## A library for property based testing

### Step 5: Since the P-value , we reject the null hypothesis.

A** logical hypothesis** is a proposed explanation possessing limited evidence. Generally, you want to turn a logical hypothesis into an empirical hypothesis, putting your theories or postulations to the test.

### Step 5: Since the P-value , we reject the null hypothesis.

Cacti experience more successful growth rates than tulips on Mars. (Until we're able to test plant growth in Mars' ground for an extended period of time, the evidence for this claim will be limited and the hypothesis will only remain logical.)

An **empirical hypothesis**, or working hypothesis, comes to life when a theory is being put to the test, using observation and experiment. It's no longer just an idea or notion. It's actually going through some trial and error, and perhaps changing around those independent variables.

## Figure 1. The rejection zone for a two-sided hypothesis test.

In order to undertake hypothesis testing you need to express your research hypothesis as a null and alternative hypothesis. The null hypothesis and alternative hypothesis are statements regarding the differences or effects that occur in the population. You will use your sample to test which statement (i.e., the null hypothesis or alternative hypothesis) is most likely (although technically, you test the evidence against the null hypothesis). So, with respect to our teaching example, the null and alternative hypothesis will reflect statements about all statistics students on graduate management courses.

## Figure 2. The rejection zone for a right-sided hypothesis test.

The null hypothesis is essentially the "devil's advocate" position. That is, it assumes that whatever you are trying to prove did not happen (*hint:* it usually states that something equals zero). For example, the two different teaching methods did not result in different exam performances (i.e., zero difference). Another example might be that there is no relationship between anxiety and athletic performance (i.e., the slope is zero). The alternative hypothesis states the opposite and is usually the hypothesis you are trying to prove (e.g., the two different teaching methods did result in different exam performances). Initially, you can state these hypotheses in more general terms (e.g., using terms like "effect", "relationship", etc.), as shown below for the teaching methods example:

## Figure 3. The rejection zone for a left-sided hypothesis test.

This is where the **alternative hypothesis** (H1) enters the scene. In an attempt to disprove a null hypothesis, researchers will seek to discover an alternative hypothesis.

## Table 1. Possible outcomes from a hypothesis test.

Depending on how you want to "summarize" the exam performances will determine how you might want to write a more specific null and alternative hypothesis. For example, you could compare the **mean** exam performance of each group (i.e., the "seminar" group and the "lectures-only" group). This is what we will demonstrate here, but other options include comparing the **distributions**, **medians**, amongst other things. As such, we can state:

## There are four steps required for a hypothesis test:

Now that you have identified the null and alternative hypotheses, you need to find evidence and develop a strategy for declaring your "support" for either the null or alternative hypothesis. We can do this using some statistical theory and some arbitrary cut-off points. Both these issues are dealt with next.