Population sampling affects pseudoreplication
‘Pseudoreplication’, or the treatment of nonindependent data points as independent, can be difficult to identify [1,2]. Failure to account for pseudoreplication increases the probability of falsely concluding that experimental treatments have real effects (i.e., making a Type I error), and can lead to applying conclusions to the wrong ‘population’ (see paragraph 5). In this light, Lazic and colleagues’ [2] recent article provides a useful resource to identify pseudoreplication when designing and analyzing experiments. However, as illustrated below, discussion of their framework introduces some confusion with respect to sources of pseudoreplication and may therefore misguide some readers for common experimental designs. Lazic and colleagues discuss pseudoreplication through examples that draw from frameworks and examples illustrated in their figures. Therefore, to clarify concepts in [2] this Formal Comment focuses on figures therein. The heart of the question ‘What is ‘N’ (sample size) in my experiment?’ lies in the notion of sample independence. ‘Independence’ implies that measurements are uncorrelated among samples; when correlations exist, analyses must account for them to obtain reliable results. Sample independence can be violated in two ways. First, an experiment’s design can render samples nonindependent. For example, as explained by Lazic and colleagues, applying a treatment simultaneously to a group of subjects (rather than to subjects individually) or interactions between subjects can induce nonindependence. Lazic and colleagues focus on this first cause of nonindependence, and they provide their Fig 3 to help assess independence within an experiment. Second, nonindependence can arise due to how a population is sampled, which Lazic and colleagues discuss less directly than they do the first source of nonindependence. To illustrate how sampling an entity of interest (the ‘population’) can generate nonindependence, imagine a study that aims to estimate the average height of people in a city. Consider two approaches to obtain height measurements (the ‘samples’). First, we might number all of the families (defined in some convenient way) in the city, randomly select 10 families, and measure the heights of 10 random people per family. We know that family members are likely more similar in height than any two randomly selected individuals from the city because family members likely share similar environments (e.g., similar diets) and (by definition) share genetics. In other words, height measurements are likely to be correlated and are therefore nonindependent due to shared environments or genetics. As a result, the variance in this data set will not properly reflect the city’s true variance in height: variance in height will be lower than the true value for the city, and standard errors (SEs) for the height estimate will be artificially small. Second, we could randomly sample 100 individuals in the city to measure. These measurements will lack correlation (they are independent), and the sample variance will correctly reflect the variance in the population and yield reliable SE.