# The shameful series of questions continues [p-value this time..]

I had a little doubt on how to interpret p-vales. Could somebody explain it to me in layman’s term. say we have a p-value of 0.00236 and t-value = -3.0565 and all this is at 5% singnificance. What should the intepretation be for this case?

You need to compare the p-value with the alpha. Suppose alpha is 5%. Since p-value < alpha, you can reject the null. P-value is the smallest value for which the null hypothesis can be rejected. If the p-value> alpha, then the null hypothesis cannot be rejected. You don’t need to compare the p value with the t value. So, looking at the t value and the t-critical will give you the same result as the comparison betn. p value and alpha. In fact, I think it saves more time and that is how most of the probs have been worked out in the CFAI text.

Thanks Ruhi, This is what Schweser taught me 1. calculate t(stat) 2. calculate DoF = n – k - 1 3. find p as alpha/2 (for 2 tailed test) 4. Flip the book to grab the t(critical) 5. Compare t(stat) to t(crit) 6a. If(ABSOLUTE[t(stat)] > t(crit)) {Reject Null} 6b. Else If(ABSOLUTE[t(stat)] < t(crit)) {Fail to Reject Null} and when I am looking at the EoChapter ques in CFAI, they all use p-value. But looking at p-values, now on, will probably save me few clock ticks I feel. Thanks again. Caveat: the ‘p’ I talked off in step-3 is the header-‘p’ needed for the t-table and not the ‘p-value’ we are talking about here

Yes, t crit and t-stat works fine too. But I think that it’s always good to know the other method too, because you might be questioned on it. In fact, I did come across a couple of Qbank problems that emphasized the concept of p.

dinesh.sundrani Wrote: ------------------------------------------------------- > I had a little doubt on how to interpret p-vales. > Could somebody explain it to me in layman’s term. > > say we have a p-value of 0.00236 and t-value = > -3.0565 and all this is at 5% singnificance. > > What should the intepretation be for this case? Dinesh: The p-value is the probability of observing the test statistic by chance if the null hypothesis is true. In your case, you have far less than a 1% chance of seeing that t-stat. So, you can CLEARLY reject the null at the 5% level (and even at the 1% level). So, a t-stat bigger than the critical value is the same as a p-value smaller than the alpha. Think of the t-stat as a measure of distance. Seeing a t-stat “further away” from the null means it’s less likely to occur by chance. So, a higher t-stat means the result is less likely to occur by chance (i.e. the probability of seeing that stat by chance is lower (ii.e. the p-value is smaller) and you can reject the null at a lower significance level or alpha).

Thanks busprof, that was very hepful insight you gave on p-value. Appreciate your help