Question

How would the correlations change if we normalized the data first?

a. Correlations will change, since the distances change when we normalize the data

b. Correlations will not change, since data are normalized by computing correlations

c. None of the above is true

Answer 1

Solution :

The correct answer is b. Correlation will not change.

For ex: suppose we have data as,

Mean of x = 4 and sd(x) = 1.5811

Mean of y = 19 and sd(x) = 10.7004

In excel use command as =average() to find mean and =STDEV() to find standard deviation sd.

to normalise we, use z-score formula , z =(x-mean)/sd

and get data as

And then using Excel command as =CORREL() select the data values inside.

We get same correlation for both the data set, r = 0.5615

Therefore the correct answer is b.