When do we reject a null hypothesis in case of following

CFA Level II
#1

In case of Heteroskedasticity, and Dickey Fuller (Unit Root test), when do we reject a null hypothesis. ie. If Stat value > Critical value, or the opposite of it. Thanks for help

#2

Reject when > critical value from table

#3

Are you sure in case of Unit Root ? Because, I just solved a topic test, and it claimed the following statement

"Because the unit root test statistic (–18.7402) is smaller than the critical value (–2.89), the AR(1) model does not exhibit a unit root" In unit root hypothesis testing, our null hypothesis is that it unit root exists. So this means that if Test stat > Critical value, then technically Ho should have been rejected, meaning unit root does not exist. However in case of above, opposite is seen.

#4

I think all t-test are rejected when l Value l (absolute value)> crtical t-value.

@125mph where have u been all day :D, I’ve been posting questions and you weren’t active like the usual, having a day off :smiley:

#5

When You reject DF, you conclude unit root does not exist.

18.74 > 2.89

you’re looking at the opposite tail

#6

Hi. Thanks a lot for replying. Could you answer my query in the 4 cases as below Suppose, Case 1: tstat=-3, Critical value = -2

Case 2: tstat=-1 Critical Value = -2

Case 3: tstat= -3 Critical Value = 2

Case 4: tstat= 2 Critical Value = -2 In the above cases, would we reject or accept the null hypothesis. Also would Case 3 and Case 4 exist, I doubt they would not. Your answer really means a lot to me.Thanks

#7

All cases can exist. You’re picking the wrong side of the distribution to compare. If those quest came on the test I would do:

case 1: reject

case 2: do not reject

case 3: reject

case 4: do not reject

Maybe ask tickersu and he can give more formal explanation.

#8

Thanks a lot man. Your answer really gave me a clarity. Is there a way to quote TickerSu here ?

#9

Yes, if your thread title includes something like “p-value”, “hypothesis”, “t-table”… he’ll usually find his way in the thread.

#10

For a 2-tailed test, the question to answer is whether the calculated value is closer to zero or farther from zero than the critical value.

  • If the calculated value is closer to zero than the critical value, don’t reject H0
  • If the calculated value is farther from zero than the critical value, reject H0
#11

Sure, these can all exist.

#1 reject Ho

#2 fail to reject Ho

#3 Fail to reject if one tail test (upper); if two tail, then -2,+2 are the critical values and reject Ho because -3 < -2

#4 Fail to reject if a one tailed test (lower) but reject if two tailed test since test stat =critical value (implies p-value = alpha)

Overall, your decision to reject the null is based on the same procedure (test statistics in the rejection region, p-value no larger than alpha). However, you need to be keenly aware of the null and alternative hypothesis in each test to know what the conclusion you make.

#12

In Dickey-Fuller testing, the null is that beta = 0 = (1-rho) so rejecting Ho suggests rho is different from 1 which means there is not a unit root. Failing to reject Ho means the data are not strongly disagreeing with rho being 1 which means the data are somewhat compatible with unit root (hence fail to reject Ho means you can’t disagree with a unit root based on the data and particular alpha level).

#13

Ahh, so test stat = critical value would be a reject and not a fail to reject? I thought the test was >, not >=?

#14

So my cases all assume two-tailed test, although there could be an issue with case 4, according to tickersu.

#15

Technically, yes if alpha and p-value are equal you would reject H0 because alpha is the threshold where you say “not more than x% of true null hypotheses will be rejected.” The issue is somewhat trivial though as most cases alpha and p value or test statistics and critical value are not actually equal. In another light, the size of the p-value conveys information regarding how much our sample contradicts what we expect under the null hypothesis. When the p-value gets smaller, there is more evidence contradicting the null. Even if you technically reject Ho with p-value .05000000… and alpha .05, do you really think this tells you something different than a p-value of .053? Hopefully, you say no because “significant” and “nonsignificant” are just ways of dichotomizing a continuous summary of evidence from the sample (the p-value). There is nothing magical about a test being significant versus not significant, it’s just a way for you to say “at this threshold, I’m willing to conclude the alternative.”