Calculates simultaneous confidence intervals (D.M. Smith).
|Controls printed output (
||Type of interval (
||Value for population mean checked as to whether in the confidence interval; default
||The required significance level; default 0.05|
||Number(s) of observations per mean|
||Estimate of variance|
||Degrees of freedom|
||Matrix of coefficients of orthogonal contrasts|
||Identifiers of mean values|
||Lower values of confidence intervals|
||Upper values of confidence intervals|
CONFIDENCE calculates a set 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 means are input using the
MEANS parameter, either in a table saved e.g. from
AKEEP, or in a variate. The replication (or number of observations in each mean) is supplied by the
REPLICATIONS parameter, either in a scalar (if all the replications are equal) or in a structure of the same type as the means. The estimate of the variance (usually a pooled estimate as given by the residual mean square in
ANOVA, and accessible using the
VARIANCE parameter of
AKEEP) and its corresponding degrees of freedom are input as scalars using the
DF parameters respectively. Confidence limits can be formed for contrasts amongst the means by supplying the matrix defining the contrasts using the
XCONTRASTS parameter. Each row of the matrix contains a contrast similarly to the specification in the
REG function in
ANOVA but, unlike
REG, the contrasts must all be orthogonal. The
LABELS parameter can be used to supply labels for the means or for the contrasts, while the
UPPER parameters allow the limits of the confidence intervals to be saved.
The type of interval to be formed is specified by the
METHOD option, with settings
smm (studentized maximum modulus),
Scheffe. The setting
individual calculates the intervals as if they were independent, each with the input probability. The setting
smm 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 privoted F statistics. Hsu (1996, Section 1.3.7) should be referred to for details of this last setting. The default setting is
smm because it produces exact simultaneous confidence intervals.
MU option lets you supply a (population) mean to be tested for inclusion in each interval, and the
PROBABILITY option allows the experiment-wise significance level for the intervals to be changed from the default of 0.05 (i.e. 5%). The interval-wise significance level is calculated according to the setting of
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).
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 'CONFIDENCE example',!t('1) 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 AKEEP Age; MEAN=Mean; REP=Rep; VARIANCE=Var; RTERM=Units AKEEP #Units; DF=Resdf CONFIDENCE [METHOD=smm] Mean; REP=Rep; VARIANCE=Var; DF=Resdf CONFIDENCE [METHOD=individual] Mean; REP=Rep; VARIANCE=Var; DF=Resdf CONFIDENCE [METHOD=product] Mean; REP=Rep; VARIANCE=Var; DF=Resdf CONFIDENCE [METHOD=bonferroni] Mean; REP=Rep; VARIANCE=Var; DF=Resdf CONFIDENCE [METHOD=scheffe] Mean; REP=Rep; VARIANCE=Var; DF=Resdf CAPTION '2) Bechhofer, Santner & Goldsman (1995), Example 4.2.5.' FACTOR [LEVELS=!(0,4,8,12)] Labels TABLE [CLASSIFICATION=Labels; VALUES=34.8,41.1,42.6,41.8] Means TEXT [NVALUES=3] CLabels; VALUES=!T('Linear','Quadratic','Cubic') MATRIX [ROWS=CLabels; COLUMNS=4; VALUES=-3,-1,+1,+3,+1,-1,-1,+1,-1,+3,-3,+1]\ Contrasts CONFIDENCE [METHOD=BONFERRONI] Means; REPLICATIONS=8; VARIANCE=11.9; DF=28;\ XCONTRASTS=Contrasts CONFIDENCE [METHOD=SMM] Means; REPLICATIONS=8; VARIANCE=11.9; DF=28;\ XCONTRASTS=Contrasts CONFIDENCE [METHOD=PRODUCT] Means; REPLICATIONS=8; VARIANCE=11.9; DF=28;\ XCONTRASTS=Contrasts CONFIDENCE [METHOD=SCHEFFE] Means; REPLICATIONS=8; VARIANCE=11.9; DF=28;\ XCONTRASTS=Contrasts CONFIDENCE [METHOD=INDIVIDUAL] Means; REPLICATIONS=8; VARIANCE=11.9; DF=28;\ XCONTRASTS=Contrasts