Take the variable Car as a random block. Do different additives have significantly different effect on boosting gas mileage? Groups       Name        Variance Std.Dev.  car:additive (Intercept) 0.9865   0.9932   car          (Intercept) 2.3299   1.5264   Residual                 0.6707   0.8190  Number of obs: 36, groups:  car:additive, 9; car, 3   Analysis of Variance Table          npar Sum Sq Mean Sq F value additive    2 4.5419   2.271  3.3857

Q: assumptions are required to perform an analysis of variance.

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