Hi,
I want to subtract two means from one antoher, but I am not sure on how to calculate the new standard deviation when doing this.
I have a mean of 0.649 with standard deviation 0.27 and from this mean I want to subtract another mean of 0.11 with standard deviation 0.03. If I do this my combined mean is 0.539, but what will be the standard deviation? I have N = 259 for the group with mean 0.649 and N = 103 for the group with mean 0.11.
I hope anyone could help me.
Thanks in advance.
Best regards,
Aloys
Subtraction of two means with their SD = (0.649 - 0.11)+- sqrt(0.27+0.03) = 0.539+- 0.548
You can do this by following the method shown in the picture
Hello Aloys,
So, score set A has a mean of 0.649, SD of 0.27, and score set B has a mean of 0.11 with SD of 0.03, and you want to know the mean and SD of a new score, C, where C = A - B.
As you guess, mean C = mean A - mean B. That's the easy one.
Variance C = Variance A + Variance B - 2*Covariance(A,B)
Or, equivalently,
Variance C = Variance A + Variance B - 2*Correlation(A,B)*SD A * SD B
In other words, you need to know how A and B correlate.
If A and B are uncorrelated, then the last term [2*Covariance(A,B)] is zero.
SD of C is square root of the variance of C
Good luck with your work.
Hi Sheikh and David,
Thank you very much for answering my question.
Best regards,
Aloys
Hi,
All you need to do is find the pooled standard deviation and since your DF changes use this link : https://www.statisticshowto.datasciencecentral.com/pooled-standard-deviation/
Good luck
Dear Aloys,
If this is your study and you have the raw data, you can calculate standard deviation easily by calculating post-pre means for each participant, then you can even calculate the STDEV in excel.
However, if this is not for your study and if you are looking for a meta-analysis, read my paper and see your options:
Article The Effects of Resistance Training on Architecture and Volum...
Regards,
Gokhan
Dear Readers of this thread:
While this is an old thread, it's important to add this clarification.
Please note that the method furnished by Sheikh Mohammad Famim Ahmed , is correct _only_ if the two variables are independent/uncorrelated (as noted in my post, above). Otherwise, it will yield an incorrect estimate of the variance of the difference scores. When two variables have a non-zero relationship, you must take that into account before computing a variance of either the sum of the scores or the difference between the scores.
Best regards to all.
Dear Dr. David Morse,
I would like to ask a question related with this thread. When we are going to work on mean difference of pre- and post- therapy, is it determined as correlated variable? If yes, how can we know the correlation of between the mean? As the illustration, we are conducting a meta-analysis in which we have to compare the mean improvement before and after therapy. One of study provide a data of 181.08 +_10.82 at the baseline and 205.92 +_ 13.4 at the end of study. How can we determine the new SD of the mean difference? Thank you
Hello Roy Bagus Kurniawan ,
You can determine the SD of a difference score by:
1. Having all the original data, and computing a difference score for each case, then computing the SD of those scores across cases.
2. Having the correlation or covariance between pre- and post-therapy scores, along with the SD of each. This information would be sufficient to estimate the SD of the scores (as noted in my first post to this thread, above).
If neither of these conditions is met, then you'll not be able to determine the correct value for the SD of the difference scores. And, yes, in a situation like comparing pre- and post-intervention scores, the scores will almost inevitably be correlated to some degree). The best you can do in such an instance is use an estimate such as sqrt(SD(pre)^2 + SD(post)^2), and acknowledge that the true value is likely smaller, but could be bigger (in the case of a negative correlation).
Good luck with your work.
Thank you Dr. David Morse for the advices and guidance
Best regards
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