Question

A student researcher conducted a new study (N=10) on intelligence using a newly created measure, the IQ-5000 and wanted to compare his results to a similar study that used a different, but the commonly used measure, the WAIS. Both studies indicated that intelligence is normally distributed, but the student wanted to convert scores into z scores for comparison. After converting the scores in his study to z scores, he got the following: -4.7, 4.8, 0.9, -6.5, 3.1, -2.8, -5.3, 7.2, -0.5, 3.8. Does it seem like his z score conversion was correct? Yes/No – explain why or why not.

Answer 1

The conversation doesn't seem correct

Since there is 99.99% chances the the z scores are in between to 3. That it 99.99% z scores are in between and .

So a z score less than or greater than 3 is very rare.

But in the given scores there are many values less than and greater than 3, which doesn't happen normally.

Also note that z scores have mean 0 and variance 1,

In the given data we have mean

But variance

So z scores conversion is not correct.