Quant - Hyp Testing - Significance

Starting to lose my mind and wondered if anyone has a clear(er) way of understanding the results of a Hypothesis Test… I know how to calculate, and when to reject/accept Null, but the result of such decision is what’s getting to me (when is it significant, what does it mean that it is significant etc). This is a general inquiry, not related to any specific question.

Any help?

I claim the IQ score of CFA candidates not less than 125, may be because I think highly of you folks. You come to me and say I don’t think so, I will run a hypothesis test to check.

H0: IQ >= 125, Ha: IQ < 125

You want to prove me wrong by showing that the average IQ is less than 125. So, if you can reject the null (IQ >= 125), then my claim may not be correct, and you accept the alternative that IQ scores are actually less than 125.

You go and sample 100 candidates and find that the average IQ is 120. The question is whether 120 is significant or not…may be it is really not different from 125 from a statistical point of view. Do your t-test and then if t_calc > t_critical then you can reject my claim (H0)…otherwise, you cannot reject it. Notice that this cannot prove me right, it can only reject my claim. In addition, you would committ a type I error if you reject my claim when it is in fact true. Hope that helps.

This is how I understand it, though my knowledge of QM is a little rusty:

Testing for significance means testing if a result is statistically significant. As you probably know from level 1, its hard to measure the true coefficients of the entire population, therefore we need to estimate them from a sample.

Just because the ANOVA table returns a slope coefficient that is very high, it doesnt mean that the true population coefficient of the explanatory variable would not be 0 - it could appear to be explanatory for the particular sample on which you ran a regression - but in reality it might no explain it all (if we used the whole population).

The purpose of hypothesis testing is to see if we can claim with a high level of confidence that our sample coefficient approximates the population coefficient - i.e. we want to be able to claim that based on this sample, the population coefficient is not zero, and therefore the independent variable really does explain the dependent variable.

Not sure if what I wrote is clear or entirely correct. I’ll check my notes and edit it if need be, or someone please correct me. Thanks.

Thanks. I use your posts as guidelines and do some questions.

What throws me off is when you are testing t significance for individual variables, and then testing the significance of the F test… I get thrown off when it reads like, t tests are not significant and F is significant etc… and then what does that realy mean…???

Thanks again.



I will try to make the big picture little clear.

I may do some research and get to the result that on average: x = 0.4 and thus conclude that x is not zero. However, stats guys won’t agree. They will ask: Are you sure? How many times have you checked x? Was it always 0.4? May be some times it was 0.3 and sometimes 0.5 as well? If yes, then it can be 0 sometimes as well. Let’s test it statistically.

This is where they bring in t statistics by converting 0.4 into t-statistic and then comparing it with the number from table. This calculation takes care of two very important variables. One is error rate (i.e. if we always got x=0.4 then error rate is zero - which is highly unlikely) and second is sample size.

Best wishes

Okay I remember a not-so-interesting epic that my grandma used to tell me when she used to teach me the power of unity. The story goes on like this: individual broom sticks may not be able to create much of a impact when you try to hit someone with them but if you bind them together and make a broom, the broom is capable enough to whack someone down, so in this case there is an external factor called unity which basically makes these sticks more powerful colletively than individually. This power is called Multicollinearty in Quant. T-tests are capabilities of indivudal sticks and F Test is the power of the broom. The only problem with this power is that we don’t perceive it as positive as we want to tackle every problem individually. This is more of a dictator’s view. This view is such that If you can figure out indivudal element that is making the most impact, you can probably beat the system by beating that particular element. For example, US administration thought if they kill Laden, the whole Al-Queda is going to fall apart, and it is true in some sense too, because here one element was driving everything.

To sum it up, even though individual factors do not exlain the results (t tests), model (F test) does because of Multicollinearity.


I claim the IQ score of CFA candidates not less than 125, may be because I think highly of you folks. You come to me and say I don’t think so, I will run a hypothesis test to check.


H0: IQ >= 125, Ha: IQ < 125

I think the null should be what you want to negate.

H0: IQ <125 One tailed test; Therefore Ha: >=125

I like the kamran’s example…it hits right on the head.

Our Hypothesis says x=0.4. Now how significantly is it close to 0.4.

So the sample will help us establish wheather the we had it 95% of the times, indicated by t-stat which in essence, measures whether the std deviation was less than 5%. A high t-stat indicates that it is pretty significant that the null is negated OR Ha is right OR ==> we can easily reject the null.

However when no as significant we may have to give up rejecting null and confirm sadly that H0"IA<125.

Please correct me if wrong

Here you are testing a different hypothesis. If you reject this formulation then you are saying that you don’t accept that the mean IQ scores is less than 125, but that doesn’t help because the original claim is that scores are >= 125. In fact, you confirmed the claim!

My problem is determining if it is statisticaly significant or not… understanding the relationship between rejecting/accepting the Null, and what the statistical meaning of that is.

Going through some questions, some of the potential MC’s were:

a) is statistically significant, xxxx explains the change in yyyy

b) is not significant, xxxx explains the change in yyy

b) is statitcally significant yyyy explains the change in xxxx

this is just a made up ‘answer’. I just get confused when I test the T’s or F’s and reject or accept based on critical and all that stuff… what is my answer? what does my answer mean?

i hope that i come across a questions that I can post for discussion.

Matori: t tests are for each variable. If you reject the null (meaning the T stat you calculate is higher than the value from the tables), that means that variable is significant.

F tests are for the ENTIRE equation ie all the variables together. For example if you are trying to explain stock returns, and your independent variables are size of company and GDP growth. the F test would test whether the size of the company and GDP growth, together, explain stock returns.

you would do two separate T tests on GDP growth and company size, to see if those individually helped explain stock returns.

Hi Kiakaha. Been some time.

I understand when to use the T and that its for individual and F is for multi. What I am struggling to figure out is…

lets say you reject Null when doing the F Test… What does that mean?

Your first part is very helpful. I am trying to learn these conclusions when doing different testings T, F, and seeing if the variables are significant and what it actually means.

Questions like this kill me:

Q: Does the information indicate the presence of seasonality? A. No, because the lag-12 autocorrelation of the residual is not significant (Having difficulties understanding when it is significant and when it is not. I am correct to say when you reject null, it is significant)? B. Yes, because the lag-12 autocorrelation of the residual is significantly different than one. C. There is not enough information provided; the autocorrelation for the first lag is also needed to detect seasonality. A: The autocorrelation in the twelfth month is not statistically different from zero. Thus, there appears to be no seasonality.

signifcance means you reject the null.

signifcance means you reject the null.

Matori: it’s C

always y is dependent, x is indep

so x is meant to explain y

Matori: with almost all these tests (unless they give you a different number) you’re testing whether the variable is significantly different from zero. ie you’re testing whether including that variable makes a difference to your prediction for Y.

If you think about a regression equation eg Y = B0 + B1(X1) + B2(X2) + e

if B1 is zero, then the B1(X1) might as well not be there at all, it’s not making any difference to your result.

So, with all these tests (again, unless they specify otherwise), the null is that the variable = 0.

If you reject the null, that means you are rejecting the idea that the variable = 0.

If it doesn’t = 0, it is affecting your overall result and ‘deserves’ to be in your equation. ie, it is significant.

Much Appreciated!