Analysis Methods

The first step in the analysis is to build a spreadsheet with the years in column 1 and the measured ring widths for each core in its own column.  In this example, data are shown for three oak trees.  Not all of the data are shown (just 1980-1996).  Each core has a different number of years based on how old the tree is.  Because of assumptions (linearity) that need to be made later, I suggest using mature trees and just using the last 30 years worth of data to examine the question of relationship between ring width and climate.

Next, create a separate worksheet (tabs at bottom) for each individual increment core.  Copy and paste the year column and the appropriate data column for each core to the appropriately labeled worksheet: 

Now what we want to do is relate ring width to known measured climate variables such as growing season precipitation, or temperature, or Palmer Drought Severity Index (PDSI) values.  BUT, we do not want the ACTUAL ring widths for each core.  We want standardized values, meaning the rings will vary from tree to tree for a variety of different reasons.  We want instead to try and isolate the important part of that ring width signal that is attributable to climate.  This can become statistically quite complicated in research applications, but for our purposes we will employ simple least squares regression to the data.  This will construct a series of expected values that lie along a best fit line.  Each ring will have a residual value (the difference between the observed ring width and the expected ring width from the equation for the line).  This can be easily determined using the Excel Add-in for Data Analysis found under the Tools option:

You will get a full regression output report, but the only portion that is necessary is the column of numbers marked "residuals".  Everything else can be deleted and the residuals column copied up next to the ring width column.  Do this for each core.  You should now have a spreadsheet that looks like this for each core:

Next, create a sheet whereby you can arrange all of the residuals side-by-side.  The next step is to take a mean of all of the residuals.  This will give you an average ring response (positive or negative) across all of the cores for each year.  Note that every regression equation for each core will be different (that is exactly what we wanted), but all we really need to know is, all other things being equal, did a specific ring in a specific year have an above-average or below-average growth for that year, and if so about how much.  Next we need to download the local climate data for our area.  The most direct way of doing this in the United States is to go to:

http://cdo.ncdc.noaa.gov/plclimprod/plsql/poemain.poe

For our example, I have retrieved growing season precipitation data (note this may require some re-organization and summarization prior to dropping into the spreadsheet).  If you align the precipitation data in a column adjacent to the mean residuals, you can then easily conduct a correlation analysis (again using the Excel data analysis add-in from the Tools option).  For this data set, you should now have a spreadsheet that looks something like this:

A probability value can be looked up in a stats table (using the appropriate degrees of freedom based on the number of rings you have in your composite or mean residual column).  Here we find a correlation of 0.503 which is not particularly strong, but it is highly significant suggesting that there is a good relationship between climate and ring width, but it is a bit sloppy (as we expected).  As a final step, I strongly encourage you to plot the data to look at your response.  This is easily accomplished in the graph option of Excel: