National open university of nigeria introduction to econometrics I eco 355

 
Errors in Hypothesis Testing
The central reason we do hypothesis testing is to decide whether or not the sample data 
are consistent with the null hypothesis.
In the second step of the procedure we identify the kind of data that is expected if the null 
hypothesis is true. Specifically, we identify the mean we expect if the null hypothesis is 
true.
If the outcome of the experiment is consistent with the null hypothesis, we believe it is 
true (we "accept the null hypothesis"). And, if the outcome is inconsistent with the null 
hypothesis, we decide it is not true (we "reject the null hypothesis").
We can be wrong in either decision we reach. Since there are two decisions, there are two 
ways to be wrong.
(i). Type I Error:
A type I error consists of rejecting the null hypothesis when it is 
actually true. This is a very serious error that we want to seldomly make. We don't want 
to be very likely to conclude the experiment had an effect when it didn't.
The experimental results look really different than we expect according to the null 
hypothesis. But it could come out the way it did just because by chance we have a wierd 
sample.
Example:
We observe that the rat pups are really heavy and conclude that prenatal 
exposure to alcohol has an effect even though it doesn't really. (We conclude, 
erroneously, that the alcohol causes heavier pups!) There could be for another reason. 
Perhaps the mother has unusual genes.

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(ii). Type II Error:
A type II error consists of failing to reject the null hypothesis when it 
is actually false. This error has less grevious implications, so we are will to err in this 
direction (of not concluding the experiment had an effect when it, in fact, did).
The experimental results don't look different than we expect according to the null 
hypothesis, but they are, perhaps because the effect isn't very big.
Example
: The rat pups weigh 17.9 grams and we conclude there is no effect. But "really" 
(if we only knew!) alcohol does reduce weight, we just don't have a big enough effect to 
see it.