CONFIDENCE procedure

Calculates simultaneous confidence intervals (D.M. Smith).


Options

PRINT = string
Controls printed output (intervals); default inte

METHOD = string
Type of interval (individual, smm, product, Bonferroni, Scheffe); default smm

MU = scalar
Value for population mean checked as to whether in the confidence interval; default * i.e. no checking

PROBABILITY = scalar
The required significance level; default 0.05


Parameters

MEANS = tables or variates
Mean values

REPLICATIONS = scalars or tables or variates
Number(s) of observations per mean

VARIANCE = scalars
Estimate of variance

DF = scalars
Degrees of freedom

XCONTRASTS = matrices
Matrix of coefficients of orthogonal contrasts

LABELS = texts
Identifiers of mean values

LOWER = tables or variates
Lower values of confidence intervals

UPPER = tables or variates
Upper values of confidence intervals


Description

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 VARIANCE and 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 LOWER and 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 individual, smm (studentized maximum modulus), product (inequality), Bonferroni and 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 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 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.

   The MU option allows you to 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 METHOD.

You can set option PRINT=* to suppress printing of the intervals; by default PRINT=intervals.


Options: PRINT, METHOD, MU, PROBABILITY.

Parameters: MEANS, REPLICATIONS, VARIANCE, DF, XCONTRASTS, LABELS, LOWER, UPPER.


Method

The methodology implemented is based on that described and reviewed in Hsu (1996), and Bechhofer, Santner & Goldsman (1995).


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.