MAT207 – Roback
Spring 2002
MAT207: Drawing Statistical Conclusions
Case Study 3.1.1 – Cloud Seeding to Increase Rainfall
Description:
Data were collected in southern Florida between 1968 and 1972 to test a hypothesis that massive injection
of silver iodide into cumulus clouds can lead to increased rainfall. (Data from J. Simpson, A. Olsen, and
J. Eden, “A Bayesian Analysis of a Multiplicative Treatment Effect in Weather Modification,”
Technometrics 17 (1975): 161-66.) On each of 52 days that were deemed suitable for cloud seeding, a
random mechanism was used to decide whether to seed the target cloud on that day or to leave it
unseeded as a control. An airplane flew through the cloud in both cases, since the experimenters and the
pilot were themselves unaware of whether on that particular day the seeding mechanism in the plane was
loaded or not (that is, they were blind to the treatment). Precipitation was measured as the total rain
volume falling from the cloud base following the airplane seeding run, as measured by radar. Did cloud
seeding have an effect on rainfall in this experiment? If so, by how much?
Graphical and Numerical Descriptions of Data:
Analyze…Descriptive Statistics…Explore (Dependent = rainfall or lograin; Factor = seeding)
Rainfall from Unseeded Days
Rainfall from Seeded Days
16
12
14
10
12
8
10
8
6
Frequency
4
4
Std. Dev = 278.43
2
Mean = 164.6
0
N = 26.00
0.0
200.0
100.0
400.0
300.0
600.0
500.0
800.0
700.0
1000.0
900.0
Std. Dev = 650.79
2
Mean = 442.0
N = 26.00
0
1200.0
0.0
1100.0
500.0
250.0
Daily rainfall (acre-f eet)
1000.0
750.0
1500.0
1250.0
2000.0
1750.0
2500.0
2250.0
2750.0
Daily rainfall (acre-f eet)
3000
10
27
2000
1000
0
Log of daily rainfall (ln acre-feet)
Frequency
6
8
28
29
6
30
4
1
2
3
51
2
52
0
-1000
26
-2
N=
26
26
Unseeded
Seeded
N=
Cloud seeding?
26
26
Unseeded
Seeded
Treatment group
Page 1
MAT207 – Roback
Spring 2002
Unseeded Clouds
Seeded Clouds
8
8
6
6
4
2
Std. Dev = 1.64
Mean = 4.0
Frequency
Frequency
4
2
Std. Dev = 1.60
Mean = 5.13
N = 26.00
0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
N = 26.00
0
1.50
2.50
2.00
7.0
Log of daily rainfall (ln acre-feet)
3.50
3.00
4.50
4.00
5.50
5.00
6.50
6.00
7.50
7.00
8.00
Log of daily rainfall (ln acre-feet)
De scri ptives
RAINFALL
SEEDING
Unseeded
Seeded
Mean
Median
St d. Deviat ion
Minimum
Maximum
Mean
Median
St d. Deviat ion
Minimum
Maximum
St atist ic
164.5885
44.2000
278.4264
1.00
1202.60
441.9846
221.6000
650.7872
4.10
2745.60
St d. Error
54.6039
St atist ic
3.9904
3.7863
1.6418
.00
7.09
5.1342
5.3964
1.5995
1.41
7.92
St d. Error
.3220
127.6299
De scri ptives
SEEDING
Unseeded
LOGRAIN
Seeded
Mean
Median
St d. Deviat ion
Minimum
Maximum
Mean
Median
St d. Deviat ion
Minimum
Maximum
.3137
Hypothesis Test for Treatment Effect:
Analyze…Compare Means…Independent Samples T test (Test Var = lograin; Group Var = seeding)
Group Statistics
LOGRAIN
SEEDING
Unseeded
Seeded
N
Mean
3.9904
5.1342
26
26
Std. Deviation
1.6418
1.5995
Std. Error
Mean
.3220
.3137
Independent Samples Test
Levene's Test for
Equality of Variances
F
LOGRAIN
Equal variances
assumed
Equal variances
not assumed
.058
Sig.
.811
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-2.544
50
.014
-1.1438
.4495
-2.0467
-.2409
-2.544
49.966
.014
-1.1438
.4495
-2.0467
-.2408
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