Confidence intervals: Types and calculations

Confidence Intervals: types and calculation
Dr. S. A. Rizwan, M.D.
Public Health Specialist
SBCM, Joint Program – Riyadh
Ministry of Health, Kingdom of Saudi Arabia

Learning objectives
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Describe the various situations for calculating CI
• Apply the formula for calculating different situations

Introduction
• Confidence intervals can be calculated for a number of statistics
• They all follow the general format
• The differences lie in the formula for standard error

Steps in calculating CI

CI for a single mean: example
• Example: find CI when sample mean =10.2, sd =10.1, N=1055,
confidence level =95%.
• z is derived from the 95% value: what value of z leaves 95% in the middle
and 2.5 % on each end of a distribution?
• For p = .975, z = 1.96
• The standard error is s/SQRT(n) = 10.1/SQRT(1055) = 0.31
• Upper limit 10.2 + 1.96*0.31 = 10.80
• Lower limit 10.2 – 1.96*0.31 = 9.59
• Hence, the confidence interval is 9.59 to 10.81

CI for a single mean: work out
• We look at a study of 200 males versus 200
females mean SAT scores. The mean SAT score
for females is 1180 with a standard deviation of
5 and for males, the mean SAT score is 1160
with a standard deviation of 6.
• Form a 95% confidence interval for the mean
SAT score for females and males

CI for a single mean: work out
Variable Obs Mean Std. Err. [95% Conf. Interval]
Females 200 1180 0.35 1179.30 1180.69
Males 200 1160 0.42 1159.16 1160.83

CI for a single proportion: work out
• A study was done on the proportion of
males and females who participate in
athletics. 480 females and 530 males
participated in the study, where 170
females and 208 males participated in
athletics
• Form a 95% CI for each of the proportion of
female and male athletes?

CI for a single proportion: work out
Females 480 0.354 0.0218 0.3113 0.3987
Males 530 0.392 0.0212 0.3506 0.4354

CI for a difference in 2 means
• The table below summarizes data
n=3539 participants attending the 7th
examination of the Offspring cohort in
the Framingham Heart Study.
• Calculate the difference in mean systolic
blood pressures between men and
women, and 95% confidence interval
for the difference in means.

Mean difference = 1.7 (95% CI: 0.44, 2.96)

CI for a difference in 2 proportions
• The following table contains data on
prevalent CVD among participants who
were currently non-smokers and those
who were current smokers in the
Framingham Offspring Study.
• Calculate the difference in prevalent
CVD between smokers and non-
smokers and a 95% CI confidence
interval for the difference.

CI for a difference in 2 proportions
Difference in prevalence = 0.0114 (95% CI: -0.0133, 0.0361)

CI for relative risk

CI for odds ratio

CI for other point estimates
• Small sample size (<30)
• Matched data
• Odds ratio
• Risk ratio
• Hazard ratio
• Regression coefficient
• Many other statistics

Advanced learning
• The methods of calculating CI may differ
depending on the formula used for a given point
estimate and hence the CI may differ
• Most of the time CI and p values agree in a
comparative situation, but sometimes they
don’t
• In some situations CI may not be symmetrical
• What are prediction intervals and uncertainty
intervals?

Take home messages
• Confidence interval is one of the corner stones of statistical inference
• Each point estimate from a sample requires a confidence interval
• Remember the general format of CI
• Remember the correct interpretation of CI for the given situation

Thank you!
Email your queries to sarizwan1986@outlook.com

Confidence intervals: Types and calculations

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