Confidence interval calculator

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					                    CONFIDENCE INTERVAL CALCULATOR (last updated 1 February 2011)

This spreadsheet can be used to calculate confidence intervals for a mean, the difference betweeen two means,
a proportion or odds, comparisons of two proportions (the absolute risk reduction, number needed to treat,
relative risk, relative risk reduction and odds ratio), sensitivity, specificity and two-level likelihood ratios. Click on
the tabs at the bottom of this screen to choose the appropriate worksheet.

The confidence interval for the difference between two means uses the method that assumes equal variances for
the two populations (see Armitage P and Berry G (1994): Statistical Methods in Medical Research (3rd ed.).
London: Blackwell, pp 108-109).
The method used to calculate a confidence interval for a proportion is the Wilson score method without continuity
correction (see Newcombe RG (1998). Two-sided confidence intervals for the single proportion: Comparison of
seven methods. Statistics in Medicine , 17, 857-872).

The method used to calculate a confidence interval for the difference between two proportions is the Newcombe-
Wilson method without continuity correction (see Newcombe RG (1998). Interval estimation for the difference
between independent proportions: Comparison of eleven methods. Statistics in Medicine, 17, 873-890). The
confidence limits for the number needed to treat are the inverse of the limits for the absolute risk reduction.
Confidence intervals for the relative risk and odds ratios are calculated using the methods described by Armitage
and Berry (Armitage P and Berry G (1994): Statistical Methods in Medical Research (3rd ed.). London: Blackwell,
p 131). The relative risk reduction and its confidence limits as 1 minus the relative risk and its confidence limits.

Confidence intervals for sensitivity and specificity are produced with the Wilson score method (see above for
reference). Confidence intervals for positive and negative likelihood ratios are calculated with the method
described by Simel and colleagues (Simel DL, Samsa GP, Matchar DB (1991). Likelihood ratios with confidence:
sample size estimation for diagnostic test studies. Journal of Clinical Epidemiology , 44, 763-70). The confidence
interval for the diagnostic odds ratio is calculated as described by Armitage and Berry (see above for reference).

The results have been checked against worked examples in the sources cited above. Nonetheless there may still
be errors. If you identify errors please contact the author, Rob Herbert, email: rherbert@george.org.au.
TO ESTIMATE A CONFIDENCE INTERVAL FOR A MEAN:

                           Enter the sample mean here:
Enter the estimated population standard deviation here:
   Enter the sample size (eg, number of subjects) here:

  Enter the required confidence interval (eg, 95%) here:   95

                                             RESULT
                    The estimated population mean is:
                                  The estimated CI is:
                                        difference of 2 means




                TO ESTIMATE A CONFIDENCE INTERVAL FOR THE DIFFERENCE
                                                 BETWEEN TWO MEANS:

                                        Enter the mean of the control group here:
     Enter the estimated population standard deviation for the control group here:
        Enter the sample size (eg, number of subjects) for the control group here:

                                   Enter the mean of the experimental group here:
Enter the estimated population standard deviation for the experimental group here:
   Enter the sample size (eg, number of subjects) for the experimental group here:

                             Enter the required confidence interval (eg, 95%) here:   95

                                                                        RESULT
                   The estimated difference between the two population means is:
                                                             The estimated CI is:




                                               Page 4
difference of 2 means




       Page 5
                         a proportion or odds




TO ESTIMATE A CONFIDENCE INTERVAL FOR A PROPORTION:

            Enter the number of "events" in the sample here:
         Enter the sample size (eg, number of subjects) here:

        Enter the required confidence interval (eg, 95%) here:   95

                                                   RESULT
                     The estimated population proportion is:
                         The estimated population odds are:




                               Page 6
a proportion or odds




      Page 7
                                     compare 2 proportions or odds




             TO ESTIMATE CONFIDENCE INTERVAL FOR THE COMPARISON
                                            OF TWO PROPORTIONS:

                      Enter the number of "events" in the control group here:
     Enter the sample size (eg, number of subjects) of the control group here:

                 Enter the number of "events" in the experimental group here:
Enter the sample size (eg, number of subjects) of the experimental group here:

                         Enter the required confidence interval (eg, 95%) here:   95

                                                                     RESULT:
                                                     Absolute Risk Reduction:
                                                     Number Needed to Treat:
                                                                 Relative Risk:
                                                      Relative Risk Reduction:
                                                                    Odds ratio:




                                                Page 8
compare 2 proportions or odds




           Page 9
TO ESTIMATE CONFIDENCE INTERVALS FOR SENSITIVITY,
     SPECIFICITY AND TWO-LEVEL LIKELIHOOD RATIOS:

                             Enter the data into this table:


                                                           Test is positive
                                                           Test is negative

     Enter the required confidence interval (eg, 95%) here:       95

                                                  RESULT:
                                                Sensitivity:
                                                Specificity:
                                 Positive likelihood ratio:
                                 Negative likelihood ratio:
                                   Diagnostic odds ratio:
               Reference standard Reference standard
                    is positive       is negative
 is positive
is negative

				
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