23.3 Notation: Mean differences

The notation used for paired data reflects how we work with the differences (Table 23.1). Apart from that, the notation is similar to that used in Chap. 22.

TABLE 23.1: The notation used for mean differences (paired data) compared to the notation used for one sample mean
One sample mean Mean of paired data
The observations: Values: \(x\) Differences: \(d\)
Sample mean: \(\bar{x}\) \(\bar{d}\)
Standard deviation: \(s\) \(s_d\)
Standard error of sample mean: \(\displaystyle\text{s.e.}(\bar{x}) = \frac{s}{\sqrt{n}}\) \(\displaystyle\text{s.e.}(\bar{d}) = \frac{s_d}{\sqrt{n}}\)
Sample size: Number of observations: \(n\) Number of differences: \(n\)