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gtlamcdf

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G 't Lam's cumulative distribution function.

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Returns the 't Lam's G cumulative distribution function of K variances and V interested degrees of freedom at the values in X.
In 1941, William G. Cochran presented a one-sided upper limit variance outlier test to check homoscedasticity. The called C test is used to decide if a single variance estimation is significantly larger than a group of variances and accounts for all variances within the range.

However, as 't Lam (2010) pointed out, the C test has limitations. It only applies to data sets of equal size. It uses critical values that are only available for the upper tail of the variance distribution, at selected numbers of data sets, selected numbers of replicates per set and only at two significance levels. Also, it will not identify an outlying low variance, but may mistake a high variance for an outlier instead. 't Lam (2010) transforms the C test into a more general 'G test'. It allows us to calculate upper limit as well as lower limit critical values for data sets of equal and unequal size at any significance level. The G test appears superior to the C test in detecting effects from low variances. The G test allows positive identification of exceptionally low variances.

For k balanced samples. The GTLAMCDF gives exactly the cdf Cochran's C upper limit.

Here a m-file analytical procedure is developed as an alternative to the homogeinity of variances test.

Syntax: function p = gtlamcdf(x,u,v,o)

Inputs:
x - 't Lam's G value
u - vector of degrees of freedom
v - degrees of freedom of the interested numerator variance;for the Cochran's ratio it corresponds to the largest variance value
o - side option (=1, both one-sided upper and lower limit by default;~=1, both two-sided lower and upper limit

Output:
p - cumulative distribition function

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