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Using the EXCEL spreadsheet to compute the HC4-based bootstrap estimate (estimate 2.3) of Ng and Wilcox (2010)

The spreadsheet on the previous page uses the recommended approach of Ng and Wilcox (2010) using their model 2.3 which they found controls for type I error when assumptions underlying regression analysis are relaxed. In particular it evaluates the t-statistic for the x by group interaction term over a series of bootstrap samples generated by a bootstrap macro which you need to add-in to EXCEL which you an download from here. Details of how to add this into EXCEL (only needs to be done once on your PC) are given on the website and in a MS Word document downloaded from this website given here. When correctly installed it should appear in the top left hand corner when you select the 'Add-Ins' tab at the top of the spreadsheet.

Once you have got the bootstrap macro read in you are ready to go. Details of how to compute the HC4 estimate and its bootstrap equivalent (estimates 2.2 and 2.3 respectively of Ng and Wilcox, 2010) are given in the MS Word document located here. The HC4 estimate is regarded as bring more robust when assumptions underlying multiple regression are violated (Cribari-Neto, 2004) in moderation alaysis. Ng and Wilcox have subsequently suggested that the bootstrap variant of HC4 better controls type I error rate.


Cribari-Neto, F. (2004). Asymptotic inference under heteroscedasticity of unknown form. Computational Statistics and Data Analysis 45 215-233.

Ng, M. and Wilcox, R.R. (2010). Comparing the regression slopes of independent groups. British Journal of Mathematical and Statistical Psychology 63 319-340.

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