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What transformation can I use to fix this residual plot (make the red line horizontal). I tried square root, log, 1/y, and squared. None of them helped.

residual plot

The data is of a 2 way ANOVA: Response Variable = time (in minutes) to teach a chimp a sign. Number of observations = 4 x 10 = 40

  1. Response variable = time (in minutes)
  2. Factor 1 = Sign (10 levels)
  3. Factor 2 = Chimpanzee (4 levels)

Time, Sign, Chimp

178              1         1
 60              2         1
177              3         1
 36              4         1
225              5         1
345              6         1
 40              7         1
  2              8         1
287              9         1
 14             10         1

 78              1         2
 14              2         2
 80              3         2
 15              4         2
 10              5         2
115              6         2
 10              7         2
 12              8         2
129              9         2
 80             10         2

 99              1         3
 18              2         3
 20              3         3
 25              4         3
 15              5         3
 54              6         3
 25              7         3
 10              8         3
476              9         3
 56             10         3

297              1         4
 20              2         4
195              3         4
 18              4         4
 24              5         4
420              6         4
 40              7         4
 15              8         4
372              9         4
190             10         4
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  • $\begingroup$ It's impossible to tell. Could you explain what the variables mean, give some brief summaries of the data characteristics, and tell us what you are trying to accomplish? $\endgroup$
    – whuber ♦
    May 10, 2021 at 21:39
  • $\begingroup$ Nonaparametric smoothing regression? $\endgroup$
    – Alexis
    May 10, 2021 at 21:41
  • $\begingroup$ @whuber just edited in the data set $\endgroup$
    – rabito
    May 10, 2021 at 21:47
  • $\begingroup$ By default, you ought to consider analyzing logarithms of response times, as Fechner's Law suggests. $\endgroup$
    – whuber ♦
    May 10, 2021 at 23:15

1 Answer 1

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The log transformation does not look bad: enter image description here

Further, the log transformation is fairly clearly indicated by $\lambda=0$ within the Box-Cox family of transformations: enter image description here

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