed for each variable across all categories.

First. Displays the first data value encountered in the data file.

Geometric Mean. The nth root of the product of the data values, where n represents the number of cases.

Grouped Median. Median that is calculated for data that is coded into groups. For example, with age data, if each value in the 30s is coded 35, each value in the 40s is coded 45, and so on, the grouped median is the median calculated from the coded data.

Harmonic Mean. Used to estimate an average group size when the sample sizes in the groups are not equal. The harmonic mean is the total number of samples divided by the sum of the reciprocals of the sample sizes.

Kurtosis. A measure of the extent to which observations cluster around a central point. For a normal distribution, the value of the kurtosis statistic is zero. Positive kurtosis indicates that, relative to a normal distribution, the observations are more clustered about the center of the distribution and have thinner tails until the extreme values of the distribution, at which point the tails of the leptokurtic distribution are thicker relative to a normal distribution. Negative kurtosis indicates that, relative to a normal distribution, the observations cluster less and have thicker tails until the extreme values of the distribution, at which point the tails of the platykurtic distribution are thinner relative to a normal distribution.

Last. Displays the last data value encountered in the data file.

Maximum. The largest value of a numeric variable.

Mean. A measure of central tendency. The arithmetic average, the sum divided by the number of cases.

Median. The value above and below which half of the cases fall, the 50th percentile. If there is an even number of cases, the median is the average of the two middle cases when they are sorted in ascending or descending order. The median is a measure of central tendency not sensitive to outlying values (unlike the mean, which can be affected by a few extremely high or low values).

Minimum. The smallest value of a numeric variable.

N. The number of cases (observations or records).

Percent of N in. Percentage of the number of cases for the specified grouping variable within categories of other grouping variables. If you only have one grouping variable, this value is identical to percentage of total number of cases.

Percent of Sum in. Percentage of the sum for the specified grouping variable within categories of other grouping variables. If you only have one grouping variable, this value is identical to percentage of total sum.

Percent of Total N. Percentage of the total number of cases in each category.

Percent of Total Sum. Percentage of the total sum in each category.

Range. The difference between the largest and smallest values of a numeric variable, the maximum minus the minimum.

Skewness. A measure of the asymmetry of a distribution. The normal distribution is symmetric and has a skewness value of 0. A distribution with a significant positive skewness has a long right tail. A

distribution with a significant negative skewness has a long left tail. As a guideline, a skewness value more than twice its standard error is taken to indicate a departure from symmetry.

Standard Deviation. A measure of dispersion around the mean. In a normal distribution, 68% of cases fall within one standard deviation of the mean and 95% of cases fall within two standard deviations. For example, if the mean age is 45, with a standard deviation of 10, 95% of the cases would be between 25 and 65 in a normal distribution.

Standard Error of Kurtosis. The ratio of kurtosis to its standard error can be used as a test of normality (that is, you can reject normality if the ratio is less than -2 or greater than +2). A large positive value for kurtosis indicates that the tails of the distribution are longer than those of a normal distribution; a negative value for kurtosis indicates shorter tails (becoming like those of a box-shaped uniform distribution).

Standard Error of Mean. A measure of how much the value of the mean may vary from sample to sample taken from the same distribution. It can be used to roughly compare the observed mean to a

hypothesized value (that is, you can conclude the two values are different if the ratio of the difference to the standard error is less than -2 or greater than +2).

Standard Error of Skewness. The ratio of skewness to its standard error can be used as a test of normality (that is, you can reject normality if the ratio is less than -2 or greater than +2). A large positive value for skewness indicates a long right tail; an extreme negative value indicates a long left tail.

Sum. The sum or total of the values, across all cases with nonmissing values.

Variance. A measure of dispersion around the mean, equal to the sum of squared deviations from the mean divided by one less than the number of cases. The variance is measured in units that are the square of those of the variable itself.

OLAP Cubes Differences

This dialog box allows you to calculate percentage and arithmetic differences between summary variables or between groups that are defined by a grouping variable. Differences are calculated for all measures that are selected in the OLAP Cubes Statistics dialog box.

Differences between Variables.Calculates differences between pairs of variables. Summary statistics values for the second variable (the Minus variable) in each pair are subtracted from summary statistics values for the first variable in the pair. For percentage differences, the value of the summary variable for the Minus variable is used as the denominator. You must select at least two summary variables in the main dialog box before you can specify differences between variables.

Differences between Groups of Cases.Calculates differences between pairs of groups defined by a grouping variable. Summary statistics values for the second category in each pair (the Minus category) are subtracted from summary statistics values for the first category in the pair. Percentage differences use the value of the summary statistic for the Minus category as the denominator. You must select one or more grouping variables in the main dialog box before you can specify differences between groups.

OLAP Cubes Title

You can change the title of your output or add a caption that will appear below the output table. You can also control line wrapping of titles and captions by typing\nwherever you want to insert a line break in the text.