# Measure to use in experiment

Suppose we have $100$ people and we obtain the average blood pressure $x$. Now suppose we have another group of $40$ people and they have an average blood pressure $\approx x$. How do we quantify the fact that the second experiment is more "efficient" than the first experiment? Would we do a power analysis? What would be the null hypothesis?

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What do you mean by saying that "the second experiment is more 'efficient' than the first experiment"? The fact that 2 groups have similar means is not what statisticians mean by 'efficiency'. –  gung Jan 14 '13 at 16:43
Note sure I pefectly understand your questions but here is my contribution. That's just mean that your two means are from samples drawn from the same a population with... a mean of x. If you don't use a referent(population) mean to compare these estimated means then you don't have null hypothesis and no power to calculate. Do you mean you want to test these means vs a referent mean, for example with a one sample t-test? If so, with about the same estimated x values (and so same effect size) in your two samples, then, by definition, you'll have much power with N=100 because of the higher N. –  Alric Jan 14 '13 at 17:26
By "efficient" I gather you mean something like: "We get roughly the same information back, at 40 per cent of the cost." Yes? If so, then you might phrase your statement in terms of the cost of uncertainty reduction or the value of information. In that case, it would be helpful to understand the larger context in which this information is intended to be used, in order to understand what are the costs of testing versus the costs of error. –  Arthur Small Jan 14 '13 at 17:42
I can't think of a meaning of "efficient" that would be tested by two groups having similar means. I think you need to think about measures of spread and precision of estimate. –  Peter Flom Jan 14 '13 at 17:51