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#1
06-05-2015
 USMLE Forums Newbie Steps History: 1 + CS Posts: 7 Threads: 3 Thanked 0 Times in 0 Posts Reputation: 10
Biostat

Researcher thinks that the new medication she was testing has a real effect upon blood pressure. sHe publishes her research, stating that the p-value of her analysis was < 0.05 and thus the medication did affect blood pressure. In truth, the medication doesn't affect blood pressure, and the data simply represented a normal (although unusual) variation. What type of error did she commit?

Please some one explain this question.

Thank You.

#2
06-05-2015
 USMLE Forums Scout Steps History: 1+CK+CS Posts: 66 Threads: 0 Thanked 101 Times in 50 Posts Reputation: 111

Quote:
 Originally Posted by novanova Researcher thinks that the new medication she was testing has a real effect upon blood pressure. sHe publishes her research, stating that the p-value of her analysis was < 0.05 and thus the medication did affect blood pressure. In truth, the medication doesn't affect blood pressure, and the data simply represented a normal (although unusual) variation. What type of error did she commit? Please some one explain this question. Thank You.
This gets into an area of stats that confuses many people. alpha and beta and type 1 and type 2 errors and "power" and "nulls" -- it's a LOT to keep straight!

So here's my quick and dirty way to do it, and it all revolves around the formula for power:

Power = 1 - beta

Power: our ability(or probability) to detect something IF it actually exists.

So what's beta? Well, if beta was 0, then according to the formula, our power would be 100%. So therefore, logically:

Beta: probability we WON'T detect a difference even if it exists.

We could use simple algebra to rearrange our formula as this:

Power + Beta = 1

or

Probability of detecting a difference + probability of failing to detect it = 1

To put it into a simple analogy:

Probability of rain tomorrow + probability of no rain tomorrow = 1

So now we can say that beta means failing to find a difference that's actually there.

So what's alpha? The opposite of course:

alpha = probability the difference you found isn't really there.

Does this sound familiar? It should, because that's exactly what a p-value is. It's the probability that the result was simply a result of random chance in our sampling.

In science and especially in medicine, we've all just decided that 5% or 0.05 is the level we call "significant."

In the example above, the researcher found a difference that had a <5% chance of being due to random chance, but it turns out really was due to random chance. Even though it wasn't likely, she committed an "alpha" error after all.

The only other terminology to remember is Type I vs Type II error, and these correspond very nicely with alpha and beta:

Alpha = Type 1
Beta = Type 2

So our researcher in this question could also be said to have committed a type 1 error.

Sorry for the long answer, but this is a common question I get from people I work with.

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