The following data on number of cycles to failure (10⁶) appears in the article “An Experimental Study of Influence of Lubrication Methods on Efficiency and Contact Fatigue Life of Spur Gears” (J. Tribol. 2018).

a. Calculate the standard deviation of each sample. Why should we be reluctant to proceed with an analysis of variance?

b. Take the logarithm of the observations. Do these transformed values adhere better to the conditions for ANOVA? Explain.
c. Perform one-way ANOVA on these transformed values.

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Lubrication condition D1 J1 J2 J4 Cycles to failure (×106) 18.79 10.44 14.62 12.53 8.35 14.62 16.70 18.79 12.53 26.10 10.44 18.27 10.44 14.62 16.70 29.23 22.97 18.50 6.26 6.26 6.26 6.26 4.70 5.22