# Hypothesis Testing (cont...)

## The structure of hypothesis testing

Whilst all pieces of quantitative research have some dilemma, issue or problem that they are trying to investigate, the focus in hypothesis testing is to find ways to structure these in such a way that we can test them effectively. Typically, it is important to:

 1 Define the research hypothesis for the study. 2 Explain how you are going to operationalize (that is, measure or operationally define) what you are studying and set out the variables to be studied. 3 Set out the null and alternative hypothesis (or more than one hypothesis; in other words, a number of hypotheses). 4 Set the significance level. 5 Make a one- or two-tailed prediction. 6 Determine whether the distribution that you are studying is normal (this has implications for the types of statistical tests that you can run on your data). 7 Select an appropriate statistical test based on the variables you have defined and whether the distribution is normal or not. 8 Run the statistical tests on your data and interpret the output. 9 Reject or fail to reject the null hypothesis.
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Whilst there are some variations to this structure, it is adopted by most thorough quantitative research studies. We focus on the first five steps in the process, as well as the decision to either reject or fail to reject the null hypothesis. You can get guidance on which statistical test to run by using our Statistical Test Selector.

## Operationally defining (measuring) the study

So far, we have simply referred to the outcome of the teaching methods as the "performance" of the students, but what do we mean by "performance". "Performance" could mean how students score in a piece of coursework, how many times they can answer questions in class, what marks they get in their exams, and so on. There are three major reasons why we should be clear about how we operationalize (i.e., measure) what we are studying. First, we simply need to be clear so that people reading our work are in no doubt about what we are studying. This makes it easier for them to repeat the study in future to see if they also get the same (or similar) results; something called internal validity. Second, one of the criteria by which quantitative research is assessed, perhaps by an examiner if you are a student, is how you define what you are measuring (in this case, "performance") and how you choose to measure it. Third, it will determine which statistical test you need to use because the choice of statistical test is largely based on how your variables were measured (e.g., whether the variable, "performance", was measured on a "continuous" scale of 1-100 marks; an "ordinal" scale with groups of marks, such as 0-20, 21-40, 41-60, 61-80 and 81-100; or some of other scale; see the statistical guide, Types of Variable, for more information).

It is worth noting that these choices will sometimes be personal choices (i.e., they are subjective) and at other times they will be guided by some other/external information. For example, if you were to measure intelligence, there may be a number of characteristics that you could use, such as IQ, emotional intelligence, and so forth. What you choose here will likely be a personal choice because all these variables are proxies for intelligence; that is, they are variables used to infer an individual's intelligence, but not everyone would agree that IQ alone is an accurate measure of intelligence. In contrast, if you were measuring company performance, you would find a number of established metrics in the academic and practitioner literature that would determine what you should test, such as "Return on Assets", etc. Therefore, to know what you should measure, it is always worth looking at the literature first to see what other studies have done, whether you use the same measures or not. It is then a matter of making an educated decision whether the variables you choose to examine are accurate proxies for what you are trying to study, as well as discussing the potential limitations of these proxies.

In the case of measuring a statistics student's performance there are a number of proxies that could be used, such as class participation, coursework marks and exam marks, since these are all good measures of performance. However, in this case, we choose exam marks as our measure of performance for two reasons: First, as a statistics tutor, we feel that Sarah's main job is to help her students get the best grade possible since this will affect her students' overall grades in their graduate management degree. Second, the assessment for the statistics course is a single two hour exam. Since there is no coursework and class participation is not assessed in this course, exam marks seem to be the most appropriate proxy for performance. However, it is worth noting that if the assessment for the statistics course was not only a two hour exam, but also a piece of coursework, we would probably have chosen to measure both exam marks and coursework marks as proxies of performance.

## Variables

The next step is to define the variables that we are using in our study (see the statistical guide, Types of Variable, for more information). Since the study aims to examine the effect that two different teaching methods – providing lectures and seminar classes (Sarah) and providing lectures by themselves (Mike) – had on the performance of Sarah's 50 students and Mike's 50 students, the variables being measured are:

 Dependent variable: Exam marks Independent variable: Teaching method ("seminar" vs "lecture only")

By using a very straightforward example, we have only one dependent variable and one independent variable although studies can examine any number of dependent and independent variables. Now that we know what our variables are, we can look at how to set out the null and alternative hypothesis on the next page.