Читать книгу Experimental Design and Statistical Analysis for Pharmacology and the Biomedical Sciences - Paul J. Mitchell - Страница 29

I have used the term ‘independent’ on a few occasions so far, and it is a term that is often used in statistics (independent observations, independent groups, independent data), and so it is important that we understand the true meaning of this term.

Consider the situation where you are interested in the heights of female students compared with those of age‐matched male students (see Chapter 5, Tables 5.1 and 5.2 for example data). There is a clear distinction between these groups based on their gender, and so the groups of female and male students are clearly independent from each other as they contain different participants or subjects and consequently produce independent data sets. Similarly, if we compared the heights of male students when they started secondary school to a different group of students at university, then these groups would also be independent since they clearly contain different participants.

In contrast, a different situation arises where a group of male students had their heights measured both on starting secondary school and again when they started university. In this situation the heights of the same participants are examined but at different time points; in such circumstances the resulting data is said to be paired.

This distinction between independent and paired groups is important since, as we shall see later, it informs our decision on the inferential statistical tests subsequently used to analysis data.

Of course, some data measurements include both independent and paired data sets. Consider the situation where the heights of female and male students are measured when they start secondary school and again when they are at university. Such data will include independent groups (based on their gender) and paired data (based on the time at which the heights were measured).

In addition to these terms, statisticians also use the terms ‘Between’ and ‘Within’ to describe different variables and factors in an experiment. The term ‘Between group variable’ refers to clear differences between independent groups used in an experiment; in the examples above then gender is a Between‐Group Variable. In contrast, the term ‘Within group variable’ refers to experimental changes experienced by the same group of participants or subjects during the course of an experiment and always occurs as a function of time; in the examples above, then the time at which the height measurements were obtained is a Within‐Group Variable.