IDL Analyst Reference Guide: Analysis of Variance

IMSL_MULTICOMP

The IMSL_MULTICOMP function performs Student-Newman-Keuls multiple-comparisons test.

Syntax

Result = IMSL_MULTICOMP(means, df, std_error [, ALPHA=value]
[, /DOUBLE])

Return Value

A one-dimensional array of length N_ELEMENTS(means) indicating the size of the groups of means declared to be equal. If the i-th element of the returned array is equal to j, then the i-th smallest mean and the next j – 1 larger means are declared equal. If the i-th element of the returned array is equal to 0, then no group of means starts with the i-th smallest mean.

Arguments

df

Degrees of freedom associated with std_error.

means

One-dimensional array containing the means.

std_error

Effective estimated standard error of a mean. In fixed effects models, std_error equals the estimated standard error of a mean.

For example, in a one-way model:

where s² is the estimate of s² and n is the number of responses in a sample mean. In models with random components, use:

where sedif is the estimated standard error of the difference of two means.

Keywords

ALPHA

Significance level of test. Must be in the interval [0.01, 0.10]. Default: Alpha = 0.01

DOUBLE

If present and nonzero, then double precision is used.

Discussion

The IMSL_MULTICOMP function performs a multiple-comparison analysis of means using the Student-Newman-Keuls method. The null hypothesis is equality of all possible ordered subsets of a set of means. This null hypothesis is tested using the Studentized range of each of the corresponding subsets of sample means. The method is discussed in many elementary statistics texts, e.g., Kirk (1982, pp. 123–125).

Example

A multiple-comparisons analysis is performed using data discussed by Kirk. The results show that there are three groups of means with three separate sets of values: (36.7, 40.3, 43.4), (40.3, 43.4, 47.2), and (43.4, 47.2, 48.7).

df = 45   
std_error = 1.6970563   
means = [36.7, 48.7, 43.4, 47.2, 40.3]   
equal_means = IMSL_MULTICOMP(means, df, std_error)   
PM, equal_means, Title = 'Size of groups of means:'   
  
Size of groups of means:   
    3   
    3   
    3   
    0