# Comparing cost changes for different groups of companies

I am conducting a research project where I have a experimental group and control group of companies and a cost data point for a base year and the year after. The years of costs are different for most of the companies so for one company the two costs may be in 2006-2007 while for another they may be from 2001-2002. Also, I do have the costs for other years if necessary.

The base year for each company was chosen because an event occurred during that year and I am trying to see if that event significantly changed a certain cost for that company.

I would like to test to see if the the change in cost is statistically different between the experimental and control group.

Also, I would like to normalize the change in cost in some way, I was thinking of calculating the percent change in cost or dividing each cost by market capitalization but any other suggestions would also be appreciated.

What statistical test/procedure would be best to use in this situation?

Also, considering that the companies can be segmented into various categories like country, market capitalization, etc, would you recommend any other procedures to further analyze the data?

Distributional Assumptions: Company's costs can be considered normal, I checked using a normality test. Sample Size: N=109 for experimental and control group, for a total of 436 data points.

• may be difference-in-difference methodology will work. – Metrics Jun 23 '13 at 3:52
• Can you describe your situation, your data & your goals more fully? You mention "market capitalization", so I'm guessing this is econ or finance, not biomedical research, but I'm mostly in the dark here. – gung Jun 23 '13 at 3:53
• I described my situation a little more and added a little more about my distributional assumptions and sample size. – ikemblem Jun 23 '13 at 15:51

It would be useful to understand the distributional assumptions you have made and also whether the companies are considered independent and to what extent confounding has been considered.

If you can make the assumption of normality and independence then is an independent samples t-test (based on the cost difference across years) appropriate? Anova may also be useful, but again, underlying assumptions must be considered.

Failing the validity of a parametric approach, if you can make some assumptions regarding symmetry, then a non-parametric approach such as a permutation test or Wilcoxon signed rank test may be of use.

• Now that I have updated my questions. Would it be possible for someone to provide a more detailed answer? – ikemblem Jul 8 '13 at 18:13

1) If you haven't done it already your cost data should be expressed in values of some base year common for all 218 companies, using some inflation/deflation index 9it doesn't matter which year). This is the least you can do to deal with the fact that data come from different years.

2) Considering the percentage change, it is a sensible thing to do to control for differences in company sizes,and hence cost levels. But note that cost structure is usually not linear in company size. So if companies vary widely in size (as indicated by for example, turnover, headcount, balance sheet value), it is awkward to assume that they belong to the same population.

3) You are referring to an "experimental" and to a "control" group. How each company ended in each group? By some "random draw" procedure? If yes, then your underlying null hypothesis is that all companies belong to the same population as regards their cost-responses, and so the two sub-samples should exhibit same characteristics, namely, sample moments, like the mean and variance. If this null is rejected, you reject the hypothesis that the companies come from the same population -nothing else.
If the companies have been grouped according to some criterion, then your underlying null hypothesis is that this criterion is not statistically significant for cost-responses. This sounds more interesting to test.

4) You write that you cannot reject the hypothesis that both sub-samples follow the normal. Then to test whether the mean value of percentage cost-change is statistically different between the two groups, you can conduct a Welch's t-test which takes into account the fact that the variances of the two sub-samples may be different.

5) You can separately test for the equality of variances, by conducting an F-test, or Levene's test in case you do not feel that the normality assumption is very strong.

6) Finally, use your eyes: obtain an estimate of the graph of the empirical densities of the two samples (say by kernel density estimation): do they look like they match?