**Introduction**

In the context of an academic paper based on quantitative methods, a hypothesis is a statement for which you are collecting evidence. The best way to understand hypotheses is through examples, so let’s walk you through one.

Let’s say you’re writing an academic paper on whether men are taller than women. You collect data from 15 men and 15 women in your class as part of this academic paper. We can now discuss what hypotheses are, how to set them up, and how you test them.

**Null and Alternative Hypotheses**

A null hypothesis (often written as H0 or H_{0}) reflects what you expect to be true if there is no effect or difference. For example, if you expect gender to have no effect on height, then your null hypothesis is that

H_{0}: Male height = female height

An alternative hypothesis (often written as HA or H_{A}) reflects what you expect to be true if there *is* an effect or difference. For example, let’s say that, having looked at global data, you have good reason to believe that men are taller than women. Now, therefore, you structure your null hypothesis to reflect two possibilities: (a) Men and women are equal in height and (b) women are taller than men:

H_{0}: Male height ≤ female height

You can understand null hypotheses better when you consider their opposites, which are alternative hypothesis. Let’s take this pair of hypotheses:

H_{0}: Male height = female height

H_{A}: Male height ≠ female height

Here, what you’re looking to prove is the alternative hypothesis, which is that men and women have different heights. Notice that different could mean two things: Men could be taller than women, or men could be shorter than women. We call this kind of alternative hypothesis two-tailed, because we are testing for the existence of two possible kinds of effects (greater or lesser height in men).

Now let’s take this pair of hypotheses:

H_{0}: Male height ≤ female height

H_{A}: Male height > female height

This kind of hypothesis is one-tailed, because we testing for only one direction of the effect: Namely, that men are taller than women.

So, as you can see, (a) null hypotheses are statements of what we expect to be true if there is no effect, (b) alternative hypotheses can have one direction or two directions in the effect, and (c) null and alternative hypotheses do not overlap.

**Testing Hypotheses**

The most frequent method of testing a hypothesis is through an inferential statistical approach that generates a *p *value. We have tutorials on inferential statistics elsewhere on BridgeText to build your knowledge. Assuming you understand the basics, let’s continue with our example.

You have data from 15 men and 15 women, and you have selected the following hypotheses:

H_{0}: Male height ≤ female height

H_{A}: Male height > female height

Assume you feed your data into a statistical program like Stata (we’ll use the following code just to generate data and findings):

set obs 30

gen gender = .

replace gender = 1 in 1/15

replace gender = 2 in 16/30

label define gender 1 "Women " 2 "Men"

label variable gender "Gender"

label value gender gender

drawnorm height1, mean(150) sd(20)

drawnorm height2, mean(170) sd(25)

replace height1 = . in 16/30

replace height2 = . in 1/15

egen height = rowmax(height1 height2)

drop height1 height2

label variable height "Height"

ttest height, by(gender)

You have just conducted an independent **samples t-test** to determine whether men are taller than women. Your readout looks like this:

We see that women’s average height, in centimeters, is 151.42, with a standard deviation of 23.08. Men’s average height, also in centimeters, is 164.65, with a standard deviation of 20.46. Because our hypothesis was one-tailed, we look at the *p *value for diff < 0, which is .054. Let’s now take a moment to examine what the *p *value means.

**Interpreting p Values in Hypothesis Testing**

The American Statistical Association (ASA) has **stated** that “A *P*-value is one of the ways of summarizing the incompatibility between the observed data and a proposed model for the data. The most common model we use, is the so-called ‘null hypothesis,’ which in practice essentially proposes…no effect whatsoever. The smaller the *P*-value, the larger the incompatibility of the data with the null hypothesis.”

Our *p *value was .054. That’s a small *p *value—note that .10 and .05 are the most common cutoffs for what counts as ‘small.’ So, at *p *< .10, we reject the null hypothesis and conclude that our data are highly incompatible with the null hypothesis that male height ≤ female height. Conversely, our data are highly compatible with the alternative hypothesis that male height > female height.

**Conclusion**

Unfortunately, hypothesis testing is complex, and the only way to really understand it is to do a lot of testing and interpretation of your own. However, you can learn a lot by looking at tutorials such as the one provided here.

BridgeText provides statistical testing, analysis, coding, and interpretation services.