I get confused on how the P value is interpreted in relation to a one tailed vs two tailed test.
For example, the textbook problems will say “interpret the p value (reject/no reject) at the 5% significance level”
If its two tailed, do we divide the 5% significance level and compared this against the p value from the regression?
Thanks,
You compare p to α; no multiplying, no dividing: straight comparison: which is bigger?
how would alpha be interepreted in relation to the significance level of 5%? Do we have to divide this 5% by 2 in a two tailed test to get the appriopriate alpha value to compare against the p value?
α is the (chosen) level of significance; in your example, α = 5%.
You compare p to α; no multiplying, no dividing: straight comparison: which is bigger?
Not sure if this applies to the curriculum scope, but if you are given a two-tail p-value for a one-tail test, you divide the p-value. Modern software often gives two-tailed p-values in regression output in the t-test for each coefficient.
Would the exam problems indicate if it was a one tailed or two tailed alpha value (in case we have to divide to get the appropriate p value to compare to the test statistic).
For example, for a level of significance of 5%, the alpha value would be 0.025 (5%/2) and use this to compare against the p value?
or are alpha values only used to compare in F tests (where we would then just assume that both the p and alpha value are just one tailed)?
If they tell you the significance level (alpha) is .05 (5%) and the test is one tailed, just compare alpha to a one-tailed p-value. My assumption, for the CFA exam scope, is they will give you a p-value with the “appropriate tailedness.” If anything you would need to know the correct critical z value to use for a one-tail test at the 5% level (1.645) vs. a two-tail test at the 5% level (1.96).
Alpha is a preselected threshold that is independent of the data and used in null hypothesis significance testing. It could use any test statistic be it F, chi-squared, t, z…
I was just saying that the real world has statistical software packages that may give you a two-tail p-value and you need to understand when to divide the p-value before making a conclusion on your hypothesis test.
S2000 should be able to better clarify if this is beyond the curriculum scope.