If we have 4 treatments for a trait and a SEM (pooled SE) for these treatments' mean, how to calculate SE for mean of each treatment from SEM?
Dear Peyman Mahmoudi,
Hope I understand your question well.
If we have three sets as x_i, y_i, and z_i, with differing numbers of measurements being n_x, n_y, and n_z.
Then you can calculate the mean values by x_bar = sum {from i=1 to i=n_x} (x_i) etc.
For each set calculate the sum of the square deviations: ssd_x = sum ((x_i - x_bar)^2) etc.
The pooled standard deviation will be: psd= sqrt(ssd_x + ssd_y + ssd_z)/(n_x + n_y + n_z - 3).
The standard error of the mean can then be calculated by: t*psd/(square root (n_x + n_y + n_z)), where t is taken from t tables and depends on the confidence level.
Best regards
In addition, if xbar is an unbiased estimate of the population mean, then the standard error and standard deviation are equivalent. As a separate issue, the confidence interval on the population mean is
xbar +/- t*psd/sqrt(n_x + n_y + n_z).
Dear Peymaneh Davoodi
Thank you for your reply. Say @we have 3 treatments (5 replicates for each) with their means to be 10, 15 and 20, and just a SEM (Pooled SE) to be 2. We have no SE for single mean. Is it possible to use SEM for calculating single SE for each treatment's mean?
I attached a picture to help understanding my question.
Thank you.
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