I have a question I would like to know how to get the difference of standard deviations. The point is that I have two measures expressed in millimeters one is before applying one treatment (7.83 ± 1.44) and the other after the treatment (4.06 ± 0.83). When expressing my data i say the treatment reduced by a 3.77(Subtracting the means of before and after treatment) .. but, how do I get the difference from the standard deviations? Can anybody help me?
Heber -
One thing though about hypothesis tests, expressing the probability of a type II error can be awkward. Just looking at a "significance" level is incomplete when they are set without consideration of power. (It is not a good idea to use 0.05 for everything. Sample size and effect size matter.)
[By the way, it sounds like you are talking about standard error, rather than sigma, standard deviation. Well, standard deviation usually refers to a population distribution, and a standard error is a standard deviation for a parameter. So it is a standard deviation, but it is probably a good idea to make a distinction where increased sample size will or will not drive the value downward.]
If you are collecting paired data, take a look at the following, it might be helpful:
https://onlinecourses.science.psu.edu/stat500/node/51
Under "The Paired t-Procedure," you will see this: "Paired t-interval:" Just under that is a plus/minus expression for a confidence interval around the mean of the differences. I think you will find that to be of more practical use than the hypothesis test. It is more easily interpretable. You could just stop there. This will give you a confidence interval around the mean difference, assuming that is what you want. (Note that you are computing a new sigma for the differences.)
[Note that you can also find confidence intervals about differences in means for independent samples of different sizes, if you run across a need for that (if dependent samples, you need to consider covariance):
https://onlinecourses.science.psu.edu/stat100/node/57]
Cheers - Jim
Thanks Jim for the information is very interesting and now I have a better view however, for example in this randomized cross-controlled clinical trial where they evaluate certain parameters with their mean and standard deviation obtain a change expressed in mean and standard deviation but when applying the Formulas in the pages that you recommended I do not get the same results. Is there no formula to express this change in the standard deviation?
At a glance, don't know what method they used. Clinical trials not my area. But whether they used matched data pairs (doesn't seem so), or used the last method I mentioned including covariances (maybe), or something else (?), you need data observations if you want to actually reconstruct this.
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