ACONFIDENCE procedure

Calculates simultaneous confidence intervals for ANOVA means (D.M. Smith).

Options

Parameters

Description

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 individual, smm (studentized maximum modulus), product (inequality), Bonferroni and Scheffe. The 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 product and 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.

The 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 ANOVA, the 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.

The 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 PRINT=intervals.

Options: PRINT, METHOD, FACTORIAL, PROBABILITY, SAVE.

Parameters: TERMS, MEANS, LOWER, UPPER.

Method

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.

References

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.

See also

Directive: ANOVA.

Procedures: AMCOMPARISON, CONFIDENCE.

Commands for: Analysis of variance.

Example

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