# State Null and Alternative Hypotheses

In the olden days, when people looked up *P* values in printed tables, they would report the results of a statistical test as "*P**P**P*>0.10", etc. Nowadays, almost all computer statistics programs give the exact *P* value resulting from a statistical test, such as *P*=0.029, and that's what you should report in your publications. You will conclude that the results are either significant or they're not significant; they either reject the null hypothesis (if *P* is below your pre-determined significance level) or don't reject the null hypothesis (if *P* is above your significance level). But other people will want to know if your results are "strongly" significant (*P* much less than 0.05), which will give them more confidence in your results than if they were "barely" significant (*P*=0.043, for example). In addition, other researchers will need the exact *P* value if they want to combine your results with others into a .

## State Null and Alternative Hypotheses

### That’s How to State the Null Hypothesis!

In the second experiment, you are going to put human volunteers with high blood pressure on a strict low-salt diet and see how much their blood pressure goes down. Everyone will be confined to a hospital for a month and fed either a normal diet, or the same foods with half as much salt. For this experiment, you wouldn't be very interested in the *P* value, as based on prior research in animals and humans, you are already quite certain that reducing salt intake will lower blood pressure; you're pretty sure that the null hypothesis that "Salt intake has no effect on blood pressure" is false. Instead, you are very interested to know how *much* the blood pressure goes down. Reducing salt intake in half is a big deal, and if it only reduces blood pressure by 1 mm Hg, the tiny gain in life expectancy wouldn't be worth a lifetime of bland food and obsessive label-reading. If it reduces blood pressure by 20 mm with a confidence interval of ±5 mm, it might be worth it. So you should estimate the effect size (the difference in blood pressure between the diets) and the confidence interval on the difference.

### State Null and Alternative Hypotheses

Here are three experiments to illustrate when the different approaches to statistics are appropriate. In the first experiment, you are testing a plant extract on rabbits to see if it will lower their blood pressure. You already know that the plant extract is a diuretic (makes the rabbits pee more) and you already know that diuretics tend to lower blood pressure, so you think there's a good chance it will work. If it does work, you'll do more low-cost animal tests on it before you do expensive, potentially risky human trials. Your prior expectation is that the null hypothesis (that the plant extract has no effect) has a good chance of being false, and the cost of a false positive is fairly low. So you should do frequentist hypothesis testing, with a significance level of 0.05.