Log-Transform Values in the range of -400 to 400. Would adding a large constant matter for log-transform? My data consists of score values in the range of -400 to 400.
I am thinking of log-transforming them, but is it statistically wise for me to make 400 as a constant?
log(x + 400)

If I have values between 0 and 400.
I know I can do log ( x + 1 ) to log-transform them successfully if I have zeroes in the dataset. Would the values of the constant matter when log-transforming?
Any input is appreciated.

It matters, sure. I don't know how it applies to your case specifically, but since the log function grows more and more slowly it effectively squeezes values more toward one another with a higher constant.
You can for instance make the variance on the log scale very small by using a huge constant, see examples below. The curves in the plot arrange themselves with increasing constant from bottom to top. We see that the log(x+500) curve barely changes over the interval of x.
x = runif(100, 0, 400)

# variance of log(x)
var(log(x))
#> [1] 1.310974

# variance of log(x+400)
var(log(x+400))
#> [1] 0.04018586

curve(log(x), from=0, to=400, ylim=c(0,7))
curve(log(x + 10), add=T)
curve(log(x + 100), add=T)
curve(log(x + 500), add=T)


Created on 2022-07-17 by the reprex package (v2.0.1)
