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Statistics Formula Sheet: STA 13, Cheat Sheet of Mathematics

Mathematics

common formula sheet for statistics.

Typology: Cheat Sheet

2022/2023

Uploaded on 12/04/2023

jim-zhu 🇺🇸

1 document

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Formula Sheet

STA 13

• Mean: 𝑥𝑥 =∑𝑥𝑥𝑖𝑖

𝑛𝑛

• Variance: 𝑠𝑠2=∑(𝑥𝑥𝑖𝑖−𝑥𝑥)2

𝑛𝑛−1

• Weighted Mean: 𝑥𝑥 =∑𝑤𝑤∙𝑥𝑥

∑𝑤𝑤

• Addition Rule: 𝑃𝑃(𝐴𝐴 ∪ 𝐵𝐵)=𝑃𝑃(𝐴𝐴)+𝑃𝑃(𝐵𝐵)− 𝑃𝑃(𝐴𝐴 ∩ 𝐵𝐵)

• Multiplication Rule: 𝑃𝑃(𝐴𝐴 ∩ 𝐵𝐵)=𝑃𝑃(𝐴𝐴)𝑃𝑃(𝐵𝐵|𝐴𝐴)

• Conditional Rule: 𝑃𝑃(𝐴𝐴|𝐵𝐵)=𝑃𝑃(𝐴𝐴∩𝐵𝐵)

𝑃𝑃(𝐵𝐵)

• Bayes’ Rule: 𝑃𝑃(𝐴𝐴|𝐵𝐵)=𝑃𝑃(𝐴𝐴)𝑃𝑃(𝐵𝐵|𝐴𝐴)

𝑃𝑃(𝐴𝐴)𝑃𝑃(𝐵𝐵|𝐴𝐴)+𝑃𝑃(𝐴𝐴𝑐𝑐)𝑃𝑃(𝐵𝐵|𝐴𝐴𝐶𝐶)

• Expected Value: ∑𝑥𝑥 ∙ 𝑝𝑝(𝑥𝑥) Variance: ∑(𝑥𝑥 − 𝜇𝜇)2∙ 𝑝𝑝(𝑥𝑥)

• Binomial: �𝑛𝑛

𝑥𝑥�𝑝𝑝𝑥𝑥𝑞𝑞𝑛𝑛−𝑥𝑥 𝜇𝜇=𝑛𝑛𝑝𝑝 𝜎𝜎2=𝑛𝑛𝑝𝑝𝑞𝑞

• Common z-scores

90% CI: 1.645 95% CI: 1.96 99% CI: 2.575

Partial preview of the text

Download Statistics Formula Sheet: STA 13 and more Cheat Sheet Mathematics in PDF only on Docsity!

Formula Sheet

STA 13

• Mean: 𝑥𝑥̅ =

∑ 𝑥𝑥𝑖𝑖 𝑛𝑛

• Variance: 𝑠𝑠 2 =

∑(𝑥𝑥𝑖𝑖 −𝑥𝑥̅)^2 𝑛𝑛−

• Weighted Mean: 𝑥𝑥̅ =

∑ 𝑤𝑤∙𝑥𝑥 ∑ 𝑤𝑤

• Addition Rule: 𝑃𝑃(𝐴𝐴 ∪ 𝐵𝐵) = 𝑃𝑃(𝐴𝐴) + 𝑃𝑃(𝐵𝐵) − 𝑃𝑃(𝐴𝐴 ∩ 𝐵𝐵)

• Multiplication Rule: 𝑃𝑃(𝐴𝐴 ∩ 𝐵𝐵) = 𝑃𝑃(𝐴𝐴)𝑃𝑃(𝐵𝐵|𝐴𝐴)

• Conditional Rule: 𝑃𝑃(𝐴𝐴|𝐵𝐵) =

𝑃𝑃(𝐴𝐴∩𝐵𝐵) 𝑃𝑃(𝐵𝐵)

• Bayes’ Rule: 𝑃𝑃(𝐴𝐴|𝐵𝐵) =

𝑃𝑃(𝐴𝐴)𝑃𝑃(𝐵𝐵|𝐴𝐴) 𝑃𝑃(𝐴𝐴)𝑃𝑃(𝐵𝐵|𝐴𝐴)+𝑃𝑃(𝐴𝐴 𝑐𝑐)𝑃𝑃(𝐵𝐵|𝐴𝐴 𝐶𝐶)

