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 $ 17$ 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 $ x_1$ denote the use of the original method and let $ x_2$ denote the use of the new method.

The set $ x = \{x_1,x_2\}$ is the independent variable. Each $ x_i$ is sometimes called the treatment (or level if $ x_i$ 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 $ y$. This indicates the amount of gastrointestinal discomfort in response to the treatment, $ x_1$ or $ x_2$.

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

$\displaystyle H_0 : \mu_1 - \mu_2 = 0 ,$ (12.1)

in which each $ \mu_i$ denotes the ``true'' average value of $ y$ at the same point in the experiment, by applying treatment $ x_i$ to all people in the world.12.1The hypothesis $ H_0$ implies that the new method has no effect on $ y$, and is generally called a null hypothesis. The negative of $ H_0$ is called an alternative hypothesis. In our case this is

$\displaystyle H_1 : \mu_1 - \mu_2 \not = 0 ,$ (12.2)

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

Steven M LaValle 2020-01-06