Solved

p-value of observation

Posted on 2011-09-05
2
393 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
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

Is Your Active Directory as Secure as You Think?

More than 75% of all records are compromised because of the loss or theft of a privileged credential. Experts have been exploring Active Directory infrastructure to identify key threats and establish best practices for keeping data safe. Attend this month’s webinar to learn more.

Question has a verified solution.

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

Suggested Solutions

Title # Comments Views Activity
Two list de-cypher 6 90
Math home work questions 5 79
Geomentry-Fundamental concepts-Angles 3 66
Triangles - computing angles 7 50
This article seeks to propel the full implementation of geothermal power plants in Mexico as a renewable energy source.
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
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.
Concerto provides fully managed cloud services and the expertise to provide an easy and reliable route to the cloud. Our best-in-class solutions help you address the toughest IT challenges, find new efficiencies and deliver the best application expe…

948 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

Need Help in Real-Time?

Connect with top rated Experts

18 Experts available now in Live!

Get 1:1 Help Now