Richard C. answered • 07/12/16
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John,
Don't think this is possible. The standard deviation is a measure of variability across all data points. If you only have one there is no variability and so, no standard deviation.
In fact, if you use the formula for the std dev with n = 1, the result is undefined.
Perhaps I don't understand the full scope of your question.
Richard C.
John,
I have some more information on this...if interested, let me know.
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07/12/16
John S.
Nice to hear back from you Dr yes I am interested John j
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07/12/16
Richard C.
John,
I did some digging and found some material I remember from my studies but never did anything with.
The single subject experimental design is not often used since it presents many statistical problems when it comes to determining the size of effect (i.e., whether the effect you observe is really significant; remember that's probably the most important concern in any statistical test). The issues are related, of course, to the fact that only one subject is measured. The experiment goes something like this, as an example:
One subject is given a treatment and then measured over repeated intervals on some dependent variable. Then the same subject is given a second treatment and again measure on the same dependent variable over the same number of repeated intervals. The results might look something like this:
Treatment A:
12
14
9
11
13
16
Treatment B
25
28
22
33
29
28
Now, on the surface, it appears that Treatment A has a different effect that B. However, like all statistical tests, we'd need to determine whether the effect is significant. That's where the problem occurs.
We can generate means and standard deviations for each of the treatment group's measurements and then find the standard errors for each. After that, things get murky.
There are some sites online that can provide you with more information re: what folks have tried.
Basically, much of the problem arises from the fact that normal assumptions usually true in designs with multiple samples and adequate sample sizes just don't hold for these types of studies.
So, while you can do this, the results, in my view, would be suspect.
Cheers.
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07/12/16
John S.
07/12/16