# Summing multiple standard deviations (repeated measures) [duplicate]

Say a set of 5 participants completed two subtests (A and B). The scores on these subtests can be summed to get a total test score. Here is the dummy data:

Participant Subtest A Subtest B Total test
1 5 9 14
2 7 0 7
3 5 6 11
4 3 3 6
5 5 2 7

Now, say we don't have access to this raw data. We only know the summary statistics of the subtests, as follows:

• Subtest A mean: 5.00
• Subtest A SD: 1.41
• Subtest B mean: 4.00
• Subtest B SD: 3.54

If I wanted to know the total mean the for the total test, I gather I can just sum the means from the subtests (5.00 + 4.00).

But how can I calculate the total SD for the total test? I've come across one possible calculation: sqrt((1.41^2)+(3.54^2)). But when I've trialed this, I don't find that it replicates the 'true' standard deviation for the total test.

Can anyone advise? The only other advice I've found on this matter assumes that the SDs I'm trying to combine are for independent groups, rather than for repeated measures.