Imagine we have collected air quality data from four sites, consisting of 100 samples from each site- one variable contains the site identifier, the second contains the NOx levels and the third contains the PM10 concentrations. the fourth variable contains data regarding the seasonality (summer, autumn, winter, spring)
question 2) what numeric or graphical methods can we use to determine if our data are normally distributed?
question 3) should the data prove to be normallydistributed, and we wanted to discover if there were any statistical differences between the two sites what would be the most appropraite test to use?
Hi Priscilla,
I recommend you the Shapiro-Wilk test to check normality. For my experience, it is more reliable than other common tests such as Kolmogorov-Smirnov or Lilliefors.
If data is normally distributed, you must perform a one-way ANOVA (four sites, four samples). If not, you can use Kruskal-Wallis test (non-parametric).
You could also try to carry out a cluster analysis to find out whether seasonality is a relevant factor or not.
Hi Priscilla,
Daniel Jato-Espino is right. Generally, you might enhance understanding of your data by sorting, classifying and graphing them first. Take a look at the distribution to see if there are anomalies from the usual picture of a normal distribution. You might discover for instance a large tail with higher levels, indicating a nearby source.
A positive normality check allows you to use parametric tests. Mostly air quality data are not normally distributed, often log normality transition is done then. But with these small samples the distinctiveness of parametric tests is hardly larger than in non-parametric tests, so Kruskall-Wallis fits well.
The distribution is skewed to the larger concentrations and therefore resembling a log-normal distribution and not a linear distribution
Your question sounds as if it is the first hand data analysis. It is important to analyse the data with simple graphic solutions like 2D plots, histograms, frequency distribution etc., Experiment with various linear and or non-linear regression techniques.
If you hate doing some basic coding use simple MS Excel sheets for data analysis.
Otherwise, I recommend simple python or R codes for generating various plots and analyse the data. You will enjoy finding new things, experiment with simple plots for various parameters. Use a good book on statistics for guidance (I have my suggestions penned towards the end).
In python use scitools package and with R you may also experiment with various readily available statistical models. R has two interesting packages ggplot2 and plot3d make use of them.
Only after preliminary playing around with the data, you may consider complicating the things. Bottom line is simple things should not be complicated unnecessarily.
Books that may be of help to you:
1. A Primer on scientific programming with python - By HP Langtangen (for python / scitools)
2. Use R - ggplot2 - By Robert Gentleman & others (for R programming)
3. Statistics in Linguistics - Christopher Butler (a book for basic statistics)
Hi Priscilla,
Which probability distribution actually best fits a particular set of air quality data depends on the characteristics of the set. The two distributions that have been used most widely for representing atmospheric concentrations are the lognormal and the Weibull. For more information on that, you can find in the book: Atmospheric Chemistry and Physics, Second Edition. John H. Seinfeld and Spyros N. Pandis. John Wiley and Sons, 2006. I recommend that you can use SPSS software to check the probability distribution of your data.
Hi Priscilla, I agree with the colleagues suggesting a log-normal distribution for pollution data. It may resemble a normal distribution for extremely high concentrations and a small standard deviation.
Hi, Priscilla, I suggest you get a copy of Environmental Statistics and Data Analysis
Wayne R. Ott, December 20, 1994 by CRC Press, Textbook - 336 Pages
ISBN 9780873718486 - CAT# L848. It is the best source for analysis of environmental data and statistics that I know. Ott is one of the world's experts in this field.
See Larsen, R.I., A New Mathematical Model of Air Pollutant Concentration Averaging Time and Frequency, Journal of the Air Pollution Control Association, Vol. 19, No. 1, pp. 24-30, 1969, which states: "...Air pollutant concentration data can be presented in digital tables (Table I) or as analog plots (Figures 1 and 2). To determine what mathematical model might best fit the actual data, a computer program was written to plot concentration data. Data were plotted for carbon monoxide, hydrocarbons, nitric oxide, nitrogen dioxide, nitrogen oxides (NO -f- NO2), oxidant, and sulfur dioxide for Chicago, Cincinnati, Los Angeles, Philadelphia, San Francisco, and Washington for each of the 3 years and for the 3-year period from December 1, 1961 to December 1, 1964. (A December 1 starting time was selected so that one of the averaging times would be for a 3-month seasonal value, starting with winter, which is defined here as the three coldest months, December, January, and February.) Analysis of these plots (a total of more than 100) indicates that the data can be described by a mathematical model with the following characteristics:
1. Concentrations are approximately lognormally distributed for all pollutants in all cities for all averaging times (same as previous model).
2. The median concentration (50 percentile) is proportional to averaging time to an exponent (and thus plots as a straight line on logarithmic paper)...
If you check Figure 2 in our paper, Fine particle air pollution and secondhand smoke exposures and risks inside 66 US casinos James L. Repace a,b,n, Ruo-Ting Jiang c, Viviana Acevedo-Bolton c, Kai-Chung Cheng c, Neil E. Klepeis c, Wayne R. Ott c, Lynn M. Hildemann, which is available on Research Gate, you'll find a comparison of indoor and outdoor PM2.5 for 66 casinos, plotted on a log-normal plot. As you can see, both distributions fit the log-normal distribution very well.
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