p- value

CFA Level II Quant
#1

Hello,

Can you please help me to understand this definition of p - value?

“It is the likelihood of the test statistics being higher than the computed test statics value assuming null hypothesis is true.”

Thanks in anticipation

#2

P value small is same as T-stat big - reject null.

so a p value of 0.01 when hypothesis is 95% one tail - reject null. as 0.01 < 0.05.

#3

Minimum (Maximum?) value you can reject the null hypothesis.

#4

simply, it’s the lowest level of significance at which you can reject the null hypothesis, that said;

  1. If the chosen α > p, you reject the null
  2. If the chosen α < p, you don’t reject the null
#5

Ya ,I agree with your point , but still not able to understand the relative comparison of T stats with itself, in the statement I originally posted.

But to best of my knowlede for p-value we conside 2-Tail test.

#6

This is technically incorrect. It it the probability of a test statistic equal to or more extreme than the current one, if the null hypothesis is true-- small point.

The statement in bold isn’t really the definition of a p-value (despite that many people say it is-- it’s just a statment about how it could be used-- more operational and poorly simplified-- and, it should never be used in this manner. Alpha should always be selected prior to seeing any data). The technical and more correct definition of a p-value is the probability of obtaining a test statistic at least as extreme as the current one, assuming that the null hypothesis is true.

Your decision rules are correct, though, if you say that a p-value less than or equal to alpha will cause a rejection of Ho.

#7

Could you be more specific with your question? Do you mean you are unsure how the p-value and alpha relate to test statistics and critical values?

In most regression output you will generate, the default is to provide a two-tailed p-value, so you would need to divide it by two (possibly need other manipulations depending on the situation) if you wanted to use it for a one-tailed test (say, bi <0). Aside from that, p-values can refer to the probability in one or two tails, up to and inclusive of the current value.

#8

I wrote an article on p vs. α that explains this fairly well: it has pictures. You’ll find it here: http://www.financialexamhelp123.com/p-vs-α/

Full disclosure: as of 4/25 I’ve installed the subscription software on my website, so there’s a charge for viewing the articles.

#9

Well I know the relationship between alpha and p value…

if alpha is greater than p then reject the null and if it is less than p dont reject the null.

So as per my orginal question : assuming null hypothesis is true , then alpha will be less than p-value.

so t stat calculated using alpha as significance level will give us small t stats as comparison to if, I would have used p-value as my significance level.

I think that is what the original statement posted by me meant to be??

Thanks

#10

This isn’t true.

You could make a Type I error.