Data analysis - Formulario

Data analysis formulario

Sample size determination

Margin of error: K- Confidence interval (CI) is a range of values that include a population value within a degree of confidence.

• 1 - α = 0.95, Z = 1.96 → α ±
• 1 - α = 0.99, Z = 2.57 → α ±

Margin of error is calculated using: p ⋅ (1 − p)

k = z ⋅ α1− n²

• Z is the value for your selected confidence level (use Z scores)
• p is the sample proportion usually use 0.5 → n is the sample size

k = critical value standard deviation ·

k = critical value standard error ·

Critical value

• t-score: when n < 30 or is not known σ‣ t α(n−1),1− 2
• z-score: when n > 30 and is known σ‣ z• α1− 2

Standard deviation or the standard error

• Standard Deviation if you know n: σ = Va r ( X̄ ) = σ = → →nn − 1sample variance population variance population standard deviation

Confidence level: z- Confidence interval (CI) is a range of values that include a population value within a degree of confidence.

kz = Va r (X )- Standard deviation- Va r (X ) → p (1 − p)

If you can use the CLT =‣ n² ∑ (X − X̄ ) Si² Otherwise S = Va r (X ) =→‣ n − 1 n

Find confidence interval

• Search in z score table
• P (−z < Z < z ) = P (Z < z ) − P (z < − z ) →‣ Sample size: n
• Find the value of z at a certain confidence level (1 - α)
• Find ̂Va r ( p) 2( )kk ̂̂v a r ( p) =→‣ z z p (1 − p)n = ̂v a r ( p)--

Regression analysis

Other formulas

Correlation ∑ (Xi − X̄ )(Yi − Ȳ )

Va r (Y ) Yn − 1 from to b b =ρρ = ρ ⋅ = ρ ⋅→– XY XYXY XY Va r (X )² 2 2S∑ ∑(Xi − X̄ ) (Yi − Ȳ )‣ Xn − 1 n − 1

First table creation

Create table with columns (end of the column values)

• Σ(1) X values
• (2) Y values
• (3) (Xi - X̄ )(Yi - Ȳ)
• (4) (Xi - X̄)²
• (5) (Yi - Ȳ)²

Compute:

• Column (1) column (2); X̄ = Ȳ =• n n
• Column (3) column (4) column (5) ²; ; S = S = S =• x y x yn − 1 n − 1 n − 1

OLS estimation

OLS estimation of the regression coefficients and interpretation of the slope:

• S ∑ (X − X̄ )(Y i − Ȳ ) column (3)x y ib = a = - b= = Ȳ X̄