Introduction How to test a probabilistic relation with a case study

value of the independent concept changes, it is likely that the value of the dependent concept changes in the predicted way. The proposition is formulated as follows: “If A is higher, then it is likely that B is higher” A probabilistic relation can be tested with a comparative case study.

7.1.2 Candidate cases

The issues regarding the universe for case selection are the same for all theory-testing case studies. See 5.1.2 for a discussion of this topic.

7.1.3 Case selection

The most common reason for conducting a comparative case study, rather than a survey, is that it is not possible to collect data from a large sample, either because there simply are no more cases or because it is not feasible in terms of access or in terms of necessary investments in time or other costs to collect data from a larger sample. If there are no more cases, the obvious case selection procedure is to include all cases that are available. If data can be collected from only a small number of cases but from more if more money or time would be available, a case selection strategy has to be chosen. The preferred selection strategy is probability sampling such as random sampling, which is in accordance with the fact that this kind of study is a quasi-survey. However, selecting a truly representative sample of a large population with a large variety of types of instances is very difficult, and it is quite likely that replication studies with different samples from the same population would result in different outcomes. For this reason it is recommended to avoid sam- pling in a large population but instead to identify very small specific populations in which the variation between the instances is much less than in the larger population. Probability sampling in such a small population is much easier and the population could even be so small that all instances of the population could be included in the study cen- sus. Generalizability could be achieved through replications in a series of small populations from different parts of the domain. It is not possible to give specific advice on the number of cases that must be selected for testing a probabilistic relation with a quasi-survey comparative case study. In general, the more cases that can be used for the analysis the better. However, the number of available cases will be limited, because otherwise a survey would have been chosen as a research strategy. The best advice for the number of instances that should be included in the study, therefore, is to select the maximum number of cases that are available and that can be handled within the resource constraints of the study.

7.1.4 Hypothesis

If the proposition states that it is likely that the value of the dependent variable increases or decreases with an increase of the value of the independent variable, then the hypothesis in a comparative case study, in which the tested part of the relation is presumed to be continuously increasing or decreasing, is that the rank order of cases according to the observed values of the dependent variable is like the rank order of cases according to the observed values of the independent variable. The prob- abilistic nature of the hypothesis is encapsulated in the word “like”. In a deterministic hypothesis the two rank orders are exactly the same.

7.1.5 Measurement

The values of the dependent and independent variables in all cases of the sample need to be measured.

7.1.6 Data presentation

If the tested part of the relation between the independent and depend- ent variables can be considered as continuously increasing or decreas- ing, the cases are ranked according to the value of the independent variable. Separately, the cases are also ranked according to the value of the dependent variable.

7.1.7 Data analysis

The data analysis consists of comparing the ranking according to the values of the independent variable with the ranking according to the value of the dependent variable. If the two rank orders are exactly the same same order of cases, the hypothesis is confirmed. If the rank