2015 Schield SS ShortcutsV0C 1

byMilo Schield

StatChat Feb 24, 2015

Slides at: www.StatLit.org/pdf/

2015-Schield-StatChat-Slides.pdf

Statistically-SignificantShortcuts

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Background & Goal

Statistical significance is one of statistics’ big ideas.

For Z-scores, statistical significance is a single value.For Chi-squared and the student-T, it is a function.For correlation and relative risk, its a complex function.

We need to focus on “big ideas” in random sampling.

Goal: To create “shortcut” formulas for statistical significance that are sufficient and memorable.

2015 Schield SS ShortcutsV0C

If |p2 - p1| > 1/Sqrt(n), then that difference is statistically significant

Q. Has anyone seen this shortcut? Where?

Yes! Seeing Through Statistics by Jessica Utts.

Q. Anywhere else?

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#1: Proportions Shortcut (SS)

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Chi-Squared 2(df+1)

Has anyone seen this shortcut anywhere?

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5

10

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Chi-s

quar

ed

Degrees of Freedom

Chi-Squared ShortcutStatistically-Significant

Chi-squared > 2(DF+1)

Actual Cutoffs

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Has anyone seen this shortcut anywhere?

Shortcut Margin of Errorfor Correlation: 2/Sqrt(N)

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0 50 100 150 200 250 300Sample Size (# of Pairs)

Correlation Shortcut (S/S)

Model (2 tail): r > 2/Sqrt(N) for #Pairs > 10r > 2/Sqrt(N-1) for #Pairs > 4

Error < 5%

Solid is the ModelDashed is Actual

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Consider two groups each of size n.Relative Risk: RR = p2/p1

RR>1 is statistically significant ifRR-1 = 2/sqrt(k1)

where k1 = n*p1 >4

Has anyone seen this shortcut anywhere?

Relative-Risk Shortcut (SS)

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T-Z: Actual vs. Model

Has anyone seen this shortcut anywhere?

1.5

2.0

2.5

3.0

3.5

4.0

2 4 6 8 10

T

Degrees of Freedom

Shortcut for 2-tail T

Actual

Model: T > 1.645 + 2/(df-1)

2015 Schield SS ShortcutsV0C

What are the costs in teaching these sufficient shortcuts for statistical significance? 1. |p2-p1| > 1/sqrt(n)2. Chi-squared: Χ2 > 2(df+1)3. Correlation: r > 2/sqrt(n-1) for n > 44. RRisk > 1+ 2/sqrt(k1): k1=n*p1, p1<p25. t-stat (2-tail): t > 1.645 + 2/sqrt(df-1)

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Question