This is an absolutely fundamental aspect of all statistical methods: the idea that all the observations, all the values on any of the variables, are independent of the others.
If you assume independence of observations you have a model of the data that allows you to test whether things are random or systematic: whether women terminate therapy early at a different rate from men, starting scores on a measure are higher for clients in one service from those in another, whether starting scores relate to client age, etc. Where observations are not independent modelling things gets much more complicated and until the mid to late 20th Century there were no readily available methods for analysing data where we know there is failure of independence of observations. The catch for much therapy practice based evidence, and for much formal therapy research, is that we very rarely have independence of observations: clients are “nested” within therapists, any work in groups creates non-independence.
If you have many clients seen by each therapist, then you can use “multi-level model” methods that estimate the importance of the non-independence but such estimation really only becomes stable if you have sufficient numbers, say 40 or more, in each group but this won’t work for typical therapy groups or families in therapy work.
Try also #
Multi-level modelling (MLM)
Chapters 5, 8 and 10.