Lecture 8: Confidence Intervals

this is a range of values that is likely to contain the true population value, based on the sample data

confidence interval

how to calculate CI

sample value + 2SE

sample value - 2SE

if the confidence interval DOES NOT contain 1.0, that means it (is/is not) significant and p is (<,>) 0.05

is significant (p<0,05)

if the CI does contain 1.0, that means it (is/is not) significant and p is (<.>) 0.05

is not significant (p>0.05)

why is it considered significant if the CI does not contain 1.0

then no difference between the 2 groups (1.0) is not plausible, which means the association is statistically significant

why is it considered not signigicant if the CI contains 1.0

that means the population could have a value of 1.0, meaning there is no difference between the 2 groups

CI and p-value (never/always) match

always

if CI excludes 1 → p_ 0.05

<

if CI includes 1.0 → p _ 0.05

>

what two things do CI and p-values communicate

is the result significant?

Is the result due to chance?

CI just give you more ______

information

possible range of the true value

p values only tell you if its significant

what is the correct way to interpret 95% CI

this interval is our best guess of where the true population value lies, based on our sample

REMEMBER: The (numerator/denominator) is the reference group

denominator

binary variable examples

yes/no

boy/girl

in binary variables, the numerator is the (shown/not shown) group

shown

in binary variables, the denominator is the (shown/not shown) group

not shown

examples of ordinal variable

income low, medium, high

variables in order that increases

in ordinal variables, how is the reference group marked

1.0, ref, …, NA

Layman’s interpretation of a 95% C

Based on my sample, the true population value is likely between the lower and upper CI limits.

Relationship between 95% CIs and random error

CIs widen when random error is higher, indicating more uncertainty.

Odds Ratio (OR)

A measure of association comparing the odds of an outcome between two groups.

Interpretation of OR = 1.0

No difference in odds between groups.

Wide confidence interval

Greater uncertainty; more random error in the estimate.

Narrow confidence interval

More precise estimate; less random error.