Calculating Standard Error From Confidence Intervals
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ratio measures are performed
Calculating Standard Deviation From Confidence Interval And Mean
on the natural log scale (see Chapter 9, Section 9.2.7). For a ratio how to calculate standard deviation from 95 confidence intervals measure, such as a risk ratio, odds ratio or hazard ratio (which we will denote generically as RR here), first calculate lower limit = ln(lower confidence limit calculate confidence interval variance given for RR) upper limit = ln(upper confidence limit given for RR) intervention effect estimate = lnRR Then the formulae in Section 7.7.7.2 can be used. Note that the standard error refers to the log of the ratio measure. When using the generic inverse variance method in RevMan, the data should be entered on the natural log scale, that is as lnRR and the standard error of lnRR, as calculated here (see Chapter 9, Section 9.4.3).
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& ViewsAt a glance News Features Editorials Analysis Observations Head to head Editor's choice Letters Obituaries Views and reviews Rapid responses Campaigns Archive For authors Jobs Hosted Research How to obtain the P... How to obtain the P value http://handbook.cochrane.org/chapter_7/7_7_7_3_obtaining_standard_errors_from_confidence_intervals_and.htm from a confidence interval Research Methods & Reporting Statistics Notes How to obtain the P value from a confidence interval BMJ 2011; 343 doi: http://dx.doi.org/10.1136/bmj.d2304 (Published 08 August 2011) Cite this as: BMJ 2011;343:d2304 Article Related content Metrics Responses Peer review Douglas G Altman, professor of statistics in medicine 1, J Martin Bland, professor of health statistics21Centre for Statistics in Medicine, University of Oxford, Oxford OX2 6UD2Department of Health Sciences, University of York, Heslington, York YO10 5DDCorrespondence to: http://www.bmj.com/content/343/bmj.d2304 D G Altman doug.altman{at}csm.ox.ac.ukWe have shown in a previous Statistics Note1 how we can calculate a confidence interval (CI) from a P value. Some published articles report confidence intervals, but do not give corresponding P values. Here we show how a confidence interval can be used to calculate a P value, should this be required. This might also be useful when the P value is given only imprecisely (eg, as P<0.05). Wherever they can be calculated, we are advocates of confidence intervals as much more useful than P values, but we like to be helpful. The method is outlined in the box below in which we have distinguished two cases.Steps to obtain the P value from the CI for an estimate of effect (Est) (a) P from CI for a differenceIf the upper and lower limits of a 95% CI are u and l respectively: 1 calculate the standard error: SE = (u − l)/(2×1.96) 2 calculate the test statistic: z = Est/SE 3 calculate the P value2: P = exp(−0.717×z − 0.416×z2). (b) P from CI for a ratioFor a ratio measure, such as a risk ratio, the above formulas should be used with the estimate Est and the confidence limits on the log scale (eg, the log risk ratio and its CI).NotesAll P values are two sided.All logarithms are natural (ie, to base e).3 “exp” is the exponential function. The formu
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OF STATISTICS > Confidence intervals > Confidence interval of a standard deviation / Dear GraphPad, Confidence interval of a standard deviation A confidence interval can be computed for almost any value computed from a sample of data, including the standard deviation. The SD of a sample is not the same as the SD of the population It is straightforward to calculate the standard deviation from a sample of values. But how accurate is that standard deviation? Just by chance you may have happened to obtain data that are closely bunched together, making the SD low. Or you may have randomly obtained values that are far more scattered than the overall population, making the SD high. The SD of your sample does not equal, and may be quite far from, the SD of the population. Confidence intervals are not just for means Confidence intervals are most often computed for a mean. But the idea of a confidence interval is very general, and you can express the precision of any computed value as a 95% confidence interval (CI). Another example is a confidence interval of a best-fit value from regression, for example a confidence interval of a slope. The 95% CI of the SD The sample SD is just a value you compute from a sample of data. It's not done often, but it is certainly possible to compute a CI for a SD. GraphPad Prism does not do this calculation, but a free GraphPad QuickCalc does. Interpreting the CI of the SD is straightforward. If you assume that your data were randomly and independently sampled from a Gaussian distribution, you can be 95% sure that the CI contains the true population SD. How wide is the CI of the SD? Of course the answer depends on sample size (n). With small samples, the interval is quite wide as shown in the table below. n 95% CI of SD 2 0.45*SD to 31.9*SD 3 0.52*SD to 6.29*SD 5 0.60*SD to 2.87*SD 10 0.69*SD to 1.83*SD 25 0.78*SD to 1.39*SD 50 0.84*SD to 1.25*SD 100 0.88*SD to 1.16*SD 500 0.94*SD to 1.07*SD 1000 0.96*SD to 1.05*SD Example Data: 23, 31, 25, 30, 27 Mean: 1.50 SD: 3.35 The sample standard deviation computed from the five values is 3.35. But the true standard deviation of the population from which the values were sampled might be quite di