Adjusted Mean

What Is an Adjusted Mean?

The adjusted mean arises when statistical averages must be corrected to compensate for data imbalances and large variances. Outliers present in data sets will often be removed in order to determine the adjusted mean because they can have a large impact on the calculated means of small populations. An adjusted mean can be determined by removing these outlier figures through regression analysis. Adjusted means are also called least-squares means.

Understanding Adjusted Means

Adjusted means are most often used in finance when there are outlier data points that have an outsized impact on the trend line for a data set. An analyst may choose to remove outliers entirely, but this is typically only done in cases where the reasons behind the outliers are known, or a rough forecast of a trend is suitable.

For researchers and professionals who want to remove outliers, multiple regression equations are the preferred method. Regression analysis provides a more accurate result and more reliable data at the conclusion of a study. Aside from regression analysis, there are also more basic ways of adjusting a mean.

One way to adjust a mean is to add categorical variables that separate the data more finely. For example, imagine a study looking at alcohol consumption in the accounting profession that finds that accountants today drink half as much as accountants did 50 years ago. While this may appear to be positive, upon deeper analysis, it is discovered that the study wasn't adjusted for gender. When sex is taken into account, it turns out that male accountants drink slightly less than accountants did 50 years ago, but the bulk of the change is the growth in the total number of female accountants. On average, the study shows that female accountants drink about the same as their female counterparts did 50 years ago. Female accountants also drink much less than male accountants today and 50 years ago. But female accountants are more numerous than ever before, effectively helping to reduce the overall level of drinking in the profession, even though their male counterparts have remained relatively static in drinking habits.

The additional variables, in this case, tell a more accurate story about the data and can be combined back into an overall mean by adding a value for sex that reflects the proportion of males to females in each sampling group. This would show a more modest dip in drinking overall in the profession. However, doing further analysis of this data may suggest that one integrated mean isn't the best way to present this data.

In this example, the sex of the participants would be considered covariates, a type of variable that the researcher cannot control but that impacts an experiment's results. Using an adjusted mean is a way of compensating for the covariates: what is the effect of the activity or behavior if there were no differences between the genders? The same types of adjustments are made for other demographic data like age, ethnicity, socioeconomic status, etc.

Example of an Adjusted Mean

In 2009, the Financial Accounting Standards Board (FASB) clarified the mark-to-market rule in order to ease pressure and instantly improve the large banks’ balance sheets. If an analyst were reviewing trends in balance sheet strength in 2010 for the trailing ten years using bank published measures, the mean average would be problematic and inaccurate because it would include to 2009 rule change.

One way to correct this is to create a coefficient of variation for the average differences between the balance sheet figures and the market values at the time, for a subset of commonly-held assets across large banks. In practice, however, banking sector analysts continued to calculate stringent mark-to-market figures after the rule clarification, so the simple solution would be to use those data-sets instead. More importantly, banks have always had a fair bit of discretion under mark-to-market rules so the balance sheet figures for held assets should always be viewed skeptically and independently verified when possible.