Moses Extreme Reactions Calculator

Calculator inputs

Group A sample

Use commas, spaces, semicolons, or new lines.

Group B sample

Each group should contain at least two values.

Trim per tail Significance level

Automatic trimming uses 5% per tail, capped so at least two control observations remain.

Example data table

Row	Group A	Group B
1	5	11
2	8	12
3	9	13
4	12	14
5	15	15
6	18	16
7	22	17
8	30	18

This example gives Group A visibly wider extremes. Use the example button to load these values into the calculator.

Formula used

1. Pooled order: Combine both groups and sort all observations into one sequence.

2. Untrimmed span: Span = max_position - min_position + 1

3. Trimmed span: Trimmed Span = position[m - t] - position[t + 1] + 1

4. Exact span probability:


                P(S_t = s) =
                [ Σ C(a - 1, t) × C(s - 2, m - 2t - 2) × C(N - a - s + 1, t) ] / C(N, m)

where N is the pooled size, m is the control size, t is trim per tail, and s is the observed span.

5. Exact one-tailed p-value: sum exact probabilities for all spans at least as large as the observed span.

Larger spans indicate that one group places more observations near both tails of the pooled order, which is the signal targeted by the Moses test.

How to use this calculator

Paste one numeric sample into Group A and the other into Group B.
Leave trimming blank for automatic 5% tail trimming or enter a whole number.
Choose a significance level such as 0.05.
Click Calculate Moses Test.
Review the primary result summary placed above this form.
Compare both directional panels because the stronger span usually identifies the group with more extreme reactions.
Use the pooled order table to audit every observation position.
Export the result summary as CSV or PDF for reporting.

Important notes

The method is intended for two independent samples.
The classic exact interpretation assumes a continuous scale with no ties.
This page keeps tied values in sorted order without tie corrections.
Trimming protects the result from a few extreme control observations.
For very large samples, exact span calculations may still be slower than simpler rank tests.

FAQs

1. What does the Moses extreme reactions test measure?

It checks whether one independent sample places more observations near both tails of the pooled order. That means the sample shows stronger extreme reactions or wider spread in rank positions.

2. When should I use this test?

Use it when two independent groups may differ mainly in extremity rather than central tendency. It is helpful when treatment can push some cases unusually high and others unusually low.

3. Why does the calculator show both directions?

The span depends on which group is treated as control. Showing both directions makes comparison transparent and helps you identify which group carries the stronger extreme-reaction pattern.

4. What does trimming do?

Trimming removes a chosen number of control observations from each tail before recomputing span. This reduces sensitivity to a very small number of extreme outliers.

5. What p-value does this calculator report?

It reports an exact one-tailed p-value for spans at least as large as the observed span. Smaller values suggest stronger evidence that the selected control group contains more extreme reactions.

6. Can I use tied values?

You can enter ties, but classic exact assumptions are strongest without them. This calculator preserves sorted order and does not apply separate tie corrections, so interpret tied datasets with caution.

7. How many observations do I need?

At minimum, each group needs two observations. In practice, somewhat larger samples are better because extremely small groups can make trimming impossible or the test less informative.

8. Is this the same as testing group means?

No. Mean tests focus on average shifts. The Moses test focuses on how strongly observations stretch toward the low and high tails of the pooled sequence.