Statistics by
Groups Results - Post-Hoc tab
Breakdown:
Descriptive Statistics by Groups
Select the Post-hoc
tab in the Statistics by Groups Results
dialog box to access options to compute post-hoc
comparisons for selected variables in the analysis.
Refer to Descriptive
Statistics by Groups (Breakdown) Introductory Overview - Post-hoc Comparisons
of Means for a discussion of the basic logic behind these tests. Discussions
of post-hoc procedures are also provided in Winer (1962), Hays (1988),
or Milliken and Johnson (1984).
In short, usually, after obtaining a statistically significant F-test from the ANOVA, you want to
know which means contributed to the effect; that is, which groups are
particularly different from each other. You could of course perform a
series of simple t-tests to compare
all possible pairs of means. However, such a procedure would capitalize
on chance. This means that the reported probability levels would actually
overestimate the statistical significance of mean differences. Without
going into much detail, suppose you took 20 samples of 10 random numbers
each, and computed 20 means. Then, take the group (sample) with the highest
mean and compare it with that of the lowest mean. The t-test
for independent samples tests whether those two means are significantly
different from each other, provided that they were the only two samples
taken. Post-hoc comparison techniques, however, specifically take into
account the fact that more than two samples were taken. A large selection
of post-hoc comparison procedures is also available in the General
Linear Model (GLM) module, including Dunnett's
test, as well as facilities for using customized error terms.
Variables.
Click this button to display the standard single
variable selection dialog box listing the variables used in the analysis.
Select the variables for which you want to perform post-hoc comparisons.
LSD
test or planned comparisons. Click this button to create
a matrix of p-value in a spreadsheet.
These p-values indicate the post-hoc
significance levels for the respective pairs of means. The LSD test is
equivalent to the t-test
for independent samples, based on the N
in the groups involved in the comparison. It offers the least amount of
protection against the increased alpha
error rate due to multiple post-hoc comparisons.
Scheffé
test. Click this button to produce a spreadsheet with the
post-hoc p-values for the Scheffé
test. The Scheffé test is usually more conservative than the Newman-Keuls
or Duncan test (see Winer, 1962).
Newman-Keuls
test & critical ranges. Click this button to produce
a spreadsheet with the post-hoc p-values
for the Newman-Keuls test. Note that
Statistica does not merely report cut-off values for p,
but computes the actual probabilities based on the distribution of the
studentized range statistics. A second spreadsheet displays the critical
ranges between ordered means, given the respective alpha
level (by default p < .05).
The Newman-Keuls test is based on the studentized range statistic. Computationally,
Statistica first sorts the means into ascending order. For each pair of
means Statistica then assesses the probability under the null hypothesis
(no differences between means in the population) of obtaining differences
between means of this (or greater) magnitude, given the respective number
of samples. Thus, it actually tests the significance of ranges, given
the respective number of samples.
Duncan's
multiple range test & critical ranges. Click this button to produce a spreadsheet with
the post-hoc p-values for the
Duncan test. A second spreadsheet displays the critical ranges between
ordered means, given the respective alpha
level (by default p < .05).
This test is based on the same logic as the Newman-Keuls procedure, however,
it uses a less conservative test criterion (see, for example, Milliken
& Johnson, 1984).
Alpha level for critical
ranges. Enter the desired Alpha
level for critical ranges into the edit field or use the microscrolls.
The default alpha level is .05. This option applies only to the
Newman-Keuls test & critical ranges
button and the Duncan's multiple range
test & critical ranges button.
Tukey
honest significant difference (HSD). Click this
button to produce a spreadsheet with the post-hoc p-values
for the Tukey HSD test. This test falls between the Newman-Keuls and Scheffé
procedures with regard to conservatism.
Tukey
HSD for unequal N (Spjotvoll & Stoline). Click this button to produce a spreadsheet with
the post-hoc p-values for the
Tukey HSD test. This test is a generalization of Tukey's test to the case
of unequal sample sizes (see Spjotvoll & Stoline, 1973, p. 975).
p-value for highlighting.
Enter the desired critical p-value
for highlighting into the edit field or use the microscrolls.
In all results spreadsheets, significant differences are highlighted.
The default p-value
for highlighting is .05.
For more details on p-value,
see Elementary
Concepts.