Goodness of fit test

[Roxie]

Hi
Does anyone know what type of goodness of fit test is performed in Design Expert when I run a linear and quadratic two-way anova design with 3 factors, 4 levels and 5 replications per level?
Is it Kolmogorov-Smirnov, Anderson-Darling, Chi-Squared or any other test?

Or could someone give me more information of how Design Expert calculates the goodness of fit test?

Thanks a lot

[Wayne]

Design-Expert performs a lack-of-fit test rather than a goodness of fit test. The variation between the model and the average observation is compared with the variation between replicates and their average. The ratio between the two variances follows an F-distribution. The F-statistic is calculated by dividing the Mean Square due to lack-of-fit by the Mean Square due to replicate variation.

Significant lack-of-fit indicates the model may not fit the data well.

For more details please see. http://www.statease.com/news/faqalert6-07.html

[Roxie]

Hello Wayne
Thanks for your answer

Could you please tell me if the next formula is the one used in the lack of fit test in Design Expert?
If not, could you correct it for me?

(pe stands for pure error)
ANOVA for lack of fit
______________DF________________SS_______________MS______________________F__________
Residual_______n-p________________RSS_________________________________________________
Lack of fit_____n-p-df(pe)__________RSS-SS(pe)_______(RSS-SSpe)/(n-p-dfpe)_____Ratio of MS
Pure Error_____df(pe)______________SS(pe)___________SSpe/dfpe___________________________

[Wayne]

There are some inconsitencies in your nomenclature, but that looks correct if parenthesis are matched up.