Transcript Lies, Damned Lies, and Statistics

Climate Change and
Extreme Events: Lies,
Damned Lies, and Statistics
By
David R. Legates
University of Delaware
And
Delaware State Climatologist
“Figures often beguile
me, particularly when I
have the arranging of
them myself; in which
case the remark
attributed to Disraeli
would often apply with
justice and force:
‘There are three kinds
of lies: lies, damned
lies, and statistics’.”
Mark Twain
Chapters from my Autobiography
North American Review, No. DCXVIII
Lies, Damned Lies, Statistics
…and Weather Observers!
DISCLAIMER
The Delaware State Climatologist
does NOT represent either the
Executive, Legislative, or Judicial
branches of government and does
not speak for the Governor or any
other State agency or official.
“Recent media coverage of events associated
with the subject of climate change has
generated some confusion as to the role of
the State Climatologist.”
Governor Minner – February 13, 2007
Heavy Rainfalls Called
Sign of Climate Change
in New Report
Severe Weather
Predicted as Norm
“Delaware…has seen a 37%
increase in storms dumping
2-inches or more of rainfall
over a 24-hour period.”
Environment America and USPIRG
“When it Rains, It Pours: Global Warming and
the Rising Frequency of Extreme Precipitation
in the United States”
Page 36
Days with Precipitation >2.0 Inches
Porter Reservoir, Wilmington DE
}
≈37%
Days with Precipitation >2.0 Inches
Porter Reservoir, Wilmington DE
Days with Precipitation >2.0 Inches
New Castle County AP, Wilmington DE
Days with Precipitation >2.0 Inches
University Farm, Newark DE
Days with Precipitation >2.0 Inches
Porter Reservoir, Wilmington DE
http://www.surfacestations.org
MMTS
http://www.surfacestations.org
Days with Precipitation >2.0 Inches
Porter Reservoir, Wilmington DE
Page 36
Dr. Willie
Soon
Harvard
University
Number of 3” Rainfalls per Year in Madison WI
ASOS
ERA
Number of 3” Rainfalls per Decade in Madison WI
ASOS
ERA
Number of 3” Rainfalls per Decade in Madison WI
“Pre-ASOS”
Number of 3” Rainfalls per Decade in Madison WI
“Pre-ASOS”
Number of 2” Rainfalls per Year in Stoughton WI
Number of 3” Rainfalls per Year in Stoughton WI
Number of 3” Rainfalls per Decade in Stoughton WI
8
7
6
5
4
3
2
1
0
1932-1941
1942-1951
1952-1961
1969-1978
1998-2008*
*Actually, an 11-year ‘decade’
What is Wrong
with the
Statistics?
Number of 2” Rainfalls per Year in Stoughton WI
FREQUENCY COUNTS!
Regarding the Dependent Variable:
• It is composed of discrete events that are
frequency counts and non-negative integers.
• Infrequently occurring events tend to cluster
around 0 and/or 1 and exhibit low frequencies at
higher values.
• It is highly positively skewed and truncated at 0 –
Thus the Mean > Median
• Error term is NOT iid ~ N(0,s2)
• \ OLS regression is inappropriate for these data!
Two Alternatives to OLS Regression:
• Poisson Regression
– Assumes a Poisson distribution, where values are nonnegative integers, and is highly positively skewed.
– Assumes Equidispersion (i.e., mean is equal to the
variance)
• Negative Binomial Regression
– Assumes a Poisson-like distribution; values are nonnegative integers and is positively skewed
– No assumption of Equidispersion; appropriate for overdispersed data (i.e., variance is greater than the mean)
Advantages of Poisson or
Negative Binomial Regression:
• Although OLS, Poisson and negative binomial
regressions yield similar results, the non-normality
of the errors leads to large standard errors and an
arbitrary increase in the level of significance of the
coefficients in OLS.
• Assumptions can be more easily met with Poisson
or Negative Binomial regression than with OLS.
• OLS regression could lead to a Type I error
(rejection of null hypothesis when true) and
erroneously conclude that the variable is changing
over time when, in fact, it is not.
Page 36
Climate Change and
Extreme Events: Lies,
Damned Lies, and Statistics
By
David R. Legates
University of Delaware
And
Delaware State Climatologist