Solved

p-value of observation

Posted on 2011-09-05
2
451 Views
Last Modified: 2012-05-12
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.
0
Comment
Question by:zhshqzyc
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
2 Comments
 
LVL 3

Assisted Solution

by:John_Arifin
John_Arifin earned 50 total points
ID: 36486302
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
 
0
 
LVL 37

Accepted Solution

by:
TommySzalapski earned 200 total points
ID: 36486738
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.
0

Featured Post

Get HTML5 Certified

Want to be a web developer? You'll need to know HTML. Prepare for HTML5 certification by enrolling in July's Course of the Month! It's free for Premium Members, Team Accounts, and Qualified Experts.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Introduction On a scale of 1 to 10, how would you rate our Product? Many of us have answered that question time and time again. But only a few of us have had the pleasure of receiving a stack of the filled out surveys and being asked to do somethi…
Article by: Nicole
This is a research brief on the potential colonization of humans on Mars.
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
Suggested Courses

617 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question