The Moses Extreme Reaction test/Moses 极端反应检验/Moses の極値反応の検定

Moses极端反应检验：
它适用于实验条件导致两个不同方向的极端反应情况（多用于医学，比如有的药物会导致一部分病人好转的同时也会导致一部分病人恶化）。
它通过比较实验组和观察组，会告诉你是否产生了极端反应

For two independent samples from a continuous field, this tests:
H0: Extreme values are equally likely in both populations
HA: Extreme values are more likely to occur in the population from which the sample with the larger range was drawn.

Span computation

Observations from both specified groups are jointly sorted and ranked, with the average rank being assigned in the case of ties. The smallest and largest ranks of the control group (the group defined by the first value in ascending order) are determined, and the span is computed as

 SPAN = The largest rank of control group-the smallest rank of control group  + 1 

If SPAN is not an integer, then it will be rounded to its nearest integer.

Significance Level

Let nc,f and ne,f be the numbers of records in the control group and experiment group respectively, incorporating the frequency weight, and g= SPAN - nc,f+2h. Then the exact one-tailed probability of span s is

where h=0. The same formula is used below where h is not zero.

Censoring the Range

The previous test is repeated, dropping the h lowest and h highest ranks from the control group, where h is a positive user-specified integer (default at the integer part of 0.05nc,f or 1, whichever is greater). If 2h>nc,f−2, then the test will be implemented using the largest integer such that 2h≤(nc,f−2).

The exact one-tailed probability is calculated by the formula above, and p1≤α rejects the null hypothesis.

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