Help please! How do you hand (calculator) calculate a p-value?

Question

I've always tested my hypotheses by comparing my t-stat or F-stat to the t-value or F-value (respectively) found in the appropriate tables. My prof wants us to also calculate the P-value. I know it's a number VERY close to zero for this particular problem (minitab likes to call it zero, but excel says otherwise:), but I do not know how to calculate this for myself. Please help! I can pretty much use any calculations that can be found in Excel (etc.) output aside from the P-value (itself). I already know to reject the hypothesis, but I need help calculating the P value. Thanks!

It's not a normal distribution. I have calculated the t and F statistics, but I need to be able to hand calculate the P-value using only the out provided by my statistical software (Descriptive Statistics, Regression Analysis, and Analysis of Variance are all fair game to use in the calculation).

Answer 1

divide 22 by 7 will give nearly equal result

Answer 2

If you have a small sample from a large population and the sample meets certain requirements, we can assume the the sampling distribution is normal. If not the sampling distribution may be represented by a t-table (because of degrees of freedom) or by an F-distribution.

I'll assume that you are working with a sampling distribution that is represented by a normal curve. You normally place the mean of the normal distribution at the sample mean and calculate the area under the normal curve tail that extends beyond the hypothesized (null hypothesis) value.

Many tables and online z-table calculators simply don't have enough accuracy for what you want here. (I'm not sure that the normal curve will be an accurate estimation technique that far off into the tail of the table anyway.) However, you can use a technique call interpolation to come up with an estimate. I'd use Excel, because the spreadsheet seems to have adequate accuracy.

Most computer languages do not have sufficient number of digits resolution to help, however, I've included a couple sources to C# languages that may help. The good thing about interpolation is the fact that the normal curve flattens out when you have a large z-value and interpolation between large z-values should be accurate.

I hope that some of the references will be of help to you. It can be difficult to find tables that have values for large z-values.

Answer 3

RE:
Help please! How do you hand (calculator) calculate a p-value?
I've always tested my hypotheses by comparing my t-stat or F-stat to the t-value or F-value (respectively) found in the appropriate tables. My prof wants us to also calculate the P-value. I know it's a number VERY close to zero for this particular problem (minitab likes to call it zero, but...

Answer 4

You solve this exactly the same as you would a t or F stat, except instead of solving for t or F, you solve for alpha! Plug in your coefficient (result) instead of t or F, but DON'T put alpha in the equation -- solve for it instead.

It's tricky to explain without a specific problem, so try to look up examples in your book or on the internet to make sure you solve this correctly.

Good luck!