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concept hierarchy for time defined as “day < month < quarter < year.” Drill-down
occurs by descending the time hierarchy from the level of quarter to the more detailed
level of month. The resulting data cube details the total sales per month rather than
summarizing them by quarter.
Because a drill-down adds more detail to the given data, it can also be per-
formed by adding new dimensions to a cube. For example, a drill-down on the
central cube of Figure 4.12 can occur by introducing an additional dimension, such
as customer group.

Slice and dice: The slice operation performs a selection on one dimension of the given
cube, resulting in a subcube. Figure 4.12 shows a slice operation where the sales
data are selected from the central cube for the dimension time using the criterion
time = “Q1.” The dice operation defines a subcube by performing a selection on two
or more dimensions. Figure 4.12 shows a dice operation on the central cube based on
the following selection criteria that involve three dimensions: (location = “Toronto”
or “Vancouver”) and (time = “Q1” or “Q2”) and (item = “home entertainment” or
“computer”).
Pivot (rotate): Pivot (also called rotate) is a visualization operation that rotates the data
axes in view to provide an alternative data presentation. Figure 4.12 shows a pivot
operation where the item and location axes in a 2-D slice are rotated. Other examples
include rotating the axes in a 3-D cube, or transforming a 3-D cube into a series of
2-D planes.
Other OLAP operations: Some OLAP systems offer additional drilling operations. For
example, drill-across executes queries involving (i.e., across) more than one fact
table. The drill-through operation uses relational SQL facilities to drill through the
bottom level of a data cube down to its back-end relational tables.
Other OLAP operations may include ranking the top N or bottom N items in
lists, as well as computing moving averages, growth rates, interests, internal return
rates, depreciation, currency conversions, and statistical functions.

OLAP offers analytical modeling capabilities, including a calculation engine for
deriving ratios, variance, and so on, and for computing measures across multiple dimen-
sions. It can generate summarizations, aggregations, and hierarchies at each granularity
level and at every dimension intersection. OLAP also supports functional models for
forecasting, trend analysis, and statistical analysis. In this context, an OLAP engine is a
powerful data analysis tool.

OLAP Systems versus Statistical Databases
Many OLAP systems’ characteristics (e.g., the use of a multidimensional data model
and concept hierarchies, the association of measures with dimensions, and the notions
of roll-up and drill-down) also exist in earlier work on statistical databases (SDBs).
A statistical database is a database system that is designed to support statistical applica-
tions. Similarities between the two types of systems are rarely discussed, mainly due to
differences in terminology and application domains.