Statistics Toolbox

barttest

Bartlett's test for dimensionality

Syntax

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

Description

ndim = barttest(x,alpha) returns the number of dimensions necessary to explain the nonrandom variation in the data matrix x, using the significance probability alpha. The dimension is determined by a series of hypothesis tests. The test for ndim=1 tests the hypothesis that the variances of the data values along each principal component are equal, the test for ndim=2 tests the hypothesis that the variances along the second through last components are equal, and so on.

[ndim,prob,chisquare] = barttest(x,alpha) returns the number of dimensions, the significance values for the hypothesis tests, and the ² values associated with the tests.

Example

• x = mvnrnd([0 0],[1 0.99; 0.99 1],20);
  x(:,3:4) = mvnrnd([0 0],[1 0.99; 0.99 1],20);
  x(:,5:6) = mvnrnd([0 0],[1 0.99; 0.99 1],20);
  [ndim, prob] = barttest(x,0.05)
  ndim =
       3
  prob =
           0
           0
           0
      0.5081
      0.6618
  

See Also
princomp, pcacov, pcares

aoctool

bbdesign