Hypothesis testing is the foundation of research. The process of developing a research hypothesis usually involves two steps: developing the broad research question, then determining the statistical alternatives that may result from testing the research question. For example, a researcher may believe age of dam influences risk of neonatal calf scours in their offspring. Data may then be collected and analyzed to explore this hypothesis. In statistical terms, we refine the broad hypothesis to a “null” and “alternative” hypothesis, that help direct our analysis. For our example of neonatal calf scours, a null and alternative hypothesis may be as follows:
Null: There is no difference in risk of neonatal calf scours between calves born to first-calf heifers or 3-year-old cows
Alternative: There is a difference in risk of neonatal calf scours between calves born to first-calf heifers and 3-year-old cows.
The null hypothesis usually states that there is no difference in outcome or risk between exposure groups, or that there is no association between the measured exposure and the outcome of interest. In the example above, we don’t specify whether age of dam will increase or decrease the risk of neonatal calf scours, so the alternative hypothesis is irrespective of direction regarding the change in risk of disease. We are simply interested in whether a difference in risk exists. The risk of disease in calves from one dam age group (e.g., first-calf heifers) may belong to a distribution where the mean risk is greater, or less, than the mean risk of disease in calves from another dam age group (e.g., 3-year-old cows). When the statistical hypothesis does not consider direction of difference, we call this a two-tailed test.
In some cases, we may consider it impossible that a deviation in risk occur in one direction. The researcher may be reasonably certain that meaningful departures from the mean risk of disease can only occur in one direction (i.e., risk of disease may only increase). In these cases, a one-tailed statistical test can be used. One-tailed alternative hypotheses are often difficult to justify, because differences in risk that occur in unexpected directions are relatively common in research. For example, studies of vaccination on-arrival in feedlots often show an increase in risk of bovine respiratory disease, which is counterintuitive to the traditional thought of vaccination decreasing risk of disease. Caution must therefore be exercised when proposing a one-tailed alternative hypothesis.
Defining and refining the hypothesis is an essential first step in conducting meaningful research. Accepting or rejecting the null hypothesis then becomes the goal of data collection, although caution should be used when interpreting results. The generalizability of results may be limited in results derived from a sample. Therefore, we can only reject the null hypothesis for the sample from which our data was obtained.