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Scientists create hypotheses to explain observations and use statistical methods to test them. A null hypothesis is constructed to contradict the explanation, and the alternative hypothesis is tested against a sample of data. Three types of tests can be applied to a data set, and researchers must agree on an interpretation of the data based on the probability that the null hypothesis is rejected when it is true. An example of hypothesis testing is a pharmaceutical company testing a new treatment to lower cholesterol.
Scientists try to establish theories or discover laws that explain observations or experimental results. The first step is to build a hypothesis, or tentative explanation, for a set of facts, and then put it to the test. Statistical methods are usually used: a sample of data is examined to see if it supports the proposed explanation. Typically, a null hypothesis will be constructed, which contradicts the explanation – this is normally denoted H0 – while the explanation itself is called the alternative hypothesis, denoted HA. Initially it is assumed that H0 is true and the researcher’s task is to demonstrate that the data do not support this conclusion.
Hypothesis testing
Usually, H0 and HA are two mutually exclusive statements: they cannot both be true. They should also be comprehensive; that is, they should cover all possible outcomes of the experimental investigation. A sample of data is obtained, against which the null hypothesis will be tested. The sample must be of sufficient size to enable valid conclusions to be drawn and must be free from any bias that could affect the result.
Researchers must therefore establish a value, or one or more sets of values, that do not support H0. If the data turn out to agree with these values, the null hypothesis will be rejected and the alternative hypothesis is then likely to be true. Test data can often be represented as a graph, with a peak in the center and a “tail” on either side. Typically, most of the values for the object under test will cluster around the middle of the range, dipping towards the low and high extremes. For example, a series of height measurements of a large sample of people will show the majority around the middle of the range and smaller numbers towards the very short and very tall ends.
There are three types of tests that can be applied to a data set. In a right-tail test, it was determined that data exceeding a certain value, known as the critical value, does not support the null hypothesis; in a left-tail test, this data is less than the critical value; in a two-tailed test, data that does not support H0 is above and below a certain value or range of values. It is not possible to completely disprove the null hypothesis; instead, researchers must agree on an interpretation of the data based on the probability that H0 is rejected when it is indeed true. This probability is known as the significance level. For example, if a certain proportion of the data is above the critical value in a right-tail test, this could indicate that there is only a 1% chance that H0 is true.
Example
A pharmaceutical company could test the results of a new treatment to lower cholesterol. In this case, the null hypothesis would be that cholesterol levels did not reduce after taking the drug, while the alternative hypothesis would be that the levels did decrease. H0 is assumed to be true and researchers then collect data for analysis in an attempt to reject it.
The data could consist of cholesterol measurements in a sample of people before and after taking the drug, compared with a similar sample who didn’t take it, over the same period. The researchers could therefore agree on how much a reduction and in what proportion of the sample that took the drug can be considered significant. This information can be used to set a critical value, such as a 10% reduction in 80% of those who took the drug. If the data falls above these values, the null hypothesis is rejected and the alternative hypothesis accepted.
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