# Will Z-scores help me compare my variables?

I have two variables:

1) Percentage of population of different geographic regions which has bought a certain category of product (say hair sprays) in the last MONTH

2) Percentage of population which has bought a specific brand of hair spray in the last YEAR.

I am trying to in which region the brand is doing better compared to the general use of hair spray, and in which it is doing worse.

Since the first variable is for a month and the second for a whole year, i can't just compare them like that. So I thought i'll transform them into z-scores, and take the difference between the two. Question: Is that a valid approach?

(Side question: the distribution of the second variable has quite a strong positive skew, while the first is fairly normal. Is that a problem?)

EDITS in response to questions:

• For variable 2 I only have data for that one particular brand, so I can't aggregate across brands. While variable 1 is only for the whole product category encompassing all brands - can't dissaggregate that either.
• Sample size is over 100 geographical regions
• I am attaching a scatter plot of the two variables. One of which shows variable 2 on a log scale.
• Just to clarify, I am not so much interested in the overall relationship between the two variables, but more in arriving at a metric that will tell me for any specific entity (region) how well it is doing on variable 2 (sales of specific brand) compared to variable 1 (sales of general product category). Now, of course, I can see that maybe the regression/scatterplot approaches suggested might be an intermediate step to achieve that goal. But how do I progress after that?

Thanks so much for the suggestions so far though!

• If your goal is to find out which region your brand is doing better (selling more) then why are you comparing last month to last year? You should be comparing across brands. – Peter Flom Jan 19 '14 at 12:00
• yeah. it's not ideal. but it's the only data i've got. At first i was tempted to just multiply the monthly data by 12 to make them comparable, but not sure if that is valid. – John Jan 19 '14 at 12:04

OK, from your comments, it seems you have data on one brand across several regions, both for one month and for one year.

Comparing your brand in one region for one month vs. one year is probably not useful; you would have N = 1 and no way to estimate variability. You could multiply month by 12, but if there was a difference between month and year you'd still not really know much - is it a property of the month?

More likely, you want to look across regions. This could answer a question such as "does our brand do better in region X vs. region Y?" For this, I'd look at two separate regressions, each with "use" as the dependent variable (either for month or for year) and with "region" as the independent variable.

This assumes that your data across regions is in comparable metrics (that is, not total number of people).

EDIT IN RESPONSE TO COMMENTS: Given what you've said, I think the best thing is to not transform the data. First, form a ratio for each region: Your brand sales/total sales (you can multiply your brand by 12 if you want to, but it isn't critical). Then use that ratio as the dependent variable in a regression with region as the independent variable

• - "OK, from your comments, it seems you have data on one brand across several regions, both for one month and for one year" -> Well not exactly. The data for the particular brand is for one month. The data for ALL brands together is for one year. - "comparable metrics" -> yes, percent of population. -I like the regression approach. so if i regress specific brand on the general variable, i could see which regions are above the regression line and which are below, right? – John Jan 19 '14 at 14:12
• Sounds good, although with your correction of what data you have, your initial approach starts to make sense. – Peter Flom Jan 19 '14 at 14:25
• Ok. great. Glad to hear I seem to be on the right track. Thanks a lot for your input! Would you just subtract the two z-scores? or maybe divide the second by the first? i am trying to arrive at one number for each region you see. (how well they are doing in relative terms) – John Jan 19 '14 at 16:00
• I will edit my answer to help – Peter Flom Jan 19 '14 at 16:05

I thought I'll report back after I have done some more research on this. The conclusion I draw from this that that two approaches could be taken.

1) Using Z-scores, as initially proposed. When intorduing Z-scores many statistics textbooks give the example of comparing grades in two school subjects, e.g I got 70 points on a math exam and 85 points in history, but math was the more difficult test. So how do i know which subject i am better in? One converts the socres into Z-scores and then i can compare them. A scholar.google search shows that a number of scientific papers have used this approach for similar problems in all sorts of situations. It appears to me close enough of an example to the problem at hand here too.

2) Using regression. Run a regression of variable 2 on variable 1. The regression line (fitted values) tell me where the sales of the specific product in a region should be given the general sales of the whole product category there, based on the overal relation ship. The difference between that and the actual datapoint (residual) tells me how well the region is doing.