What are pairwise statistics?

Pairwise statistics are statistics that are calculated between pairs of observations in your data set. Minitab calculates pairwise averages, differences, and slopes. Pairwise statistics are important to many nonparametric techniques.

Pairwise averages (also called Walsh averages)

Pairwise averages (also called Walsh averages) are the means of each possible pair of values in your data set, including the pair of each value with itself.

For example, the data set {1, 3} has three pairs: 1 paired with itself, 1 paired with 3, and 3 paired with itself. The pairwise averages are the means of these pairs. So this data set has three pairwise averages: 1, 2, and 3.

Pairwise differences

When you have two columns of equal length, and you pair each value from the first column with each value from the second column, the differences between the paired values are called pairwise differences.

For example, the following data set contains four pairs: {2, 1}, {2, 3}, {5, 1}, and {5, 3}. The pairwise differences equal the differences between the values in each pair. For this data set, the pairwise differences are: 1, -1, 4, and 2.

A B
2 1
5 3

Pairwise slopes

You can calculate pairwise slopes when you have two columns of equal length, when each row represents a coordinate point on the X-Y plane. For example, the following data contain three coordinate points, which are on the scatterplot: (3, 1), (5, 7), and (9, 4). The pairwise slopes for these data are the slopes of the straight lines drawn between each pair of coordinates.

A B
Point A 3 1
Point B 5 7
Point C 9 4

  • Slope AB = (7 – 1) / (5 – 3) = 3
  • Slope AC = (4 – 1) / (9 – 3) = 1/2
  • Slope BC = (4 – 7) / (9 – 5) = –3/4

Indices for pairwise statistics

When you calculate pairwise statistics, you can choose to store the indices. Each index shows which observations are paired to calculate the specified statistic. For example, if you calculate the pairwise average between the first and third observations, the indices are 1 and 3.

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