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

$$H_0 : \mu_1 - \mu_2 = 0 ,$$ (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

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

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