 Don’t use polynomial trends with an order greater than two, however, as it’s easy to misinterpret the meaning of higher order polynomial trends.
The absolute value of R2 is as important as how the relative values of R2 for both types of trend are. Any R2 value that’s less than about 0.35 can be a result of random chance, so any conclusions based on such a low R2 should be well explained. The higher the R2 value is, the more certain it is that the trend is real.
While I’ve assumed data vs. time thus far, it’s also useful to graph one set of data vs. another, such as in the case of global temperature anomaly vs. atmospheric CO2 concentration. To do this, you generate a “scatter” chart (instead of a “line” chart) with CO2 on one axis and temperature on the other. Then you can generate both trends and the R2 values for comparison. In the case of CO2 and temperature, the positive trends and the high R2 values indicate that there’s a pretty strong correlation between high CO2 concentrations and higher temperature anomaly.
Cross-correlation of temp anomaly with CO2 concentration for CO2 lagging temp by 8 years. Note:1890 through 2000 are hidden for convenience.
Finally, while correlation does not prove causation, there is a way to check if causation is likely via correlations. To test causation, you run a set of what are known as “cross-correlations” between two sets of data. We do this with the Excel function “CORREL” where we select the two data series. In order to check if a causal claim is reasonable, you can run cross-correlations with different delays between one set of data and another. You delay one set of data by starting it a certain number of cells late and finishing the other set of data the same number of cells early. Square the correlation result to get the R2 value.
Be careful with cross-correlations. First, you can get in trouble fast if you’re just guessing about a correlation and don’t have some understanding of what you’re correlating (think of the high correlation between global warming and the drop in number of pirates). Second, CORREL assumes a linear relationship between the datasets you’re cross-correlating, so it can give wrong answers when there’s a non-linear relationship. But CORREL is still a good starting point for figuring out where you need to ask more questions.
Spreadsheet programs can be very powerful tools for quickly and easily checking claims based on statistical analyses of data. While I used a climate-based example, the same approach can be taken with regard to nearly any source of data, and I’ve used similar analyses to sanity-check health and economic data in the past.
* From the quarterly newsletter SEJournal, Summer 2011 issue.