Thresholds for Cook's Distance
In addition to a cut-off of 1, Hair et al mention that some people also use 4/(N-k-1) as a threshold for Cook’s distance which gives a lower threshold than 1 (e.g. this is 4/(27-1-1) = 0.16 for k predictors and N points with k=1 predictor and N=27 points). A third threshold of 4/N is also mentioned as a threshold in
Bollen, Kenneth A.; and Jackman, Robert W. (1990) Regression diagnostics: An expository treatment of outliers and influential cases,
and also in
Fox, John and Long, J. Scott (eds.); Modern Methods of Data Analysis (pp. 257-91). Newbury Park, CA: Sage
which gives 4/27 = 0.14 in the above example.