The divisor, 3.92, in the formula above would be replaced by 2 × 2.0639 = 4.128.įor moderate sample sizes (say between 60 and 100 in each group), either a t distribution or a standard normal distribution may have been used. For example the t value for a 95% confidence interval from a sample size of 25 can be obtained by typing = tinv(1-0.95,25-1) in a cell in a Microsoft Excel spreadsheet (the result is 2.0639). Relevant details of the t distribution are available as appendices of many statistical textbooks, or using standard computer spreadsheet packages. The numbers 3.92, 3.29 and 5.15 need to be replaced with slightly larger numbers specific to the t distribution, which can be obtained from tables of the t distribution with degrees of freedom equal to the group sample size minus 1. If the sample size is small (say less than 60 in each group) then confidence intervals should have been calculated using a value from a t distribution. In our case, the confidence interval is between 2.902 and 3.098. Add and subtract the margin of error from the mean value to obtain the confidence interval. Multiply this value by the z-score to obtain the margin of error: 0.05 × 1.959 0.098. The standard deviation for each group is obtained by dividing the length of the confidence interval by 3.92, and then multiplying by the square root of the sample size:įor 90% confidence intervals 3.92 should be replaced by 3.29, and for 99% confidence intervals it should be replaced by 5.15. Compute the standard error as /n 0.5/100 0.05. If the sample size is large (say bigger than 100 in each group), the 95% confidence interval is 3.92 standard errors wide (3.92 = 2 × 1.96). Most confidence intervals are 95% confidence intervals.
Again, the following applies to confidence intervals for mean values calculated within an intervention group and not for estimates of differences between interventions (for these, see Section 7.7.3.3). When making this transformation, standard errors must be of means calculated from within an intervention group and not standard errors of the difference in means computed between intervention groups.Ĭonfidence intervals for means can also be used to calculate standard deviations. As a check, this is in substantial agreement (within rounding error) of the standard error calculated directly from the data : both are 0.6723. 7.7.3.2 Obtaining standard deviations from standard errors and confidence intervals for group meansĪ standard deviation can be obtained from the standard error of a mean by multiplying by the square root of the sample size: Its half width (margin of error) is t c S / n ( 51.47860 48.66417) / 2 1.407215. For the current version, please go to /handbook/current.
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