Ecological Archives A021-001-A2

Deborah K. Letourneau, Inge Armbrecht, Beatriz Salguero Rivera, James Montoya Lerma, Elizabeth Jiménez Carmona, Martha Constanza Daza, Selene Escobar, Víctor Galindo, Catalina Gutiérrez, Sebastián Duque López, Jessica López Mejía, Aleyda Maritza Acosta Rangel, Janine Herrera Rangel, Leonardo Rivera, Carlos Arturo Saavedra, Alba Marina Torres, and Aldemar Reyes Trujillo. 2011. Does plant diversity benefit agroecosystems? A synthetic review. Ecological Applications 21:9–21.

Appendix B. Salquero-Rivera method for calculating a grand standard deviation for a series of measurements each of which has an associated standard error or standard deviation.

Population mean and standard deviation:

We have n samples each with mean value, standard error and sample size.

So

Sample 1:
Sample 2:

.
.
.

Sample n:

Where:

Equation B.1 relates standard error with standard deviation and sample size n

(B.1)

If we square Eq. B.1, we get Eq. B.2

(B.2)

Furthermore, variance for any sample is defined by Eq. B.3

(B.3)

Replacing B.3 in B.2 we have:

(B.4)

and

(B.5)

Replacing B.5 in B.4, we get

(B.6)

Therefore

(B.7)

Equation B.7 is applied for each sample n

Then, we have for population variance the Eq. B.8

(B.8)

By Eq. B.6, we get population variance in terms of sampling data

(B.9)

where

(B.10)

and

(B.11)

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