The choice of null hypothesis depends on the focus of our investigation. In dimensionality analyses, we could say: "My null hypothesis is that these data are multidimensional. We need strong evidence to reject multidimensionality." Or "My null hypothesis is that these data are unidimensional. We need strong evidence to reject unidimensionality". Both hypotheses are valid, but we do need to make sure that our audience is clear about our premise.
This situation is encountered throughout statistical analysis. Which hypothesis is the null hypothesis? It is our choice depending on how we conceptualize the problem to be solved. For instance, a correlation of 0.0 is the null hypothesis when we are looking for a correlation between variables, but a correlation of 1.0 is the null hypothesis when we are looking for a lack of collinearity between variables.
Linacre J.M. (2010) Which Hypothesis is the Null Hypothesis?, Rasch Measurement Transactions, 2010, 23:4, 1242
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