A Hypothesis

A hypothesis is a specific statement of prediction. It describes in concrete terms what you expect will happen in your study. Not all studies have hypotheses. Sometimes a study is designed to be exploratory (see Level I research). If there is no formal hypothesis, then perhaps the purpose of the study is to explore some area more thoroughly in order to develop some specific hypothesis or prediction that can be tested in future research. A single study may have one or many hypotheses.

Hypothesis test is formulated by two statements, one that describes the prediction and one that describes all the other possible outcomes with respect to the hypothesized relationship. The prediction is that variable X and variable Y will be related whether it's a positive or negative relationship.

Then the only other possible outcome would be that variable X and variable Y are not related. Usually, we call the hypothesis that you support (your prediction) the alternative hypothesis, and we call the hypothesis that describes the remaining possible outcomes the null hypothesis.

Sometimes we use a notation like h_a or h₁ to represent the alternative hypothesis (your prediction), and h or h₀ to represent the null case. You have to be careful here, though. In some studies, your prediction might very well be that there will be no difference or change.

In this case, you are essentially trying to find support for the null hypothesis and you are opposed to the alternative.

One-tailed Hypothesis.

If your prediction specifies a direction, and the null therefore is the no difference prediction and the prediction of the opposite direction, we call this a one-tailed hypothesis.

For instance, let's imagine that you are investigating the effects of a new road tracking system for haulers and that you believe one of the outcomes will be that there will be less travel time as the drivers will be monitoring on-line. Your two hypotheses might be stated something like this:

The null hypothesis for this study is:

h₀: As a result of the new road tracking system for Haulers Company, there will either be no significant difference in travel time or there will be a significant increase in travel time.

Which is tested against the alternative hypothesis:

h_a: As a result of the new road tracking system for Haulers company, there will be a significant decrease in travel time.

The alternative hypothesis -- your prediction that the new system will decrease travel time -- is shown below.

The null must account for the other two possible conditions: no difference or an increase in travel time. The figure shows a hypothetical distribution of travel time differences. We can see that the term "one-tailed" refers to the tail of the distribution on the outcome variable.

<insert One-tailed Graph>

Two-tailed Hypothesis.

When your prediction does not specify a direction, we say you have a two-tailed hypothesis.

For instance, let's assume you are studying new packaging system. In this case, you might state the two hypotheses like this:

The null hypothesis for this study is:

h₀: As a result of new packaging system of the, there will be no significant difference average weight from the old system.

Which is tested against the alternative hypothesis:

h_a: As a result new packaging system, there will be a significant difference in average weight.

The term "two-tailed" refers to the tails of the distribution for your outcome variable.

<insert Two-tailed Graph>

Hypothetical-Deductive Model

The important thing to remember about stating hypotheses is that you formulate your prediction (directional or not), and then you formulate a second hypothesis that is mutually exclusive of the first and incorporates all possible alternative outcomes for that case.

When your study analysis is completed, the idea is that you will have to choose between the two hypotheses. If your prediction was correct, then you would (usually) reject the null hypothesis and accept the alternative. If your original prediction was not supported in the data, then you will accept the null hypothesis and reject the alternative.

The logic of hypothesis testing is based on these two basic principles: 

• the formulation of two mutually exclusive hypothesis statements that, together, exhaust all possible outcomes 
• the testing of these so that one is necessarily accepted and the other rejected

Hypothesis testing seems a convoluted and formalistic way to ask research questions. However, it encompasses a long tradition in statistics called the hypothetical-deductive model, and sometimes we just have to do things because they're traditions. And anyway, if all of this hypothesis testing was easy enough so anybody could understand it, how do you think statisticians would stay employed?

In logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.

Top Down Approach

Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a top-down approach.

We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to be able to test the hypotheses with specific data -- a confirmation (or not) of our original theories.

Thus the process is:

1. Theory
2. Hypothesis
3. Observation
4. Confirmation

Bottom Up Approach

Inductive reasoning works the other way, moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a bottom up approach. 

In inductive reasoning, we begin with specific observations and measures, begin to detect patterns and regularities, formulate some tentative hypotheses that we can explore, and finally end up developing some general conclusions or theories. 

Thus the process is from:

1. Observation
2. Pattern
3. Tentative Hypothesis
4. Theory

These two methods of reasoning have a very different "feel" to them when you're conducting research. Inductive reasoning, by its very nature, is more open-ended and exploratory, especially at the beginning. Deductive reasoning is narrow in nature and is concerned with testing or confirming hypotheses.

Even though a particular study may look like it's purely deductive most research involves both inductive and deductive reasoning processes at some time in the project. Even in the most constrained experiment, the researchers may observe patterns in the data that lead them to develop new theories.

Since level III studies are designed to test hypotheses, the way the hypotheses is written will greatly affect the study design.  Writing the hypothesis correctly will save effort later.  The way the hypotheses are written is similar to that of the examples we have considered in the preceding pages. 

For example:

Drivers who undergo training in defensive driving will have significantly lower number of accidents than those who do not undergo training in defensive driving.

The first clause of a hypothesis will identify both the sample and one position of the independent variable.  In the above hypothesis, this clause is “Drivers who undergo training in defensive driving”.   Drivers is the sample, and undergo training in defensive driving is one position of the independent variable.

The next clause specifies the direction the dependent variable is expected to take as a result of the independent variable.  In the example, this clause is have significantly lower number of accidents.  The dependent variable is number of accidents, and the direction in which it is expected to change is significantly lower. 

The last clause of the hypothesis case provides the other position of the independent variable.  In this case, those who do not undergo training in defensive driving specifies the group that will provide the comparison as another position of the independent variable.

A well-written hypothesis will contain all three clauses.  The first describes the experimental group, the second specifies the expected result, and the third describes the comparison group. 

The above example can be categorized as:

Clause 1: “Drivers who undergo training in defensive driving

Clause 2: “will have significantly lower number of accidents”.

Clause 3: “than those who do not under training in defensive driving.”

Dividing your hypothesis into three components and checking that each component includes the necessary information will make writing the hypothesis easier.