Content
Summary for indvidual patient data

Mean and standard deviation (SD) calculation

From data for each patient into a single mean and SD

A) Needed values

To estimate the mean and standard deviation from data presented individually for each person, you need the following values:

  1. Data for each individual

B) Steps

  1. In the Input table: put each of the previous values into the corresponding cells
  2. Click submit
  3. In the Output table: you will get the mean, standard deviation, and total number for the needed group

C) Equations

The output was calculated upon the following equations:

1) Mean (x̄):

xˉ = n/N\textbf{x̄ = } n/N

Where: x̄; mean; n; is the total sum of values, N; is the total number of values

2) Standard deviation (SD):

SD = 1N−1∑i=1N(xi−xˉ)2 \textbf{SD = }\sqrt{\frac{1}{N-1} \sum_{i=1}^{N}\left(x_{i}-\bar{x}\right)^{2}}

Where: xi; an individual value, x̄; mean, N; total number of values.

D) Citation and equations source

  1. Pearson Karl 1894 III. Contributions to the mathematical theory of evolution. Proc. R. Soc. Lond. 54: 329–333. http://doi.org/10.1098/rspl.1893.0079 (opens in a new tab). (III. Contributions to the mathematical theory of evolution | Proceedings of the Royal Society of London (royalsocietypublishing.org) (opens in a new tab))

  2. Krijnen, W. P. (2009). Applied Statistics for Bioinformatics using R. GNU Free Document License. (http://cran.freestatistics.org/doc/contrib/Krijnen-IntroBioInfStatistics.pdf (opens in a new tab))

  3. Galton, F. (1886). Regression Towards Mediocrity in Hereditary Stature. The Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263. https://doi.org/10.2307/2841583 (opens in a new tab). (Regression Towards Mediocrity in Hereditary Stature. on JSTOR (opens in a new tab))

  4. Montgomery, D. C., & Runger, G. C. (1994). Applied Statistics and Probability for Engineers. In European Journal of Engineering Education (Vol. 19, Issue 3). https://doi.org/10.1080/03043799408928333 (opens in a new tab).

E) Additional notes

In the meta-analysis, usually, we need to do this conversion when a study or more reports the data for each patient alone (for example: blood pressure for each patient, but other studies report the mean and SD for the whole group). Hence, if you want to conduct a meta-analysis pooling all studies’ mean and SD, then you need to use this calculation to get the mean and SD instead of data for each patient alone.

Group combinationUnit conversion