Inferential analysis of data (12 in book) pg 99 Flashcards
What are the 2 types of hypothesis?
The null hypothesis: H
The alternative hypothesis: H
Example: If we were testing to see whether a new analgesic was more effective than the existing analgesic and we had a theory that it
was more effective the statistical hypotheses would be set up as follows:
HO: There is no difference between the new and old analgesic drug.
HA : The new analgesic is more effective than the old analgesic.
H0: Mdn (New) = Mdn (old)
HA: Mdn (new) < mdn (old)
H0: Mdn (New) = Mdn (old)
HA: Mdn (new) < mdn (old)
H0 means null hypothesis
HA means alternative hypothesis
Mdn means median
we test the alternative against the null
One or two tailed test examples
The hypothesis test that we set up
had a direction - we were hoping that the new drug would be better than the old. This type of test is said to be one tailed.
If we had a situation where we had two new drugs (X and Y) and we were not sure whether there was any difference between them
then the hypotheses would need to be set up slightly differently. The null hypothesis would be very similar to that used in the
previous example:
H0: There is no difference between drug X and drug Y
The alternative hypothesis would be slightly different:
HA: There is a difference between drug X and drug Y
This type of test is said to be two tailed. It could go either way and we have no opinion as to which way that will be.
The statistical hypotheses would be as follows:
H : Mdn (X) = Mdn (Y)
H : Mdn (X) ≠ Mdn (Y)
one or two tailed
The statistical hypotheses would be as follows:
H : Mdn (X) = Mdn (Y)
H : Mdn (X) ≠ Mdn (Y)
one or two tailed
What is a Type 1 Error?
A Type I Error occurs when H0 is rejected when in fact it should have been retained. The probability of a type I error occurring is less or equal to the significance
level chosen. Reducing this level (e.g. from 5% to 1%) will obviously reduce the risk of a type I error, but will inevitably increase the risk of a type II error. This type of
error means that you have in reality backed a loser by, for instance, deciding that a new drug is (more) effective when it isn’t.
What is a Type 2 error?
A Type II Error occurs when H0 is retained when in fact it should have been rejected. If it is not appropriate to use a less stringent probability level, an increase in
sample size will reduce the risk of a type II error. This type of error means that you have missed a winner by, for instance, deciding that a new drug is not effective
or better than the current drug when it is.
Clinically which would be the more serious error? Type 1 or type 2
Type 1
Hypothesis test vs the confidence interval
A hypothesis test gives the probability (p value) of whether the mean value of the sample could reflect the population mean. This is a point estimate and could vary from sample to sample.
A confidence interval is more informative than a hypothesis test, since it provides a range of estimated values for the unknown population parameter.
