Hypothesis testing

CFA Level II Quant
#1

Hello,

I am confuse about when we cant reject null hypothesis then, what is difference between these two conclusion ?

  1. Can not conclude that corelation cooefficient is significant.

  2. Can conclude that corelation cooefficient is not signigicant .

Thanks

#2

The null hypothesis is that the slope is zero. If we do not have enough evidence to reject the null hypothesis, then we conclude that the slope might not be significant (i.e., that it might be zero).

#3
  1. and 2) are the same, but they are answering different questions.

In the first one the researcher might asking if the coefficient is different than zero (statistically significant).

In the second one he might asking if the coefficient is equal to zero (not statistically significant)

The common questions are like the second one, so the 2) is the common answer too.

Regards

#4

Hi ,

For above query the details are as following :

n=36 ; Correlation Cooefficient = -0.28 ; significance level = 5% and critical value = 2

Calculated t = -1.7

Clearly we will reject Ho

after this I am confused about significant part.

Do I have to link this with p value to conclude that cooefficient is significant or second option of my original query is just a statement to confuse candidate.

Thanks

#5

Hi,

When we can not reject the null hypothesis that means there is no statistically significant relation between the variables.

thus we can conclude second conclusion but in answer its first one.

Thanks

#6

This is not tricky. I think you missing some things.

Correlation coefficient can be from -1 to +1, so its center is Zero. If you check the T-test for testing correlation coefficient significance, you can see that the T-test can be negative too. So, if your calculated t is -1.7, your t critical value must be -2, not 2. Why? Because this is a two-tailed test. In this case, as the calculated t is higher than critical (remeber they are negatives), you FAIL to reject the Ho, or you accept the alternative hypotesis.

I prefer to use the absolute value of the calculated T and the critical values, so I dont get confused when they are negatives.

| calc. T | > | critical value | = Reject Ho

| calc. T | < | critical value | = Fail to Reject Ho (accept the alternative)

Pro Tip Of The Day !

All T-test use n - 2 degrees of freedom.

Regards

#7
#8

(A): I’m agree with your statement. Thats why we cannot say “Accept the alternative”, we say “Fail to reject the null”. I wrote it just to make it easier to differientiate from Fail to Reject Ho (this always a confusing part when learning Hyphotesis test" for students)

(B): Isn’t it going against A) ?

©: Ok with this, but be careful when replying like this, you can generate confusion. It seems you renaming what I wrote when in fact you are claryfing your statement (A)

(D): At least, T-tests for slopes, intercept and other coefficients in regression analysis is done with n-2 df

#9
#10

(A) I meant that “accept the alternative” is usually used instead of “Fail to reject Ho” which is wrong because the reasons we have already exposed.

(B) Ok.

© Lets this part there.

(D) Yes, you right, my bad. Df = n - k -1, just rememberd now why you need an adequate or minimal number of observations when your model has many variables. Using many variables and a few observations causes your DF are reduced bad so your Confidence Intervals for coefficients are wider giving you more uncertainty about the results. Models must be parsimonious !