Calculates simultaneous confidence intervals for
ANOVA means (D.M. Smith).
|Controls printed output (
||Type of interval (
||Limit on the number of factors in each term; default 3|
||The required significance level; default 0.05|
||Save structure to provide the tables of means and associated information; default uses the save structure from the most recent
||Treatment terms whose means are to be required|
||Saves the means|
||Saves the lower limits|
||Saves the upper limits|
ACONFIDENCE calculates sets of simultaneous confidence intervals i.e. intervals whose formation takes account of the number of intervals formed, and the fact that the intervals are (slightly) correlated because of the use of a common variance (see Hsu 1996 and Bechhofer, Santner & Goldsman 1995). The methodology implemented in the procedure closely follows that described in Section 1.3 of Hsu (1996).
The type of interval to be formed is specified by the
METHOD option, with settings
smm (studentized maximum modulus),
individual setting calculates the intervals as if they were independent, each with the input probability. The
smm setting calculates the intervals as correlated, each with a probability adjusted for the multiplicity of intervals. The two settings
Bonferroni calculate the intervals as independent, but with a probability adjusted for the multiplicity of intervals. These two settings produce very similar intervals although the Bonferroni intervals are always slightly larger. The final setting
Scheffe calculates the intervals using pivoted F statistics; see Hsu (1996, Section 1.3.7). The default setting is
smm because it produces exact simultaneous confidence intervals.
TERMS parameter specifies a model formula to define the treatment terms whose means and confidence intervals are required. The means (and the necessary associated information) are usually taken from the most recent analysis of variance (performed by
ANOVA), but you can set the
SAVE option to a save structure from another
ANOVA if you want to examine means from an earlier analysis. As in
FACTORIAL option sets a limit on the number of factors in each term (default 3). Note: intervals cannot be formed for means whose effects are estimated in different strata.
MEANS parameter can save the means. If the
TERMS parameter specifies a single term,
MEANS should be set to a table. If
TERMS specifies several terms, you must supply a pointer which will then be set up to contain as many tables as there are terms. Similarly the
LOWER parameter can save the lower bounds of the confidence intervals, and the
UPPER parameter can save the upper bounds.
You can set option
PRINT=* to suppress printing of the intervals; by default
The methodology implemented is based on that described and reviewed in Hsu (1996), and Bechhofer, Santner & Goldsman (1995). For specific details of the tests these books should be referred to.
Bechhofer, R.E., Santner, T.J. & Goldsman, D.M. (1995). Design and Analysis of Experiments for Statistical Selection, Screening, and Multiple Comparisons. Wiley, New York.
Hsu, J.C. (1996). Multiple Comparisons Theory and Methods. Chapman & Hall, London.
Commands for: Analysis of variance.
CAPTION 'ACONFIDENCE example',!t('Hsu (1996), Multiple Comparisons,',\ 'Theory and Methods, Table 1.1'); STYLE=meta,plain FACTOR [LABELS=!t('20-29','30-39','40-49','50-59','60-69');\ VALUES=6(1...5)] Age VARIATE Standard,New; VALUES=\ !(57,53,28,60,40,48,70,85,50,61,83,51,55,36,31,28,41,32,\ 18,39,53,44,63,80,76,67,75,78,67,80),\ !(72,27,26,71,60,45,52,26,46,52,53,58,83,65,40,66,50,44,\ 40,55,70,55,61,60,60,37,45,58,54,69) TREATMENT Age ANOVA Standard-New ACONFIDENCE [METHOD=smm] Age ACONFIDENCE [METHOD=individual] Age ACONFIDENCE [METHOD=product] Age ACONFIDENCE [METHOD=bonferroni] Age ACONFIDENCE [METHOD=scheffe] Age