An example of pseudoreplication. Two rats are sampled from a population with a mean (μ) of 50 and a standard deviation (σ) of 10, and ten measurements of an arbitrary outcome variable are made on each rat. The first (incorrect) 90% CI uses all 20 data points and does not account for the hierarchical nature of the data. For the second 90% CI, the mean of the ten values for each rat are calculated first, and then only these two averaged values are used for the calculation of the CI. The error bar on the left is incorrect because each of the 20 data points are not a random sample from the whole population, but rather samples within two rats. This is evident from the fact that the 10 points are normally distributed around the mean of their respective rats, but not normally distributed around the population mean (horizontal grey line), as would be expected when independent samples are randomly drawn from a population. Increasing the number of observations on each rat does not lead to a more precise estimate of μ, which requires more rats. Note that 90% CI are plotted for clarity because the graph needs to be greatly compressed to display the 95% CI.
Lazic BMC Neuroscience 2010 11:5 doi:10.1186/1471-2202-11-5