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barttest

Bartlett’s test

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Syntax

ndim = barttest(x,alpha)
[ndim,prob,chisquare] = barttest(x,alpha)

Description

example

ndim= barttest(x,alpha)returns the number of dimensions necessary to explain the nonrandom variation in the data matrixxat thealphasignificance level.

example

[ndim,prob,chisquare] = barttest(x,alpha)also returns the significance values for the hypothesis testsprob, and theχ2values associated with the testschisquare.

Examples

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Open Live Script

Generate a 20-by-6 matrix of random numbers from a multivariate normal distribution with meanmu = [0 0]and covariancesigma = [1 0.99; 0.99 1].

rngdefault% for reproducibilitymu = [0 0]; sigma = [1 0.99; 0.99 1]; X = mvnrnd(mu,sigma,20);% columns 1 and 2X(:,3:4) = mvnrnd(mu,sigma,20);% columns 3 and 4X(:,5:6) = mvnrnd(mu,sigma,20);% columns 5 and 6

Determine the number of dimensions necessary to explain the nonrandom variation in data matrixX. Report the significance values for the hypothesis tests.

[ndim, prob] = barttest(X,0.05)
ndim = 3
prob =5×10.0000 0.0000 0.0000 0.5148 0.3370

The returned value ofndimindicates that three dimensions are necessary to explain the nonrandom variation inX.

Input Arguments

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Input data, specified as a matrix of scalar values.

Data Types:single|double

Significance level of the hypothesis test, specified as a scalar value in the range(0,1).

Example:0.1

Data Types:single|double

Output Arguments

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Number of dimensions, returned as a positive integer value. The dimension is determined by a series of hypothesis tests. The test forndim = 1tests the hypothesis that the variances of the data values along each principal component are equal, the test forndim = 2tests the hypothesis that the variances along the second through last components are equal, and so on. The null hypothesis is that the number of dimensions is equal to the number of the largest unequal eigenvalues of the covariance matrix ofx.

Significance value for the hypothesis tests, returned as a vector of scalar values in the range(0,1). Each element inprobcorresponds to an element ofchisquare.

测试统计数据为每个dimension’s hypothesis test, returned as a vector of scalar values.

Version History

Introduced before R2006a