boothomvargr

Bootstrap Homogeinity of Variances Test Graphical Approach.

The bootstrap is a way of estimating the variability of a statistic from a single data set by resampling it independently and with equal probabilities (Monte Carlo resampling). Allows the estimation of measures where the underlying distribution is unknown or where sample sizes are small. Their results are consistent with the statistical properties of those analytical methods (Efron and Tibshirani, 1993).

The name 'bootstrap' originates from the expression 'pulling yourself up by your own bootstraps' and refers to the basic idea of the bootstrap, sampling with replacement from the data. In this way a large number of 'bootstrap samples' is generated, each of the same size as the original data set. From each bootstrap sample the statistical parameter of interest is calculated (Wehrens and Van der Linden, 1997)

Here, we use the Non-parametric Bootstrap. Non-parametric bootstrap is simpler. It does not use the structure of the model to construct artificial data. The data is instead directly resampled with replecement.

The homogeneity of variances test is a useful tool in many scientific applications. Boos and Brownie (2004) and Conover et al. (1981) give a broad review.

As Kumar et al. (Forthcoming issue, 2011) did, here a m-file graphical procedure using bootstrap method is developed as an alternative to the homogeinity of variances test.

BOOTHOMVARGR treats NaN values as missing values, and removes them.

Syntax: function boothomvargr(x,s,alpha)

Inputs:
x – data nx2 matrix (Col 1 = data; Col 2 = sample code)
s - boot times or number of Bootstrap simulations (resamplings)
alpha - significance level (default=0.05)

Outputs:
- Summary statistics from the samples
- Graphics of the bootstrap procedure to test equality of variances (Null-hypothesis is rejected if any of the variances lie ouside the decision lines)