Sample Size Determination for Testing the Variance Compound in a One-Way Random Effects Model

摘要

Towarranthighqualityofindustriallyproducedfood,forsomeoftheingredientswewanttoprovethatthevariationbetweensamplesdoesnotexceedacertainlimit.Forthispurpose,asamplingschemewithnsamplesanalyzedk-timeseachisemployed.Datafromacorrespondingexperimentcanbeanalyzedusingaone-wayrandomeffectsmodel.Weareprimarilyinterestedinthevariationoftherandomeffectandwanttoshowthatthisvariationissufficientlysmall.Theobjectiveofthispaperistodeterminetheoptimalcombinationofnandksuchthatthepowerofacorrespondingtestissufficientlyhighwhilethetotalnumberofanalyzesnkisminimized.Tothisend,weconsiderboththeclassicalapproximateupperconfidencelimitandatestbasedongeneralizedp-values,andwederivethedistributionsoftherespectivestatistics.Thisallowsustodeterminethepowerofthecorrespondingtestsbymeansofsimulations.Itisfoundthattheapproachbasedongeneralizedp-valuesismorepowerfulthantheclassicalone.Finally,samplingrecommendationsaregivenbasedonpriorestimatesonthewithinandbetweensamplesvariation.