I am playing with `shapiro.test`

from R and checking for non-normality of error variance.

`> shapiro.test(residuals(fit)) Shapiro-Wilk normality test data: residuals(fit) W = 0.9525, p-value = 0.0003303 > shapiro.test(residuals( lm( sqrt(V1)~V2 ,data=market) ) ) Shapiro-Wilk normality test data: residuals(lm(sqrt(V1) ~ V2, data = market)) W = 0.8895, p-value = 5.89e-08 > shapiro.test(residuals( lm( log(V1)~V2 ,data=market) ) ) Shapiro-Wilk normality test data: residuals(lm(log(V1) ~ V2, data = market)) W = 0.7698, p-value = 1.95e-12 > shapiro.test(residuals( lm( 1/(V1) ~ V2 ,data=market) ) ) Shapiro-Wilk normality test data: residuals(lm(1/(V1) ~ V2, data = market)) W = 0.3954, p-value < 2.2e-16 `

The p-value for normality test is <0.001. So I did a transformation on `V1`

, `log(Y)`

, `inverse(Y)`

and `sqrt(Y)`

but their p-values gets even smaller. Does this mean that these transformations don't work? I also did a `boxcox`

transformation, and I get p-value of 0.3. So in that case, `boxcox`

is the best remedy only in this case? Or should I just use `boxcox`

in the future for remedy of non-normality? The rest of the usual transformation methods are useless?

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#### Best Answer

1) Why are you transforming the residuals?

2) why are you *testing* them for normality?

3) what do you mean by 'did a boxcar'? [Resolved]

4) what do the data look like? e.g. what does a QQ plot show?

—

Log, inverse and sqrt are all Box-Cox transformations (up to linear rescaling). Transformation may not be the best idea, but taking transformation as a given, *rather* than just throw transformations and data and hoping one sticks, find out what your data look like!