Is it typical for group means of composite z-scores to have means with values of the same magnitude but opposite signs? I developed a composite score by converting four items to z-scores, then I summed up the z-scores to form a composite measure. 
However, when I've calculated means to compare finding for two different groups on a couple datasets using this composite score, the mean scores are the same distance from zero. 
For example,


*

*For one dataset, M1= 0.76 and M2= -0.76 

*For anotherdataset M1= 1.34 and M2= -1.34. 


Is this typical finding for this type of composite score? 
It seems odd to me.
 A: Yes. That's normal assuming the sample sizes for your two groups are equal, which if you have repeated measures data then they generally will be.
Example with equal group sizes
Here's a simulated example.
set.seed(1234)
rawscore <- rnorm(100, 5, 2)
g <- c(rep(0:1, 50))
rawscore <- rawscore + g
Data <- data.frame(g, rawscore)
Data$z <- scale(Data$rawscore)
tapply(Data$z, Data$g, mean)

##       0       1 
## -0.2159  0.2159 



*

*This simulates 100 observations with mean 5 and sd 2.

*And assigns the data to one of two groups (group 0; and group 1)

*I've added g to the raw scores to make group one have a systematically higher mean.

*We can then standardise the raw score using the overall mean and standard deviation. 

*Now if we look at the mean, we see that the mean in each group is of the same magnitude but opposite sign.


Example with unequal group sizes
rawscore <- rnorm(100, 5, 2)
g <- c(rep(c(0, 0, 0, 1), 50))
rawscore <- rawscore + g
Data <- data.frame(g, rawscore)
Data$z <- scale(Data$rawscore)
tapply(Data$z, Data$g, mean)

##        0        1 
## -0.03008  0.09024 



*

*This example is the same as above, but has three times as many participants in group 0, and as such the mean for group 0 is reversed and a third of the mean of group 1 in magnitude.

