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Confidence Intervals

Confidence Intervals. Nancy D. Barker, M.S. Statistical Inference. Statistical Inference. Statistical Inference. Statistical Inference. Statistical Inference. Hypothesis Testing Is there evidence that the population parameter, e.g., RR , OR , IDR is different from the null value?

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Confidence Intervals

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  1. Confidence Intervals Nancy D. Barker, M.S.

  2. Statistical Inference

  3. Statistical Inference

  4. Statistical Inference

  5. Statistical Inference

  6. Statistical Inference • Hypothesis Testing • Is there evidence that the population parameter, e.g., RR, OR, IDR is different from the null value? • Interval Estimation • How do we determine the precision of the point estimate by accounting for sampling variability?

  7. Confidence Intervals The goal: Use sample information to compute two numbers, L and U, about which we can claim with a certain amount of confidence, say 95%, that they surround the true value of the parameter.

  8. General CI Formulas • Arithmetic scale measures: • Multiplicative scale measures: *Note: The variance in this formula refers to the variance [ln (point estimate)].

  9. Confidence Interval • Mean:

  10. Confidence Interval • Mean: Example: Calculate a 95% CI for the mean Sample Mean: 26.2 Sample standard deviation: s=5.15 Sample size: n=32

  11. Confidence Interval Calculate a 90% CI for the mean Sample Mean: 26.2 Sample standard deviation: s=5.15 Sample size: n=32 Calculate a 99% CI for the mean Sample Mean: 26.2 Sample standard deviation: s=5.15 Sample size: n=32

  12. Confidence Interval • Proportion: Example: Calculate a 95% CI for the proportion Sample proportion: 0.34 Sample size: n=400

  13. 95% Confidence Interval • Difference between proportions:

  14. 95% CI for difference between proportions • Example

  15. Interpretation of CI

  16. Large Sample95% Confidence Interval for RR • Risk Ratio (multiplicative scale) Which is equivalent to: Where, *Uses a Taylor Series approximation for the variance

  17. Large Sample 95% Confidence Interval for RR

  18. Large Sample95% Confidence Interval for OR • Odds Ratio (multiplicative scale) Which is equivalent to *Uses a Taylor Series approximation for the variance

  19. Large Sample 95% Confidence Interval for OR

  20. Large Sample95% Confidence Interval for IDR • Incidence Density Ratio (Multiplicative scale) Which is equivalent to *Uses a Taylor Series approximation for the variance

  21. Large Sample95% Confidence Interval for IDR

  22. Properties of Confidence Intervals • The wider the CI, the less precise the estimate. • The more narrow the CI, the more precise the estimate. • Note: The confidence interval does not address the issue of bias.

  23. What affects the Confidence Interval • The level of confidence • Sample Size • Variation in the data • For RR, OR, IDR, the strength of the association

  24. Confidence Interval vs. P-value Similarities • Multiple formulas, (approximate and exact) • Neither account for bias • Statistically equivalent (Theoretically!) Differences • CI provides same information as a statistical test, plus more • CI reminds reader of variability • CI provides range of compatible values (interval estimation) • CI more clearly shows influence of sample size

  25. Confidence Interval vs. P-Value

  26. Confidence Interval vs. P-Value

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