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#1




pvalue 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 pvalue is the likelihood of type 1 error. But i am still not sure i understood pvalue clearly. How do we calculate pvalue? 
#3




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 pvalue is greater than 10%, for example 14%, then we would not reject H0 at the 10% significance level. If the pvalue 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




pvalue vs level of significance
I like to think of the significance level as a benchmark as to what the pvalue 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 pvalue, 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




Thanks.I think i now get it

#6




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#8




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 pvalue calculation will be the same in both fields. The significance level is an assumption. The pvalue is an actual calculation or probability. 
#9




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