Badr Alghamdi
العربية
Lessons

Multiple comparisons: three differences looked real, one survives the family

Type each comparison with its difference and standard error, then the family size. Of three differences at 3.0, 2.6 and 2.2 in a family of 8, one survives, and the rest are not called false.

Your prediction before the experiment

A difference that clears one interval keeps clearing it when more comparisons join the declared family. The family-size trace is visible. Move its control once to reveal which statements remain established.
A difference that clears one interval keeps clearing it when more comparisons join the declared family. The family-size trace is visible. Move its control once to reveal which statements remain established.

What stays the same

Typed statements
Their estimates, standard errors and the order you typed
Criterion
The same direction, threshold and family confidence
Only movement
The number of statements in the declared family

Try a scenario

The family-size trace

Statements surviving at each checked family sizeThe declared family contains 8 comparisons and 1 statements survive. The step line shows how that survivor count changes as the declared family grows.0123Surviving statementscurrent familysurvivors148Declared family size
8 comparisons

This whole count alone moves the chart. It may exceed the number of rows shown here.

Typed criterion and statements

Favourable direction

%
Comparison rows
Comparison 1
Comparison 2
Comparison 3

Boundary

The calculation names statements that survive the typed family criterion. It does not score or rank suppliers, select a winner, or call another statement false.

Here is the maths

The formula, in words

Turn the family confidence into alpha. Divide alpha across both interval tails and all statements in the declared family, then multiply that normal critical value by each typed standard error. For higher, the lower edge must be strictly above the threshold. For lower, the upper edge must be strictly below it.

Mi=z(1−α2 m) SEiM_i = z\left(1-\frac{\alpha}{2\,m}\right)\,\mathrm{SE}_i

where MiM_i is the margin for one statement, zz the normal critical value, α\alpha the family alpha, mm the declared family size, and SEi\mathrm{SE}_i the typed standard error.

A worked example

At 95% family confidence and family size 8, the two-sided critical value is about 2.73. With standard error 1, the lower edges for estimates 3.0, 2.6 and 2.2 are about 0.27, -0.13 and -0.53. Only the first is strictly above threshold 0, so 1 statement survives.

What this does not model

The intervals do not rank suppliers, establish that an excluded statement is false, choose a confidence level, test dependence, or replace the family you declared with only the rows currently displayed.

What the sweep checks

Every whole family size from 1 through the declared size is checked. The first point where a supplier name disappears is reported, and names always remain in typed order.

Source basis

The method is standard simultaneous inference using Bonferroni family confidence mathematics and the union bound. No definition or procedure from sold guidance is reproduced.

Any score, rank, weight, or winner field remains outside this lesson and receives no answer.

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