Question

Assume that you have done two different studies on the same sample of people.

Explain how you could use z-scores to compare the data in one study with the data of the other.

What are some of the limitations or benefits of using z-scores to do this type of comparison?

Answer 1

When we have data from the same sample of people on two different studies we could use the z-scores to perform a paired z-test i.e we could check if the mean paired difference from data of the two studies differ significantly or not.

We could calculate the difference for each pair and name it d

z-score is computed as

This z-score follows a N(0,1) under null hypothesis and therefore to perform a test we have to see if observed z-score lies in the acceptance region or the critical region.

The assumptions of the paired z-test are:

1. The data are continuous (not discrete).

2. The data, i.e., the differences for the matched-pairs, follow a normal probability distribution.

3. The sample of pairs is a simple random sample from its population. Each individual in the population has an equal probability of being selected in the sample.

4. The population standard deviation of paired differences is known.

There are few limitations when using these tests. Sample sizes may range from a few to several hundred. If your data are discrete with at least five unique values, you can often ignore the continuous variable assumption. Perhaps the greatest restriction is that your data come from a random sample of the population. If you do not have a random sample, your significance levels will probably be incorrect.