Giving anti‐oxidant vitamins A, C, and E as a dietary supplement will improve walking distance in patients with PAD.8
The null hypothesis (denoted by the symbol H0) would be:
H0: Giving anti‐oxidant vitamins A, C, and E as a dietary supplement will not improve walking distance in patients with PAD.
H0 is the negation of H1, suggesting that the vitamin supplements will make no difference. It is not the opposite, which would state that giving supplements reduces walking distance.
It is easier, in statistical terms, to set about disproving H0. If we can show that H0 is probably not true, there is a reasonable chance that our hypothesis is true. Box 1.2 summarizes the necessary steps. The statistical basis for taking this apparently convoluted approach will become apparent in Chapter 5.
BOX 1.2 Testing the hypothesis
1 Formulate the Hypothesis (H1)
2 Formulate the Null Hypothesis (H0)
3 Try to disprove the Null Hypothesis
1.4.3 Hypothesis Generating Versus Hypothesis Testing
Some studies are observational rather than experimental in nature. The purpose of these studies is often to help in the generation of hypotheses by looking in the data for relationships between different subgroups and between variables. Once the relationships have been described, it may be necessary to set up a new study which is designed to test a specific hypothesis and to establish causal relationships between the variables relating to exposure and outcome. For example, Ancel Keys observed that there was a strong association between the average amount of saturated fat consumed in a country and the rate of death from coronary heart disease: the more saturated fat consumed, the higher the death rate. Numerous studies were carried out subsequently to test the hypothesis that saturated fat causes heart disease. Some repeated Ancel Keys’ original design comparing values between countries, but with better use of the available data, including more countries. Other studies compared changes in saturated fat consumption over time with changes in coronary heart disease mortality. Yet other studies looked at the relationship between saturated fat consumption and risk of heart disease in individuals. Not all of the studies came to the same conclusions or supported the hypothesis. It took some time to understand why that was the case.
1.4.4 Design
The Dodecahedron: ‘If you hadn’t done this one properly, you might have gone the wrong way’.
When designing an experiment, you should do it in such a way that allows the null hypothesis to be disproved. The key is to introduce and protect a random element in the design.
Consider some research options for the study to test whether anti‐oxidant vitamins supplements improve walking distance in peripheral arterial disease (PAD). In the sequence below, each of the designs has a weakness, which can be improved upon by introducing and protecting further elements of randomization.
1 Choose the first 100 patients with PAD coming into the clinic, give them the treatment, observe the outcome.Patients may naturally improve with time, without any intervention at all. Alternatively, there may be aplacebo effect (patients show improvement simply as a result of having taken part in the study because they believe they are taking something that is beneficial and alter their behaviour accordingly), even if the treatment itself is ineffective.
This is a weak observational study. Introduce a control group which receives a placebo.
1 Allocate the first 50 patients to the treatment group, the next 50 to the placebo group.If the two groups differ by age, sex, or disease severity, this could account for apparent differences in improvement between the groups.
This is a weak experimental study. Introduce matching.
1 Match patients in pairs for age, sex, disease severity; assign the first patient in each pair to receive treatment, the second patient to receive a placebo.
The person assigning patients may have a subconscious preference for putting one patient first in each pair. Does the patient know which treatment they are getting?
This is a weak placebo‐controlled intervention trial. Introduce randomization and blinding.
1 Allocate patients to treatment or placebo randomly within pairs. Make sure that the researcher does not know which patient is to receive which treatment (the researcher is then said to be ‘blind’ to the allocation of treatment). Make sure that the patient does not know which treatment they are receiving (keep the patient ‘blind’ as well). This makes the study ‘double blind’.
2 Conduct a placebo‐controlled randomized double‐blind intervention trial.
‘Randomization properly carried out is the key to success.’
(Sir Ronald Fisher)
Intervention studies of this type are often regarded as the most robust for testing a hypothesis. But sometimes randomized controlled trials are not ethical, especially if the exposure may be harmful (e.g. smoking, or increasing someone’s saturated fatty acid intake), or it is not possible to blind either the subjects or the researchers because the treatment being given is so obviously different from the placebo. In these cases, it is possible to mimic intervention studies in samples that are measured at baseline and then followed up over months or years. These types of studies raise issues about how to deal with factors that cannot be controlled for but which might affect the outcome (e.g. in a study looking at the impact of diet on risk of cardiovascular disease, the influence of smoking and diabetes) and changes in the general environment (e.g. indoor smoking bans) that have the potential to affect all the subjects in the study. Complex statistical analysis can be used to cope with some of these design issues. The ability to test the hypothesis in a robust way remains.
1.4.5 Statistics
The Dodecahedron: ‘Just because you have a choice, it doesn’t mean that any of them has to be right’.
Statistical tests enable you to analyze data in order to decide whether or not it is sensible to accept your hypothesis. There are literally thousands of values that can be calculated from hundreds of tests, but unless you know which test to choose, the values that you calculate may not be appropriate or meaningful. One of the main aims of this book is to help you learn to choose the test which is right for the given research problem. Once you have decided which test is appropriate for your data, the calculation is a straightforward manipulation of numbers. It is vitally important, however, to learn which data to use, how the manipulation is carried out, and how it relates to the theoretical basis which will enable you to make the decision about the truth of your hypothesis.
Most of the time it is better to use a computer to do the computation for you. Even if you enter the values correctly and generate a meaningful outcome, the computer will not tell you if your hypothesis is true. For that, you need to know how to interpret the results of the tests.
1.4.6 Interpretation
The Dodecahedron: ‘If you want sense, you’ll have to make it yourself’.
Every statistical test will produce a number (the test statistic) which you then need to interpret. This is the last stage and often the most difficult part of statistical analysis. The final emphasis in every chapter that deals with statistical tests will be on how to interpret the test statistic. We will also look at the SPSS output