Convert Confidence Intervals To Standard Error
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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. Confidence intervals for means can also be used to calculate standard deviations. Again, the convert confidence interval to standard deviation following applies to confidence intervals for mean values calculated within an intervention group and not for
Convert Confidence Interval To Standard Deviation Calculator
estimates of differences between interventions (for these, see Section 7.7.3.3). Most confidence intervals are 95% confidence intervals. If the sample size is large (say calculate confidence interval from standard error in r bigger than 100 in each group), the 95% confidence interval is 3.92 standard errors wide (3.92 = 2 × 1.96). The standard deviation for each group is obtained by dividing the length of the confidence interval by 3.92, and then confidence intervals margin of error multiplying by the square root of the sample size: For 90% confidence intervals 3.92 should be replaced by 3.29, and for 99% confidence intervals it should be replaced by 5.15. 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. The numbers 3.92, 3.29 and 5.15 need to be replaced with slightly larger numbers specific to the t distribution, which can
Confidence Intervals Variance
be obtained from tables of the t distribution with degrees of freedom equal to the group sample size minus 1. Relevant details of the t distribution are available as appendices of many statistical textbooks, or using standard computer spreadsheet packages. 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). The divisor, 3.92, in the formula above would be replaced by 2 × 2.0639 = 4.128. For moderate sample sizes (say between 60 and 100 in each group), either a t distribution or a standard normal distribution may have been used. Review authors should look for evidence of which one, and might use a t distribution if in doubt. As an example, consider data presented as follows: Group Sample size Mean 95% CI Experimental intervention 25 32.1 (30.0, 34.2) Control intervention 22 28.3 (26.5, 30.1) The confidence intervals should have been based on t distributions with 24 and 21 degrees of freedom respectively. The divisor for the experimental intervention group is 4.128, from above. The standard deviation for this group is √25 × (34.2 – 30.0)/4.128 = 5.09. Calculations for the control group are performed in a similar way. It is important to check that the confidence interval is symmetrical about the mean (the distance between the lower lim
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machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up http://handbook.cochrane.org/chapter_7/7_7_3_2_obtaining_standard_deviations_from_standard_errors_and.htm and rise to the top Standard error from OR and HR up vote 3 down vote favorite 1 I'm planning to combine several observational studies, some of which have produced odds ratios and some hazard ratios. How do I get the standard error from the odds ratio $1.57$ ($95\%$ CI: $1.08-2.27$) and the standard error from the hazard ratio $1.56$ ($95\%$ CI: $0.96-2.52$)? meta-analysis standard-error share|improve this question edited Aug 1 '11 at http://stats.stackexchange.com/questions/13705/standard-error-from-or-and-hr 17:46 Bernd Weiss 5,7042138 asked Aug 1 '11 at 10:41 Kate 162 add a comment| 1 Answer 1 active oldest votes up vote 6 down vote You can back-calculate the standard errors from the CIs. Odds and hazard ratios are typically analyzed on the log scale. So, you will find that on the log scale, you get a symmetric confidence interval around the log of the estimate. For example, for $OR = 1.57$, you get $log(OR) = 0.451$ and the lower and upper CI bounds on the log scale are $0.077$ and $0.820$. Now these CI bounds are calculate with $log(OR) \pm 1.96 \times SE$, which implies that $SE = (UB - LB) / (2 \times 1.96)$. So, we get: $SE = (0.820 - 0.077) / (2 \times 1.96) = 0.189$. The same things works for the hazard ratio, where you will find that $SE = 0.246$. Note that these standard errors are for the log odds ratio and the log hazad ratio. But this is the scale we work on anyway when combining results from several studies with these outcome measures. share|improve this answer answered Aug 1 '11 at 12:07 Wolfgang 8,92812147 Thank you very much! –Kate Aug 1 '11 at 12:23 3 @Kate If you feel that my answer is
than the score the student should actually have received (true score). The difference between the observed score and the true score is called the error score. S true = S http://home.apu.edu/~bsimmerok/WebTMIPs/Session6/TSes6.html observed + S error In the examples to the right Student A has an http://www.graphpad.com/support/faqid/1381/ observed score of 82. His true score is 88 so the error score would be 6. Student B has an observed score of 109. His true score is 107 so the error score would be -2. If you could add all of the error scores and divide by the number of students, you would have confidence interval the average amount of error in the test. Unfortunately, the only score we actually have is the Observed score(So). The True score is hypothetical and could only be estimated by having the person take the test multiple times and take an average of the scores, i.e., out of 100 times the score was within this range. This is not a practical way of estimating the amount of error in the convert confidence interval test. True Scores / Estimating Errors / Confidence Interval / Top Estimating Errors Another way of estimating the amount of error in a test is to use other estimates of error. One of these is the Standard Deviation. The larger the standard deviation the more variation there is in the scores. The smaller the standard deviation the closer the scores are grouped around the mean and the less variation. Another estimate is the reliability of the test. The reliability coefficient (r) indicates the amount of consistency in the test. If you subtract the r from 1.00, you would have the amount of inconsistency. In the diagram at the right the test would have a reliability of .88. This would be the amount of consistency in the test and therefore .12 amount of inconsistency or error. Using the formula: {SEM = So x Sqroot(1-r)} where So is the Observed Standard Deviation and r is the Reliability the result is the Standard Error of Measurement(SEM). This gives an estimate of the amount of error in the test from statistics that are readily available from any test. The relationship between these statistics can be seen at the right. In the first row there is a low Standard Deviation
Graphpad.com FAQs Find ANY word Find ALL words Find EXACT phrase The confidence interval of a standard deviation. FAQ# 1381 Last Modified 22-March-2009 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 You are probably already familiar with a confidence interval of a mean. 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. A free GraphPad QuickCalc does the work for you. Interpreting the CI of the SD is straightforward. If you assume that your data were randomly andindependently sampled from a Gaussian distribution, you can be 95% sure that the CI computed from the sample SD 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 The sample standard deviation computed from the five values shown in the graph above is 18.0. But the