Today, September 16, is World Ozone Day. You don't hear much about the ozone layer any more.
But there’s a good reason that, almost 30 years ago, the United Nations designated today to as a day to raise awareness of the ozone layer: unlike dots and apple dumplings, this fragile shield of gas in the stratosphere, which acts as a natural sunscreen against dangerous levels of UV radiation, is critical to sustain life on our planet.
In this post, we'll join the efforts of educators around the globe who organize special activities on this day, by using Minitab to statistically analyze ozone-related data. You can follow along using the data in this Minitab project. If you don't already have it, you can download Minitab here and use it free for 30 days.
Orthogonal Regression: Can You Trust Your Data?
Before you analyze data, it's important to verify that your measuring system is accurate. Orthogonal regression, also known as Deming regression, is a tool used to evaluate whether two instruments or methods provide comparable measurements.
The following sample data is from the National Institute of Standards (NIST) web site. The predictor variable (x) is the NIST measurement of ozone concentration. The response variable (y) is the measurement of ozone concentration using a customer's measuring device.
In Minitab, choose Stat > Regression > Orthogonal Regression.Enter C1 as the Response (Y) and NIST as the Predictor (X). Enter 1.5 as the Error Variance ratio (Y/X) and click OK.
Note: The error variance ratio is based on historic data, not the sample data. Because the ratio is not available for these data, we'll use 1.5 purely for illustrative purposes. To learn more about this ratio, and how to estimate it, see the comments following this Minitab blog post.
Orthogonal Regression Analysis: Device versus NIST
The fitted line plot shows the two sets of measurements appear almost identical. That's about as good as it gets:
Now look at the numerical output. If there's perfect correlation, and no bias, you'd expect to see a constant value of 0 and a slope of 1 in the regression equation.
Error Variance Ratio (Device/NIST): 1.5
Device = - 0.263 + 1.002 NIST
Predictor Coef SE Coef Z P Approx 95% CI
Constant -0.26338 0.232819 -1.1313 0.258 (-0.71969, 0.19294)
NIST 1.00212 0.000430 2331.6058 0.000 ( 1.00128, 1.00296)
To assess this, look at the 95% confidence intervals for the coefficients. The confidence interval for constant includes 0. The confidence interval for the predictor variable (NIST) is extremely close to 1, but does not include 1. Technically, there is some bias, although it may be too small to be relevant. In cases like this, rely on your practical knowledge in the field to determine whether the amount of bias is important.
I'm no ozone expert, but given the sample measurements, I'd speculate that this tiny amount of bias is not critical.
Plotting the Size of the Ozone Hole
Usually holes just get bigger over time. Like the holes in my socks and sweaters.
But what about the size of the hole in the ozone layer above Antarctica?
As part of the Ozone Hole Watch project, NASA scientists have been tracking the size of the ozone hole of the Southern Hemisphere for years. I copied the data into a Minitab project, and then used Graph > Time Series Plot > Multiple to plot both the mean ozone hole area and the maximum daily ozone hole area, by year.
The plot shows why the ozone hole was such a big deal back in the 1980's. The size of the hole was increasing at extremely high rates, trending toward a potential environmental crisis. No wonder, then, that on September 16, 1987, the United Nations adopted the Montreal Protocol, an international agreement to reduce ozone-depleting substances such as chlorofluorocarbons. That agreement, eventually signed by nearly 200 nations, is credited with stabilizing the size of the ozone hole at the end of the 20th century, according to NASA and the World Meteorological Organization.
One-Way ANOVA: Seasonal Changes in the Ozone Layer
The ozone layer is not static, but varies by latitude, season, and stratospheric conditions. On average, the "typical" thickness of the ozone layer is about 300 Dobson units (DU).
The Lauder Ozone worksheet in the Minitab project linked above contains random samples of total ozone column measurements taken in Lauder, New Zealand in 2013. For this analysis, the seasons are defined as Summer = Dec-Feb, Fall = Mar-May, Winter = June-August, and Spring = Sept-Nov.
To evaluate whether there are statistically significant differences in mean ozone by season using Minitab, choose Stat > ANOVA > One-Way... In the dialog box, select Response data are in a separate column for each factor level. As Responses, enter Summer, Fall, Winter, Spring. Click Options, and uncheck Assume equal variances. Click Comparisons and check Games-Howell. After you click OK in each dialog box, Minitab returns the following output.
At a 0.05 level of significance, the p-value (≈ 0.000) is less than alpha. Thus, we can conclude that there is a statistically significant difference in mean ozone thickness by season. The plot shows that the mean ozone is lowest in Summer and Fall, and highest in Spring.
Look at the 95% confidence intervals (CI). Are any seasons likely to have a mean ozone thickness less than 300 DU? Greater than 300 DU? Based on the pairwise comparisons chart, for which seasons does the mean ozone layer significantly differ?
The ozone layer is just one factor in the myriad complex relationships between human activity and the global environment. So these analyses are just the tip of the iceberg—one that's melting as we speak.