Statistics by
Groups Results - ANOVA & Tests tab
Breakdown:
Descriptive Statistics by Groups
Select the ANOVA
& tests tab in the Statistics
by Groups Results dialog box to access options to perform ANOVAs
and test ANOVA
assumptions.
Analysis
of Variance. Click this
button to produce a spreadsheet with the results of univariate
analyses of variance for each dependent variable. If statistically significant,
it can be concluded that the means across the groups are different in
magnitude; use the options on the Post-hoc tab to identify significant
differences between individual groups (means). Note that if multiple categorical
factors are specified, Statistica computes the
one-way analysis of variance treating the interaction of the multiple
factors as a single group. This is equivalent to investigating the interaction
among multiple factors. Use the General
Linear Model (GLM) or ANOVA/MANOVA module to compute complete
univariate and multivariate analysis of variance tables (see also Methods
for analysis of variance). However, note that the one-way ANOVA available
from this dialog box is particularly suited for quickly analyzing one-way
univariate designs with very many groups.
Perform Welch's F-Test.
Select this check box to include the computation of Welch's F statistic
to test for equality of means when the variances are unequal.
Tests
of homog. of variances. Two tests for the homogeneity of
variance assumption are available in this group box. For more information
on the importance of the homogeneity of variance assumption, see Homogeneity
of Variances in the ANOVA/MANOVA
module.
Levene test. Click the Levene test button to produce a spreadsheet
containing the Levene
test for each selected dependent variable. The significance tests
reported by the Analysis of variance
option (see above) are based on the assumption that the variances in the
different groups are the same (homogeneous). A powerful statistical test
of this assumption is Levene's
test (however, see also the description of the Brown-Forsythe
modification of this test below). For each dependent variable, an analysis
of variance is performed on the absolute deviations of values from the
respective group means. If the Levene test is statistically significant,
the hypothesis of homogeneous variances should be rejected. Note that
the F statistic (in ANOVA) provides
a robust test for mean differences as long as 1) the N
per group is greater than 10 (and, in particular, in the case of equal
N), and 2) the means
across groups are not correlated with the standard
deviations across groups. (The assumption of uncorrelated means and
standard deviations can easily be checked by producing the Plot
of means vs. standard deviations from this tab.) Thus, a significant
Levene test does not necessarily call into question the validity of the
ANOVA results. Also, in the case of unbalanced designs (i.e., unequal
N per group), the Levene test
is itself not very robust, as has recently been pointed out in, for example,
Glass and Hopkins (1996; see also the description of the Brown-Forsythe
tests option).
Brown-Forsythe tests. Click
the Brown & Forsythe tests button
to produce a spreadsheet containing the Brown
& Forsythe test for each selected dependent variable. The significance
tests reported by the Analysis of Variance
option are based on the assumption that the variances in the different
groups are the same (homogeneous). A powerful statistical test of this
assumption is provided via the Levene's
test (homogeneity of variances) option. Recently, some authors (e.g.,
Glass and Hopkins, 1996) have called into question the power of the Levene
test for unequal variances. Specifically, the absolute deviation (from
the group means) scores can be expected to be highly skewed; thus, the
normality assumption for the ANOVA of those absolute deviation scores
is usually violated. This poses a particular problem when there is unequal
N in the two (or more) groups that are to be compared. A more robust test
that is very similar to the Levene test has been proposed by Brown and
Forsythe (1974). Instead of performing the ANOVA on the deviations from
the mean, you can perform the analysis on the deviations from the group
medians. Olejnik
and Algina (1987) have shown that this test gives quite accurate error
rates even when the underlying distributions for the raw scores deviate
significantly from the normal
distribution. However, recently, Glass and Hopkins (1996, p. 436)
have pointed out that both the Levene test and the Brown-Forsythe modification
suffer from what those authors call a "fatal flaw," namely,
that both tests rely on the homogeneity of variances assumption (of the
absolute deviations from the means or medians), and hence, it is not clear
how robust these tests are in the presence of significant variance heterogeneity
and unequal N.
p-value
for highlighting. The
default p-value
for highlighting is .05.
You can adjust this p-value by
entering a new value in the edit box or using the microscrolls.
For more details on p-value,
see Elementary
Concepts.
Categorized
normal prob. plots. Click this button to produce a cascade
of normal
probability plots for the selected dependent variables, categorized
by the grouping
variables. The standard variable
selection dialog box is first displayed if more than one dependent
variable has been selected via the Variables option. See
also the ANOVA
overview for an explanation of the normality assumption.
Categorized
half-normal p-plots. Click this button to produce a cascade
of half-normal
probability plots for the selected dependent variables, categorized
by the grouping variables. The standard variable selection dialog box
is first displayed if more than one dependent variable has been selected
via the Variables
option.
Categorized
detrended p-plots. Click this button to produce a cascade
of detrended
normal probability plots for the selected dependent variables, categorized
by the grouping variables. The standard variable
selection dialog box is first displayed if more than one dependent
variable has been selected via the Variables option.
Plot
of means vs. std. devs. Click this button to plot the means for selected variables
across groups against the respective standard
deviations. The standard variable selection dialog box is first displayed
if more than one dependent variable has been selected via the Variables option. This
plot is useful in order to spot potential outliers
among the means that may contribute to an erroneous conclusion of statistically
significant differences between means. One of the most common and most
serious violations of assumptions
for ANOVA is when the means are correlated
with the standard deviations across groups. For example, suppose there
are 5 groups of 10 observations each. If in one group, two observations
are extreme outliers, the variance
in that group will be much larger and the mean will be very different
(larger or smaller) from the grand mean. However, for the overall F test (ANOVA) the pooled (averaged)
within-group variance is taken as an estimate of the error variance. Thus,
the reliability of the outlier mean will be overestimated, and the ANOVA
may erroneously yield a significant F
statistic.
Interaction
plots. Click this button to produce an interaction plot
of means by groups. Interaction plots are produced according to the following
specifications, within the levels of any additional grouping factors.
More than one dependent variable was
selected for the current analysis. In this case, when you click
on the Interaction plots button,
the resulting Select
the Variables for Interaction Plot dialog box displays each
of the previously selected dependent variables. You can select only those
variables that you want plotted, or click OK
to accept the default selection (all variables in the list); each variable
in the resulting interaction plots is represented by a different line
color or pattern. Clicking OK
in this dialog box displays the Arrangement
of Factors dialog box (see below).
One dependent variable was selected
for the current analysis. Since you have already selected the dependent
variable to plot, when you click the Interaction
plots button, the Arrangement of Factors
dialog box is displayed (see below). In this interaction plot, the grouping
variables are represented by different line colors and patterns.
Arrangement of factors dialog box.
Once you select the variables (see above) to be plotted, the Arrangement of Factors
dialog box is displayed, where you can assign two (if two or more dependent
variables are selected) or three (if one dependent variable is selected)
grouping variables to different aspects of the interaction plot (line
pattern, lower x-axis, upper x-axis).
Plot confidence intervals for the mean.
Select this check box to display the confidence
interval for the mean (error bars) on the Interactions
plots. Use the corresponding field to specify the exact confidence
interval for the mean to be used on the plot. The default value is 95%.