• Expected Value: ∑ 𝑥𝑥 ∙ 𝑝𝑝(𝑥𝑥)^ Variance: ∑(𝑥𝑥 − 𝜇𝜇)^2 ∙ 𝑝𝑝(𝑥𝑥)

• Binomial: �

� 𝑝𝑝 𝑥𝑥^ 𝑞𝑞 𝑛𝑛−𝑥𝑥^ 𝜇𝜇 = 𝑛𝑛𝑝𝑝 𝜎𝜎 2 = 𝑛𝑛𝑝𝑝𝑞𝑞

• Common z-scores

90% CI: 1.645 95% CI: 1.96 99% CI: 2.

z-score: 𝑧𝑧 = 𝑥𝑥−𝜇𝜇 𝜎𝜎 𝑋𝑋 = 𝜇𝜇 + 𝑧𝑧𝜎𝜎 𝑧𝑧 = 𝑥𝑥̅−𝜇𝜇 𝜎𝜎 �√𝑛𝑛
Sample Size: 𝑛𝑛 = �𝑧𝑧 𝛼𝛼 � 2 � 2 𝑠𝑠 2 (𝐸𝐸)^2 𝑛𝑛 = �𝑧𝑧 𝛼𝛼 � 2 � 2 𝑝𝑝�(1−𝑝𝑝�) (𝐸𝐸)^2
Linear Combination: 𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑋𝑋 𝜇𝜇𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝜇𝜇𝑋𝑋 𝜎𝜎𝑌𝑌^2 = 𝑏𝑏 2 𝜎𝜎𝑋𝑋^2

Statistics Formula Sheet: STA 13, Cheat Sheet of Mathematics

Related documents

Partial preview of the text

Download Statistics Formula Sheet: STA 13 and more Cheat Sheet Mathematics in PDF only on Docsity!

Formula Sheet

STA 13

• Mean: 𝑥𝑥̅ =

• Variance: 𝑠𝑠 2 =

• Weighted Mean: 𝑥𝑥̅ =

• Addition Rule: 𝑃𝑃(𝐴𝐴 ∪ 𝐵𝐵) = 𝑃𝑃(𝐴𝐴) + 𝑃𝑃(𝐵𝐵) − 𝑃𝑃(𝐴𝐴 ∩ 𝐵𝐵)

• Multiplication Rule: 𝑃𝑃(𝐴𝐴 ∩ 𝐵𝐵) = 𝑃𝑃(𝐴𝐴)𝑃𝑃(𝐵𝐵|𝐴𝐴)

• Conditional Rule: 𝑃𝑃(𝐴𝐴|𝐵𝐵) =

• Bayes’ Rule: 𝑃𝑃(𝐴𝐴|𝐵𝐵) =

• Expected Value: ∑ 𝑥𝑥 ∙ 𝑝𝑝(𝑥𝑥)^ Variance: ∑(𝑥𝑥 − 𝜇𝜇)^2 ∙ 𝑝𝑝(𝑥𝑥)

• Binomial: �

� 𝑝𝑝 𝑥𝑥^ 𝑞𝑞 𝑛𝑛−𝑥𝑥^ 𝜇𝜇 = 𝑛𝑛𝑝𝑝 𝜎𝜎 2 = 𝑛𝑛𝑝𝑝𝑞𝑞

• Common z-scores

90% CI: 1.645 95% CI: 1.96 99% CI: 2.

• HT Conclusion:

Condition Conclusion

Original claim does not

include equality, and you

reject H 0.

“There is sufficient evidence to support the claim

that … (original claim)”

Original claim does not

include equality, and you

fail to reject H 0.

“There is not sufficient evidence to support the

claim that … (original claim)”

Original claim includes

equality, and you reject H 0.

“There is sufficient evidence to warrant rejection

of the claim that … (original claim).”

Original claim includes

equality, and you fail to

reject H 0.

“There is not sufficient evidence to warrant

rejection of the claim that … (original claim).”