The Language of Hypothesis Testing

The process begins by developing a research question. For example, does the new medication, Lovastatin, reduce cholesterol levels? The research question is converted into a formal scientific hypothesis, which has two parts: The and the . The null hypothesis is stated suggesting that the medication has no effect on cholesterol. In a setting of a clinical trial with treatment and placebo groups, the null hypothesis would be phrased, “Persons (i.e. a population of persons) treated with lovastatin have the same cholesterol levels as persons not treated with lovastatin. The alternate hypothesis would be stated, “Persons treated with lovastatin have different (higher or lower) cholesterol levels than persons not treated with lovastatin. This alternate hypothesis is stated as a 2-tailed hypothesis, which considers it possible that lovastatin has the opposite effect of that anticipated by the researchers. – in this case of no difference in cholesterol levels between persons treated with lovastatin and persons not treated with lovastatin.

So for the above example, if you were doing a two-tail test, yourp-value would equal 0.022.

We usually use a t-test for a study of this design. Using our example of a clinical trial of lovastatin, the p-value would be interpreted as the chance of obtaining a between-group difference in mean cholesterol levels as large or larger than that which was observed solely through sampling error from a theoretical distribution of between group differences that had a true mean of zero (i.e. the null hypothesis).

Support or Reject Null Hypothesis

The p value is just one piece of information you can use when deciding if your is true or not. You can use other values given by your test to help you decide. For example, if you run an, you’ll get a p value, an f-critical value and a .

In the above image, the results from the show a large p value (.244531, or 24.4531%), so you would not reject the null. However, there’s also another way you can decide: compare your f-value with your f-critical value. If the f-critical value is smaller than the f-value, you should reject the null hypothesis. In this particular test, the p value and the f-critical values are both very large so you do not have enough evidence to reject the null.

the null hypothesis is not rejected when it is false c.

Example question:The average wait time to see an E.R. doctor is said to be 150 minutes. You think the wait time is actually less. You take a of 30 people and find their average wait is 148 minutes with a standard deviation of 5 minutes. Assume the distribution is normal. Find the p value for this test.

failing to reject the null hypothesis when it is false.

Graphically, the p value is the area in the tail of a . It’s calculated when you run hypothesis test and is the area to the right of the test statistic (if you’re running a two-tailed test, it’s the area to the left and to the right).

rejecting the null hypothesis when it is true.

In the ideal world, we would be able to define a "perfectly" random sample, the most appropriate test and one definitive conclusion. We simply cannot. What we can do is try to optimise all stages of our research to minimise sources of uncertainty. When presenting P values some groups find it helpful to use the asterisk rating system as well as quoting the P value:

rejecting the null hypothesis when it is false.

Sometimes, you’ll be given a proportion of the population or a percentage and asked to support or reject null hypothesis. In this case you can’t compute a test value by calculating a (you need actual numbers for that), so we use a slightly different technique.

If Z(critical) = 2.04, what is the p-value for your test?

When you run a , you compare the p value from your test to the you selected when you ran the test. Alpha levels can also be written as percentages.