To introduce a method of estimating the mean and standard deviation based on the median, range and sample size. Therefore, the quantitative data without providing the mean and standard deviation can also be used in a meta-analysis. Examples were given to illustrate how to apply the estimation method.
The averages and standard deviations of several subgroups in a study are sometimes need to be combined in meta-analysis, the calculating method to do this was given in this paper. Firstly, a commonly used incorrect calculating method to do the combination was pointed out; it origins from metrology and should be applied in the combination of standard deviations of several groups of measurements of the same object, and it's not fit for the combination of several subgroups' data in meta-analysis. Meanwhile the calculating error of this method was tested with real and constructed data and its impact on the conclusion of meta-analysis was analyzed. The incorrect method may result in a big calculating error with the real research data and even lead to an incorrect conclusion with the constructed data. The correct formula was deduced and given, the calculating result of the correct formula equals the true value when neglecting the round error. The error analysis of the incorrect method was then done with the correct formula and an accurate combination result can only be got when meeting the condition given by this paper. The correct method in this paper should be used to combine standard deviations in the future researches.
Sample size, mean and standard deviation are necessary when conducting meta-analysis for continuous outcomes. Advanced methods of data extraction were needed if the mean and the standard deviation couldn’t be obtained from a literature directly. Eight methods were introduced and two examples were given to illustrate how to apply the methods.