MedicalStat

## Confidence Intervals

Decimals:

The approximate intervals are calculated using the Z-Distribution (standard normal distribution).
The exact intervals are calculated using the T-Distribution.

## Confidence and Prediction Interval of Mean

What is known?
Mean SD N

Approx: SE % PI
% CI
Null Hypothesis (H0) Z Value P value
Mean

Exact: SE % PI
% CI
Null Hypothesis (H0) T Value P value
Mean

## Confidence Interval of Proportion

What is known?
Events (cases) N

Approx: Proportion SE % CI
Null Hypothesis (H0) Z Value P value
Proportion

Exact: Proportion SE % CI
Null Hypothesis (H0) T Value P value
Proportion

## Confidence Interval of Slope (Regression Coefficient)

The slope of a line is in this case the β value in the expression $$Y = \beta X + \alpha \: (+error)$$ from a linear regression. N is the number of points (x, y). The degrees of freedom is DF = N - 2. The correlation coefficient R2 is defined by $$R^2 = \frac{SSR}{SST}$$ or $$R^2 = 1 - \frac{SSE}{SST}$$

SST = Sum of the Squares (Total) = SSE + SSR
SSR = Sum of the Squares (due to Regression)
SSE = Sum of Squares (due to Error)

What is known?
β (slope) R2 N

Approx: SE % CI
Null Hypothesis (H0) Z Value P value
β

Exact: SE % CI
Null Hypothesis (H0) T Value P value
β