Statistics in Crosstabs

Overview

MarketSight runs a variety of statistical tests based on the column variables, row variables, and options you have specified in your crosstab design. For more information on how to interpret your results, see Interpreting Significance.

Standard Rules

All statistical tests in MarketSight:

  • Ignore rows and columns of data that sum to zero
  • Assume that samples are taken randomly from large populations
  • Assume that data contained in cells are independent
  • For tests on means, MarketSight assumes the data in each column are independent and normally distributed
  • For tests on frequencies, MarketSight assumes the data in each cell are independent

Statistical tests are NOT run in the following circumstances:

  • The data you want to compare is in two or more separate tables
  • A continuous variable without value ranges is placed in columns
  • Shared values for variables are displayed in columns
  • Cell count is under 5
  • There is unequal variance

Tests Comparing Means

Test Name Description
ANOVA Analysis of Variance (ANOVA) is tested using an F-test. The F-test
determines whether or not the row variable's means are equal to one
another for all columns. A prerequisite for ANOVA is the Levene test
for equality of variances.ANOVA is not run for multiple response variables.
T-test T-tests, in the form of Fisher's Least Significant Difference (LSD) test, are
used to find whether or not two independent means are equal to one
another. For both contrast and pairwise tests, this form of T-test is run
when the option to "Correct for Type I errors" is  disabled.A modified
version of a T-test is run for multiple response variables, for both contrast
and pairwise tests.
Corrected contrast T-test Corrected T-tests, in the form of Scheffé tests, are used for contrast tests
when the option to "Correct for Type I errors" is enabled.No correction is
applied for multiple response variables.
Corrected pairwise T-test Corrected T-tests, in the form of Tukey-Kramer tests, are used for pairwise
tests when the option to "Correct for Type I errors" is enabled. No correction
is applied for multiple response variables.

Tests Comparing Column Proportions

Test Name Description
Chi-squared Tests whether or not a relationship exists between the column variable(s)
and the row variable in  relatively large crosstabs.A modified version of a
Chi-squared test is run for multiple response variables.
Fisher's Exact Tests whether or not a significant relationship exists between the column
variable(s) and the row variable in relatively small crosstabs with 2 cells
per row and 2 cells per column (2x2).Used for both contrast and pairwise
tests to determine whether two column proportions are equal to one another
for cells with low cell counts.Fisher's Exact test is not run for multiple
response variables.
Z-test Determines whether or not two column proportions are equal to one another
for relatively large crosstabs.Used for both contrast and pairwise tests.
A modified version of a Z-test is run for multiple response variables for both
contrast and pairwise tests.
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