Hypothesis

What is a hypothesis?

A hypothesis is an assumption that is neither proven nor disproven. In the research process, a hypothesis is usually formulated before the data are analyzed. Data, for example from an experiment or a survey, are then evaluated using a hypothesis test. The test can lead you to reject or not reject the null hypothesis, but it does not prove either hypothesis.

Usually, hypotheses are formulated starting from a literature review. Based on the literature review, you can then justify why you formulated the hypothesis in this way.

An example of a hypothesis could be: "Men earn more than women in the same job in Austria."

To test this hypothesis, you need data, e.g. from a survey, and a suitable hypothesis test such as the t-test or correlation analysis. Don't worry, numiqo will help you choose the right hypothesis test.

Formulating a hypothesis

In order to formulate a hypothesis, a research question must first be defined. A precisely formulated hypothesis about the population can then be derived from the research question, e.g. men earn more than women in the same job in Austria.

Hypotheses are not simple statements; they are formulated in such a way that they can be tested with collected data in the course of the research process.

To test a hypothesis, it is necessary to define exactly which variables are involved and how the variables are related. Hypotheses can describe differences or associations between variables. A causal hypothesis requires a study design that supports causal conclusions; a statistical association alone does not establish causation.

Null (H0) and Alternative Hypothesis (H1)

A hypothesis test compares two competing statements about a population parameter. These are called the null hypothesis and the alternative hypothesis, abbreviated as H0 and H1.

The hypothesis that you want to test or that you have derived from the theory usually states that there is a difference or association, for example, average salary differs by gender. This is the alternative hypothesis.

The null hypothesis usually states that there is no difference or association, for example, average salary does not differ by gender. A hypothesis test assesses how compatible the observed data are with H0. The result is a decision to reject or not reject H0, not proof that either hypothesis is true.

Types of hypotheses

What types of hypotheses are available? The most common distinction is between difference and correlation hypotheses, as well as directional and non-directional hypotheses.

Difference hypotheses

Difference hypotheses compare groups, for example, a group of men and a group of women. Correlation hypotheses concern the relationship between variables, for example, age and height.

Difference hypotheses test whether there is a difference between two or more groups.

Examples of difference hypotheses are:

• The "group" of men earns more than the "group" of women.
• Smokers have a higher risk of heart attack than non-smokers
• There is a difference between Germany, Austria and France in terms of hours worked per week.

In these examples, the grouping variable is categorical, such as gender, smoking status, or country. The outcome may be categorical, ordinal, or metric; its scale and the study design determine which statistical test is suitable.

Correlation hypotheses

Correlation hypotheses state that two variables are associated, for example, height and body weight.

Correlation hypotheses are, for example:

• The taller a person is, the heavier he or she is.
• The more horsepower a car has, the higher its fuel consumption.
• The better the math grade, the higher the future salary.

As can be seen from the examples, correlation hypotheses often take the form "The more..., the higher/lower...". Thus, at least two ordinally scaled variables are being examined.

Directional and non-directional hypotheses

Hypotheses are divided into directional and non-directional or one-sided and two-sided alternative hypotheses. If the alternative contains words such as "higher than" or "lower than," it is directional.

In the case of a non-directional hypothesis, one often finds building blocks such as "there is a difference between" in the formulation, but it is not stated in which direction the difference lies.

• With a non-directional hypothesis, the only thing of interest is whether there is a difference in a value between the groups under consideration.
• In a directional hypothesis, what is of interest is whether one group has a higher or lower value than the other.

Non-directional hypotheses

Non-directional hypotheses test whether there is a relationship or a difference, and it does not matter in which direction the relationship or difference goes. In the case of a difference hypothesis, this means there is a difference between two groups, but it does not say whether one of the groups has a higher value.

• There is a difference between the salary of men and women (but it is not said who earns more!).
• There is a difference in the risk of heart attack between smokers and non-smokers (but it is not said who has the higher risk!).

In regard to a correlation hypothesis, this means there is a relationship or correlation between two variables, but it is not said whether this relationship is positive or negative.

• There is a correlation between height and weight.
• There is a correlation between horsepower and fuel consumption in cars.

In both cases it is not said whether this correlation is positive or negative!

Directional hypotheses

Directional hypotheses additionally indicate the direction of the relationship or the difference. In the case of the difference hypothesis a statement is made which group has a higher or lower value.

• Men earn more than women
• Smokers have a higher risk of heart attack than non-smokers

In the case of a correlation hypothesis, a statement is made as to whether the correlation is positive or negative.

• The taller a person is, the heavier that person tends to be.
• The more horsepower a car has, the higher its fuel consumption.

The p-value for directional hypotheses

A directional alternative and the decision to use a one-sided test must be specified before examining the data. Statistical software can then calculate the appropriate one-sided p-value directly.

For some symmetric tests, the one-sided p-value equals half the two-sided p-value only when the observed effect is in the prespecified direction. If it is in the opposite direction, simply dividing by two gives the wrong result. Do not choose the direction after seeing the data. More about this in the tutorial about the p-value.

If you select a directed alternative hypothesis in numiqo for the calculated hypothesis test, the conversion is done automatically and you only need to read the result.

Step-by-step instructions for testing hypotheses

• Literature research
• Formulate the null and alternative hypotheses
• Define the variables and their scale levels
• Determine the hypothesis type and whether the test is one-sided or two-sided
• Choose the significance level before analyzing the data
• Choose a test that fits the hypothesis, study design, scale levels, and assumptions
• Plan any adjustment needed when testing multiple hypotheses
• Report the estimated effect size and confidence interval where appropriate

The next tutorial is about hypothesis testing. You will learn what hypothesis tests are, how to find the right one and how to interpret it.