Andrew Bechard and Michael Drebot – Looking for Trends in Climate Change

Your presentation to the class was very good, and your paper contains a great deal of very good and interesting statistical work. You have applied linear regression and the Mann-Kendall test for trends pretty well to questions about the (relatively) long-term changes in temperature and precipitation at two locations in the US (Buffalo, NY and El Paso, TX). The section on background concerning global warming, the presentation, and the overall level of writing are not as strong, though.

For instance, you never really clearly state exactly what it is that you are trying to do (see comment 1 below). There are many places where you have used ways of saying things (“up north,” “down in Texas,” etc.) that are fine in everyday speech, but not that appropriate in formal writing. The sections describing the statistical work are somewhat repetitive and the presentation of the figures and graphs in the text could be improved. For instance, I think the main tables of temperature and precipitation data from the two locations could have been put in an appendix at the end of the paper. The displayed tabular format for the results of the calculations (copied and pasted from Excel?) does not look as good as what you could have created by typing in the numerical results directly in Word.

Specific Comments

1) Your introductory section is weak because you never actually say exactly what it is that you are going to do. Moreover, the sentence: “In comparison of the two different areas and their differences in climates, one relationship can be thought of; does the temperature in an area affect the amount of precipitation that falls throughout a given period?” is misleading in that regard. What your project was really aimed at doing was mainly determining whether different statistical methods could demonstrate the existence of trends in either temperature or precipitation in these locations. Then a second question was whether there was a correlation between temperature and precipitation trends. From a technical point of view, there is no way for an analysis like the one you are doing to yield an answer to a question like the one that you posed in the quoted sentence. You seem to be asking whether changes in temperature cause changes in precipitation. No statistical analysis can answer questions like that. Plus, that scientific question depends on too many other things to have a single, definite answer. There are areas on Earth where temperatures have increased and that have seen precipitation increases, and others where temperatures have increased that have seen precipitation decreases over the past 50 years. Global climate change has different effects in different regions.

2) This is vague and not too accurate scientifically. The issue is that the gases reflect some of the heat radiating from the Earth’s surface back into the atmosphere.

3) What you did was fine for this project, but you should not make overstated claims like this. Your results only show that there are trends over time in the two specific locations that you studied. They do not say anything more general or anything about the general relation between conditions in the north and south of the US.

4) The fact that Buffalo is on Lake Erie certainly adds to the levels of precipitation (primarily because of “lake effect” snow). The overall climate there is more directly affected by the facts that Buffalo is near the northern boundary of the US and not on a sea coast.

5) Whether or not the method used to compute the regression was “slow and tedious” has nothing to do with the subject of the paper. This whole paragraph should have been drastically pared down to just say that computations were done with the statistical functions of Microsoft Excel, including the Data Analysis package.

6) These graphical tables of computational results don’t look very good. It would have been much better to create tables in Word, using the same fonts as the rest of the text. Also, in statistics, the symbol μ is almost always used for a population mean. Since you are discussing a statistical test on a slope in a regression line, use a different letter here. Finally, a couple of technical points: The test here is actually a t-test and the alternative hypothesis is actually H_{a} : slope ≠ 0. So the rejection region for the test with α = .05 would come from a t-distribution with a number of degrees of freedom equal to the number of data points n, minus 2. For n = 47, this would put the boundaries of the rejection region at about ±1.96 instead of 1.645.

7) In using the formula for the Mann-Kendall variance V, you should explain what the ∑ t_{k}(t_{k} − 1)(2t_{k} + 5) terms are for, and how you would compute them.

8) Again, the hypotheses of the Mann-Kendall test involve the question whether an overall trend exists or not. μ usually stands for a population mean. Also, saying “the data is significant” is not the right way to result the results of a statistical test of hypotheses. Say “there is evidence to reject H_{0} (p = whatever)”

9) You should be aware that one general effect of global climate change is that many of the drier areas (e.g. North Africa, parts of Asia, etc.) are actually getting drier as average temperatures have increased. The data you analyzed don’t show evidence to say that is happening in El Paso, but it would be a natural question to ask whether that is happening in the southwestern US and northern Mexico.

Final Project Grades

Presentation: A- (92)

Paper Content: A (95)

Paper Form: B (85)