# 皮爾遜相關係數明顯大於斯皮爾曼等級相關係數的解釋是什麼？

• 完整數據集：\$ \ rho \$ = 0.381（p值：0.000），\$ \ rho_r \$ = 0.151（p值：0.131）

• 已移除一個異常值：\$ \ rho \$ = 0.336（p值：0.001），\$ \ rho_r \$ = 0.125（p值：0.213）

• 已刪除三個異常值：\$ \ rho \$ = 0.167（p值：0.100），\$ \ rho_r \$ = 0.076（p值：0.459）

This is a simple dataset, where the points come alternating from two linear functions:

The pearson correlation detects, there is a general upwards motion in the combined data (red an black together) and is r=.453 The spearman correlation just sees the ranks, which are distributed like this:

There is a high and a low rank alternating, so no clear trend for spearman. Spearman r = .079 This pearson is 5.7 times as high and you can easily increase that value by extending the row. You can even easily get a negative Spearman for a positive Pearson by just leaving out the last value. So there is nothing in the way of a compbination of a large Pearson and a small Spearman r and the above picture is even a bit similar to your's.

You can easily see how I constructed the data by looking at them:

1, -.01, 2, -.02, 3, -.03, 4, -.04, 5, -.05, 6, -.06, 7, -.07, 8, -.08, 9, -.09, 10

Hope that helps, Bernhard