Candidate cases How to test a deterministic relation with a case study

6.1.4 Hypothesis

If the proposition states that the value of the dependent concept increases or decreases deterministically with an increase of the value of the independent concept, then the hypothesis in a longitudinal case study can be formulated as follows: Hypothesis: For each pair of measurement points in time, the value of the dependent variable at one point of the pair differs in the predicted direction from the dependent variable’s value at the other point of the pair. If the predicted relation between the independent and dependent variable is a continuously increasing or continuously decreasing relation or the predicted relation can be considered as a set of continuously increasing or decreasing separate relations, then for each separate continuously increasing or decreasing relation, the hypothesis can be formulated as follows: Hypothesis: The rank order of the measurement points in time, according to the observed values of the independent variable, is exactly the same as the rank order of the measurement points according to the observed values of the dependent variable. If, for instance, ■ the five measurement points were times t 1 , t 2 , t 3 , t 4 , and t 5, , and ■ A 1 , A 2 , A 3 , A 4 , and A 5 are the values of the independent vari- able at these points, and ■ B 1 , B 2 , B 3 , B 4 , and B 5 are the values of the dependent variable at these points, and ■ the independent variable is ranked according to increasing value for example, A 4 , A 5 , A 3 , A 1 , A 2 , then, for a predicted continuously increasing or decreasing relation between the independent and the dependent variable, it is predicted that the dependent variable has exactly the same rank order B 4 , B 5 , B 3 , B 1 , B 2 , or the exact reverse order depending on whether the proposition states that the value of the dependent variable increases or decreases deterministically with an increase of the value the independent variable. If the proposition states that the value of the dependent variable increases or decreases deterministically and continuously increasing or decreasing with an increase of the value the independent variable, then the hypothesis in a comparative case study can be formulated as follows: Hypothesis: The rank order of cases, according to the observed values of the independent variable, is exactly the same as the rank order of the cases according to the observed values of the dependent variable.