#### Formulating a hypothesis

In the simplest case, scientists want to determine a binary outcome for a hypothesis of interest: true or false. In more complicated cases, there may be many mutually exclusive hypotheses, and scientists want to determine which one is true. For example, which among different locomotion methods is the most comfortable? Proceeding with the simpler case, suppose that a potentially better locomotion method has been determined in terms of VR sickness. Let denote the use of the original method and let denote the use of the new method.

The set is the independent variable. Each is sometimes called the treatment (or level if takes on real values). The subjects who receive the original method are considered to be the control group. If a drug were being evaluated against applying no drug, then they would receive the placebo.

Recall from Section 12.3 that levels of VR sickness could be assessed in a variety of ways. Suppose, for the sake of example, that EGG voltage measurements averaged over a time interval is chosen as the dependent variable . This indicates the amount of gastrointestinal discomfort in response to the treatment, or .

The hypothesis is a logical true/false statement that relates to . For example, it might be

 (12.1)

in which each denotes the true'' average value of at the same point in the experiment, by applying treatment to all people in the world.12.1The hypothesis implies that the new method has no effect on , and is generally called a null hypothesis. The negative of is called an alternative hypothesis. In our case this is

 (12.2)

which implies that the new method has an impact on gastrointestinal discomfort; however, it could be better or worse.

Steven M LaValle 2020-11-11