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All Drugs   CASE    CONTROL
AVG         11.07   7.88
ST DEV      3.58    2.95
# SUBJECTS  7399    3537

NM DRUGS        
AVG         5.49    3
ST DEV      4.33    2.51
# SUBJECTS  6831    2507

Ho - Cases and controls are prescribed the same numbers of medication alpha =.05

I've got some data like those above and I wish to compare if the cases took significantly more drugs than the controls. These tables are two separate, but related data. When I ran a t test the respective t-stats were like 49 and 39. Should I be using a different test here?

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It's not that the 'sample sizes are too large', it's that you're asking a different question than you want the answer to, and the sample size is large enough that you can finally see that there's a problem. So in fact the sample size is probably just large enough. My hope is that you might figure out the right question to answer, rather than throw away data (whether by choosing a low power test or by more direct means) in order to keep asking the wrong question of your data. If a hypothesis test was the right question, the results wouldn't bother you at all. – Glen_b Feb 18 '14 at 1:57
@Glen_b can you expound on that, please? My goal is to demonstrate that one group takes more drugs than the other group. I'm an (obvious) stats newbie here and will take advice willingly :) – wootscootinboogie Feb 18 '14 at 2:00
Effect sizes and standard errors will answer that question very clearly. I'd suggest drawing a nice picture. – Glen_b Feb 18 '14 at 2:01

With both groups being so large, you're essentially guaranteed to find a significant difference at $\alpha = 0.05$. It may be more informative to give your readers a point estimate of the effect size (in this case: difference between the group means) accompanied by a confidence interval.

Based on the summary data you've provided, the 95% confidence intervals of the difference between the group means would be approximately {3.06, 3.32} and {2.35, 2.63}. Your statistical package should give you the exact number.

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I was kind of worried about the sizes being too large. Thanks for the heads up! – wootscootinboogie Feb 17 '14 at 14:55

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