The ANOVA F-test to compare the means of k normally distributed populations is not applicable when the variances are unknown. 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). The bootstrap procedure here addressed is the parametric one: one-way random or fixed model with the usual normality assumptions and heterogeneous error variances. According to Lee (1994), the parametric bootstrap results are more accurate that the nonparametric.
Here, we develops the m-function of the Krishnamoorthy et al. (2007) parametric bootstrap approach for ANOVA with unequal variances. According to its results. It is the best among other three compared tests with respect to the Type I error rates.
Syntax: function pbootkanovahet(x,s,alpha)
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)
- Summary statistics from the samples
- Decision on the null-hypothesis tested