One Tailed Two Tailed

[Karthik & Vaidy]

Hi David

I have a basic question. How will you decide whether a test is one tailed or two tailed. I shall be thankful to you if you can illustrate with this example.

Further I referred one web site which states In a one-tailed test, the critical region will have just one part . If our sample value lies in this region, we reject the null hypothesis in favour of the alternative.

In a two-tailed test, one is looking for either an increase or a decrease. Kindly excuse me for asking this basic question.

 

[David Harper CFA FRM]

Hi Karthik

Your null is a "straw man:" you hope to defeat it. The alternative is your belief/hope, so it should be revealed in the phrasing of the question-hypothethis. Please note these two examples from Gujarati:

Gujarati 7.08 http://forum.bionicturtle.com/viewthread/1315/
Here a test for the beta of a stock.
Normally, we think something like "is the beta different than 1.0?" and as this can go either direction, implies two-tail
But here the question is "A security whose beta coefficient is greater than 1 is called a volatile or aggressive security" so we are looking for (hoping for, maybe) a beta greater than 1.0. Our hunch (hypothesis) here explicitly in one-tailed since we are looking only in the one direction (greater than). That's our alternative, so the null must be "everything that remains:" beta < or equal to 1.0

Gujarati 7.07 http://forum.bionicturtle.com/viewthread/1314/
Here is a more difficult test of the slope.
Normally, and for exam purposes almost always, we are testing for the signifance of the (beta) coefficient. Which simply means the null is beta = 0 and the alternative is < or > so it is a two-tailed test.
Here the belief (or "hunch") is that the slope should be positive, so this is a sneaky question almost, because it is not explicit in the phrasing, but the idea is: we want to show a positive relationship so our null will be "slope is less than or equal to 0;" i.e., one tailed. In this case, again, our hunch is really one-sided, we have no hope for a negative beta, so we just test the one side.

another way to look at this is: the one-tailed implies that we have some explicit conviction about the direction/difference between null and hypothesized value.
Otherwise, our default is two-tailed: e.g., the typical sign test of regression coefficient is two-tailed, as our default lacks conviction about the direction.

Also, another tip: the null must have the "=" in it, so null must be either
sample stat = hypothesized paramater, or
sample stat <= hypothesized paramater
sample stat >= hypothesized paramater

the alternatives do not have the = so they are:
<>
>
<, or

David