Question

Can someone provide me the formula, or statement, to calculating the P-value given a (1) z-statistic value, (2) t-statistic value, and (3) f-statistic value (include left tail, right tail, two-tailed for all 3). I've searched all over but the descriptions and videos just don't cut it. They just look at the respective table and pop a value out of no where without providing an actual formula or statement that says given this statistic, use this formula, or follow these simple steps. It's always here is the table, and seconds later, out comes a P-value without writing anything down, showing their work.

Answer 1

1. The pvalue by using z-statistics is obtained by using the formula

In case of one tail test

P(Z>=z) where z is the absolute value of z statistic.

It can be obtained by using z table.

Suppose the value is 1.34

We have to check the value of 1.3 in fourth column.

Or by using R command:

P=1-pnorm(1.43, 0,1)

For two tail test multiply P by 2.

I. e pvalue=2P

2. To obtained pvalue by using t statistic.

We have to check in the pvalue table of t- distribution table.

In which we have to go for the value of the statistic and need to locate in the respective degrees of freedom.

By using R command:

P=1-pt(t, DF) ##for one tail test

For two tail test Pvalue=2P

3. To obtain the pvalue for f distribution we have to look into the f distribution table. For a particular f value we have to check in the respective degrees of freedom in the nuemarator and denominator.

By using R command:

P=pf(f, df1, df2)