# Test to measure statistical significance of z-scores?

I'm a med student with an interest in maths/stats.

I'm looking for a quantitative analysis of a teamwork model (how people change in a team environment). The data is in two sets, before and after. Both sets have a mean of 35 (they are supposed to have the same total and mean). However one has an SD of 8.15 and the other has an SD of 4.89. Just wondering if there was a way to see if these are statistically significant (using SDs or z-scores)?

Just a basic explanation would be great.

Thanks,

MG

• Do you just want to test if the SD's differ? You could use Levene's test. – gung - Reinstate Monica Oct 20 '15 at 12:26

You have a couple of options for tests of your two samples to define the significance of the difference. One of the major factors in these tests is the sample size. (For example, conducting the tests with 7 samples yields very different results than data with the same means and standard deviations but with 200 samples.)

If the data is Gaussian, then the $F$-test for Equality of Two Variances would be the most sensitive, simple, and appropriate method.

Levene's Test tends to be the most robust as it calculates the distances from the median to each data point (instead of the mean). The test is easy to implement, even in a basic spreadsheet environment, and is included in most statistical packages.

The Bartlett's Test has results which tend to lie between the $F$-test and Levene's test. The Minitab website, which provides help beyond the scope of their proprietary software, notes some issue with Bartlett's Test and that the user may wish to exercise caution when using the same test from other software applications.

The $\chi^2$ test can also be used in most software and is similar to the $F$-test.

A Quantile-Quantile plot is a simple graphical method which would be easy to conduct in this instance where the number of observations remain the same for both groups.

A less common solution would be the bihistogram, which can be implemented in R. The bihistogram plots the histograms of the two datasets "back to back" as it were and helps to graphically portray the difference and similarities between two samples.