Nordvästra Skånes Vatten och Avlopp (Sweden)

Mielke etal. (2021) proposed a stepwise multiple testing procedure (MTP) based on marginal p-values for rejecting at least k out of m null hypotheses. Briefly, the MTP cannot reject less than k hypotheses, but this property improves the power to reject k or more hypotheses relative to the stepdown MTP of Holm (1979). Mielke etal. discussed why such an MTP is of interest in the context of biosimilarity developments. This article describes how a slight modification of Holm's simple direct arguments can be used as an alternative to the closed-testing arguments of Mielke etal. to show the strong control of the family-wise error rate. This modification is based on a Holm-type formulation of the rejection algorithm where each step involves a single ordered p-value. With k equal to one, the stepwise MTP reduces to Holm's stepdown MTP. The MTP is valid quite generally. A version of the MTP with weights for hypotheses is also described and discussed. As in the case without weights: (a) a modification of Holm's arguments can be used; (b) with k equal to one, the MTP reduces to Holm's MTP with weights; and (c) the MTP is valid quite generally.

Process residuals, sludge with high oil content, were treated by composting. In lab-scale (100 litre) trials initial oil con centrations (30 to 50 g kg-1 dry matter) were, depending on composting conditions, reduced 55 to 90% during a period of 60 to 120 days.