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#1
01-25-2006, 09:56 AM
 Calliou Member Join Date: Feb 2004 Posts: 92
p-value and level of significance

Can someone please explain to me how they are related and how they are different? All i understood was level of significance = P( reject H0 / H0 is true)= P(type 1 error)

and p-value is the likelihood of type 1 error.
But i am still not sure i understood p-value clearly.
How do we calculate p-value?
#2
01-25-2006, 11:24 AM
 NewTubaBoy Member CAS Join Date: Jul 2004 Location: Boston Studying for CAS 8 Favorite beer: Blue Moon Posts: 1,391

They're the same thing.
#3
01-25-2006, 11:18 PM
 Howard Mahler Member CAS Join Date: May 2002 Location: Boston, MA Posts: 1,858

To a first approximation they are the same.

However, here is a typical example.
One would choose to test a hypotheis at for example the 10% significance level. (In practical applications and some exam questions, the significance level is chosen in advance, prior to performing the test or seeing the data.)

If the p-value is greater than 10%, for example 14%, then we would not reject H0 at the 10% significance level.
If the p-value is less than 10%, for example 8%, then we would reject H0 at the 10% significance level.

I hope this helps a little.

Howard Mahler
#4
01-26-2006, 12:42 AM
 2cek Join Date: May 2005 Posts: 16
p-value vs level of significance

I like to think of the significance level as a benchmark as to what the p-value must be in order to accept/reject the hypothesis test. However, the significance level also plays a part in constructing confidence intervals and/or prediction intervals. When constructing a confidence interval you again are using a significance level or benchmark which determines how wide the interval will be and with how much confidence you are sure the parameter estimate is within the interval. Here is a thought for confidence intervals: The higher the significance level the wider the confidence interval is. i.e. If you are 99% sure the parameter estimate falls within the confidence interval it had better be quite wide. Where as if you use a 70% interval you are not that sure and the interval will be smaller.

When I think of p-value, I think actual probability. In a hypothesis test you are testing an observed sample and calculating a probability of Ho being true. Of course once you have this actual probability you will compare it to the benchmark(significance level) to see whether the hypothesis test is accepted or rejected.
#5
01-26-2006, 08:51 AM
 Calliou Member Join Date: Feb 2004 Posts: 92

Thanks.I think i now get it
#6
01-26-2006, 11:03 AM
 NewTubaBoy Member CAS Join Date: Jul 2004 Location: Boston Studying for CAS 8 Favorite beer: Blue Moon Posts: 1,391

Quote:
 Originally Posted by 2cek I like to think of the significance level as a benchmark as to what the p-value must be in order to accept/reject the hypothesis test. However, the significance level also plays a part in constructing confidence intervals and/or prediction intervals. When constructing a confidence interval you again are using a significance level or benchmark which determines how wide the interval will be and with how much confidence you are sure the parameter estimate is within the interval. Here is a thought for confidence intervals: The higher the significance level the wider the confidence interval is. i.e. If you are 99% sure the parameter estimate falls within the confidence interval it had better be quite wide. Where as if you use a 70% interval you are not that sure and the interval will be smaller. When I think of p-value, I think actual probability. In a hypothesis test you are testing an observed sample and calculating a probability of Ho being true. Of course once you have this actual probability you will compare it to the benchmark(significance level) to see whether the hypothesis test is accepted or rejected.
I think this is a good explaination... just dont get confused... becuase they are the exact same number.
#7
01-26-2006, 11:17 AM
 Bühlmann Member SOA AAA Join Date: Nov 2005 Studying for nothing ever again Favorite beer: Corona Light Posts: 1,844

yes it is. thanks for posting that.
#8
01-26-2006, 12:21 PM
 2cek Join Date: May 2005 Posts: 16
The Same?

The probability of accepting Ho when Ho is true and the likelihood of the sample being of the same form as Ho are not the same thing.
They are quite different. Depending on the profession in which the statistical analysis is being performed, the significance level will vary. For example, in the medical profession someone may want to use a 1% significance level where as a statistician may use a 10% significance level. The significance level is a matter of how precise you ought to be or how much fluctuation you can tolerate. However, given the same problem, the p-value calculation will be the same in both fields. The significance level is an assumption. The p-value is an actual calculation or probability.
#9
01-31-2006, 01:08 PM
 Frenchie Member SOA Join Date: May 2003 Location: Mississippi Studying for Exam C College: Georgia State University - Alumni Favorite beer: Stella!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Posts: 8,597

Quote:
 Originally Posted by Howard Mahler To a first approximation they are the same. However, here is a typical example. One would choose to test a hypotheis at for example the 10% significance level. (In practical applications and some exam questions, the significance level is chosen in advance, prior to performing the test or seeing the data.) If the p-value is greater than 10%, for example 14%, then we would not reject H0 at the 10% significance level. If the p-value is less than 10%, for example 8%, then we would reject H0 at the 10% significance level. I hope this helps a little. Howard Mahler
I am having trouble following some examples of obtaining the p-values, specifically for an F-statistic. I'm just not seeing it. Can you perhaps come up with an example and show me how to get the p-value using the tables?
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