Interestingly, I have always been told that the null hypothesis contains the equality....EVERY TIME! Yet, what do we see in formula 5.11 in Miller's chapter 5? ...an equality in the alternative hypothesis. What is the deal?
Hypothesis Testing
- Thread starter brian.field
- Start date
hi @brian.field, i think it is meant of a rule of thumb that H0: always contains the = .
I did not realized that it is always the case, it is just often easier to claculate with H0: containing the =, than with < or >.
You can devinde the Hypotheses as you like. Often t-Test or other tests are testing to equallity of (e.g. means etc.), but you can define it as you like, the crux is then how to set the ranges for rejection and acception.
Maybe @David Harper CFA FRM could help us here in order to check if he agrees with me?
thx
I did not realized that it is always the case, it is just often easier to claculate with H0: containing the =, than with < or >.
You can devinde the Hypotheses as you like. Often t-Test or other tests are testing to equallity of (e.g. means etc.), but you can define it as you like, the crux is then how to set the ranges for rejection and acception.
Maybe @David Harper CFA FRM could help us here in order to check if he agrees with me?
thx
Thanks @Aenny - that is totally reasonable. What is a bit strange to me is the degree to which my instructors have forced us to remember the convention of equality in the null (I also required my students to do the same when I taught statistics!) I expect that there are always exceptions but Miller doesn't seem to address his (unconventional) usage at all.
Incidentally, @David Harper CFA FRM also insists on the equality in the null is the related video lecture. I would be curious to know if the formal reasoning for this convention.
Hi @brian.field ,
coming from an other perspective maybe the reason why the 'equal sign' is always within the H0 is maybe because of the definition of type I and type II error, the power of a test (1 - beta) and the significance level (alpha)?
On the other hand I would suggest adressing the equallity to Ho is kind of assumption we need to take in order to be able to do the calculations. We calculate the test-statistic and get a specific value. That value we compare with the p-values of our distribution. So in the end we compare the teststatistic being equal smaller or bigger than the p-value. Therefore we also need to state in the Hypothese being equal, smaller or equal or bigger than equal, in order to also use the p-value as cutoff value.
From the calculation view we do not use H1. We just test if we accept or reject H0. That makes sense to me, because testing to equality is easier than testing to inequality.
Does that make sense to you?
coming from an other perspective maybe the reason why the 'equal sign' is always within the H0 is maybe because of the definition of type I and type II error, the power of a test (1 - beta) and the significance level (alpha)?
On the other hand I would suggest adressing the equallity to Ho is kind of assumption we need to take in order to be able to do the calculations. We calculate the test-statistic and get a specific value. That value we compare with the p-values of our distribution. So in the end we compare the teststatistic being equal smaller or bigger than the p-value. Therefore we also need to state in the Hypothese being equal, smaller or equal or bigger than equal, in order to also use the p-value as cutoff value.
From the calculation view we do not use H1. We just test if we accept or reject H0. That makes sense to me, because testing to equality is easier than testing to inequality.
Does that make sense to you?
Last edited:
What i understand about Null Hypothesis ( H0 ) is as follows:
1. If the original claim includes equality (<=, =, or >=), it is the null hypothesis.
2. If the original claim does not include equality (<, not equal, >) then the null hypothesis is the complement of the original claim.
3. The null hypothesis always includes the equal sign. The decision is based on the null hypothesis.
1. If the original claim includes equality (<=, =, or >=), it is the null hypothesis.
2. If the original claim does not include equality (<, not equal, >) then the null hypothesis is the complement of the original claim.
3. The null hypothesis always includes the equal sign. The decision is based on the null hypothesis.
jairamjana
Member
I would say that H0 should contain an equality sign or variants of the equality sign only for convenience sake... For e.g in a typical least squares regression, take the case of the explanatory variable x(i) which has coefficients Beta(1) .. We say that when Beta(1) = 0 , then the so called explanatory variable x(i) do not explain the y(i) at any level of i .. So obviously if we state Ho : Beta(1) = 0.. We look to reject this judgement imposed on our Beta parameter.. We do that by
b1 / SE of b1 which is the test statistic .. If this value is above the rejection region which we normally define as the deviate of 5% level of significance.. then the null hypothesis is rejected .. And hence alternate hypothesis is obviously that the explanatory variable x(i) explains y(i)..
b1 / SE of b1 which is the test statistic .. If this value is above the rejection region which we normally define as the deviate of 5% level of significance.. then the null hypothesis is rejected .. And hence alternate hypothesis is obviously that the explanatory variable x(i) explains y(i)..
Hi
We make the alternate hypothesis the thing of which we want to test the significance ,here we want test the significance of the statement that "x is equal to or less than 45%" so we make it the alternate hypothesis.And the complement of the alternate is the null hypothesis.Please don't get confused by statements that null should include = and alternate should include >,< etc.
thanks
We make the alternate hypothesis the thing of which we want to test the significance ,here we want test the significance of the statement that "x is equal to or less than 45%" so we make it the alternate hypothesis.And the complement of the alternate is the null hypothesis.Please don't get confused by statements that null should include = and alternate should include >,< etc.
thanks
I admit that I learned this tip a long time ago (ie, the null needs to include the equality) and don't recall the source, but it seems to me that we need the null to include the equality in order to conduct the test? For example, in a test of the sample mean, if the null is: population mean > 46, what's our p-value based on? We're going to use (X - 46)/SE, which is using =46 as the null hypothesis. It seems to me the "=" is implicity necessary because our (hypothesis) test needs to occur at some exact point and that point is given by the "=", while the alternative does not need an "equality point" because it is only defined as a negation.
Similar threads
- Locked
- Sticky