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p-value of observation

Posted on 2011-09-05
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Can you explain the example?

In the above example we thus have:

null hypothesis (H0): fair coin; P(heads) = 0.5
observation O: 14 heads out of 20 flips; and
p-value of observation O given H0 = Prob(= 14 heads or = 14 tails) = 0.115.


I am not sure how to get 0.115? Thanks.
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Question by:zhshqzyc
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by:John_Arifin
John_Arifin earned 50 total points
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The p-value of head only = 0.057659149169921875, it is rounded to 0.058
The p-value of head or tail = 2 x 0.057659149169921875 = 0.11531829833984375 rounded to 0.115
 
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TommySzalapski earned 200 total points
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Forgive me if this explanation is too basic. I'm attemping to answer this in such a way that you can understand no matter how much you know.

A hypothesis is an attempt to explain an observation. It's kind of a fancy guess. So when you see a lot of data, you can make a hypothesis on what the probabilities involved are.

In this example, someone has guessed (hypothesized) that the coin is a fair coin (so the probability of each flip is 50/50 heads or tails). We ran an experiment to test that and found that in 20 flips, 14 were heads and 6 were tails.

Now we need the p-value which is the probability that we would see results like we saw (or more extreme) assuming the guess is true.
If it is true that the coin is fair, then there is roughly a 5.8% chance that we would see 14 or more heads. But since we are testing if the coin is fair, 14 heads would be as significant as 14 tails. So the probability that we see 14 or more of any one side (heads or tails) is twice that of the heads (or roughly 11.5% in this case).

So assuming the coin is fair there is about an 11.5% chance that data as extreme as we saw in our experiment should happen. Since (in most cases) 11.5% is not low enough to reject the hypotheis, we can say that it has not been disproven.
Note: we certainly can not say it is proven. In fact, you really can't "prove" anything with 100% certainty in pure science since there is always a chance (even if a miniscule one) that your result was a coincidence.
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