# How to Set Up a Hypothesis Test: Null versus Alternative

A hypothesis is a statement that can be used to predict the outcome of future observations. The , or no-difference hypothesis, is a good type of hypothesis to test. This type of hypothesis assumes no difference between two states. Here is an example of a null hypothesis: 'the rate at which grass grows is not dependent on the amount of light it receives'. Even if I think that light affects the rate at which my grass grows (probably not as much as rain, but that's a different hypothesis), it is easier to disprove that light has no effect than to get into complicated details about 'how much light', or 'wavelength of light', etc. However, these details can become their own hypotheses (stated in null form) for further experimentation. It is easiest to test separate s in separate experiments. In other words, don't test the effects of light and water at the same time until after you have tested each separately.

### Hot Spot: Scattered papers = hypothesis rejected

You should decide whether to use the one-tailed or two-tailed probability before you collect your data, of course. A one-tailed probability is more powerful, in the sense of having a lower chance of false negatives, but you should only use a one-tailed probability if you really, truly have a firm prediction about which direction of deviation you would consider interesting. In the chicken example, you might be tempted to use a one-tailed probability, because you're only looking for treatments that decrease the proportion of worthless male chickens. But if you accidentally found a treatment that produced 87% male chickens, would you really publish the result as "The treatment did not cause a significant decrease in the proportion of male chickens"? I hope not. You'd realize that this unexpected result, even though it wasn't what you and your farmer friends wanted, would be very interesting to other people; by leading to discoveries about the fundamental biology of sex-determination in chickens, in might even help you produce more female chickens someday. Any time a deviation in either direction would be interesting, you should use the two-tailed probability. In addition, people are skeptical of one-tailed probabilities, especially if a one-tailed probability is significant and a two-tailed probability would not be significant (as in our chocolate-eating chicken example). Unless you provide a very convincing explanation, people may think you decided to use the one-tailed probability after you saw that the two-tailed probability wasn't quite significant, which would be cheating. It may be easier to always use two-tailed probabilities. For this handbook, I will always use two-tailed probabilities, unless I make it very clear that only one direction of deviation from the null hypothesis would be interesting.

### the null hypothesis is not rejected when it is false c.

Which alternative hypothesis you choose in setting up your hypothesis test depends on what you’re interested in concluding, should you have enough evidence to refute the null hypothesis (the claim). The alternative hypothesis should be decided upon before collecting or looking at any data, so as not to influence the results.

### Suppose that you are unable to reject the hypothesis.

The p-value tells you how unlikely this sample (ora more extreme one) is if the null hypothesis is true. The moreunlikely (surprising, unexpected), the lower the p-value, and the more confident you can feelabout rejecting H0.

### failing to reject the null hypothesis when it is false.

This same idea —the null hypothesis H0 is innocent till proven guilty —explains why you use 0.26 (o) to figure expected successes andfailures, not 0.08(). Again, the county claims that there’s no racialbias. If that’s true, if there’s no funny business goingon, then in the long run 26% of members of jury pools should beAfrican American.

### rejecting the null hypothesis when it is false.

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.