CHEGR 3745 Statistical Treatment of Experimental Data
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1 CHEGR 3745 Statistical Treatment of Experimental Data
description
CHEGR 3745 Statistical Treatment of Experimental Data. Normal Distribution. Mean, Variance, and Standard Deviation. Normal Probability Function. Population A. Population D. Population B. Population C. Is Population D different from Population A? Population B? Population C? -2?. - PowerPoint PPT Presentation
Transcript of CHEGR 3745 Statistical Treatment of Experimental Data
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CHEGR 3745Statistical Treatment of
Experimental Data
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Normal Distribution
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
60 65 70 75 80 85 90
Measured Value
Pro
bab
ilit
y
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Mean, Variance, and Standard Deviation
1 , =AVERAGE(.....) in Excel
N
ii
xx
N
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2 1 , =VAR(...) in Excel1
N
ii
x xs
N
2 , =STDEV(...) in Excels s
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Normal Probability Function
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Population A
Population B
Population C
Population D
• Is Population D different from– Population A?– Population B?– Population C?– -2?
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How Willing are You to be Wrong?
• Never!
• 1% of the time?
• 5% of the time?
• 50% of the time?
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Confidence Intervals
; ( , )
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tsMean x
Nt student's t - statistic f df
alpha risk
df N
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d.f 0.01 0.05 0.10
1 63.66 12.71 6.31
2 9.92 4.30 2.92
3 5.84 3.18 2.35
4 4.60 2.78 2.13
5 4.03 2.57 2.02
6 3.71 2.45 1.94
7 3.50 2.36 1.89
8 3.36 2.31 1.86
9 3.25 2.26 1.83
10 3.17 2.23 1.81
11 3.11 2.20 1.80
12 3.05 2.18 1.78
13 3.01 2.16 1.77
14 2.98 2.14 1.76
15 2.95 2.13 1.75
16 2.92 2.12 1.75
17 2.90 2.11 1.74
18 2.88 2.10 1.73
19 2.86 2.09 1.73
20 2.85 2.09 1.72
t-distribution
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ExampleSample Corrosion Rate
MPY
1 3.1
2 2.2
3 3.6
213..709.0503.0
97.22
fdssx
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d.f 0.01 0.05 0.10
1 63.66 12.71 6.31
2 9.92 4.30 2.92
3 5.84 3.18 2.35
4 4.60 2.78 2.13
5 4.03 2.57 2.02
6 3.71 2.45 1.94
7 3.50 2.36 1.89
8 3.36 2.31 1.86
9 3.25 2.26 1.83
10 3.17 2.23 1.81
11 3.11 2.20 1.80
12 3.05 2.18 1.78
13 3.01 2.16 1.77
14 2.98 2.14 1.76
15 2.95 2.13 1.75
16 2.92 2.12 1.75
17 2.90 2.11 1.74
18 2.88 2.10 1.73
19 2.86 2.09 1.73
20 2.85 2.09 1.72
t-distributiont = 4.30
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Confidence Intervals
4.3 0.7092.96
32.96 1.76
tsMean x
nMean
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Is the Mean Equal to 5?Comparing a Mean with a Constant
2
2.96 54.96
0.5033
(5 for this example)
( , ) 4.30
;
;
Mean is not equal to 5
obs
critical
obs critical
obs critical
x Mt
sN
x Measured mean
M Target mean
t t table df
If t t x M
If t t x M
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Are the Means of Two Populations Equal?Comparing Two Means
1 2
1 2
2 21 1 2 2
1 2
22 21 2
1 2
2 22 21 2
1 2
1 2
1 1
1 1
2
. .
1 1
obs
pool
pool
x xt
sN N
N s N ss
N N
s sN N
d fs sN N
N N
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1 2
1 2
( , . .)
;
;
critical
obs critical
obs critical
t f d f
If t t x x
If t t x x
Example
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Sample Corrosion Rate, MPY
1.0 M NaOH
Sample Corrosion Rate, MPY
0.5 M NaOH
1 4.0 1 3.5
2 4.6 2 3.2
3 3.7 3 3.7
4 3.9 4 3.8
5 3.1
Mean 4.05 3.46
Variance 0.15 0.093
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Are the Means of Two Populations Different? Comparing Two Means
2 21 1 2 2
1 2
1 2
1 2
2
2 2
1 1 4 1 0.15 5 1 0.0930.34
2 4 5 2
4.03 3.462.47
1 1 1 10.34
4 5
0.15 0.0934 5
. . 5.7 6.00.15 0.093
4 54 1 5 1
( , . .) 2.4
pool
obs
pool
critical
N s N ss
N N
x xt
sN N
d f
t f d f
1 2
1 2
5
;
;obs critical
obs critical
If t t x x
If t t x x
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Does a Treatment Change Anything?Paired Testing
2
2
0
1
( , )
;
;
diff
obs
diff
diff
diff
critical
obs critical
obs critical
xt
s
Nx Average of the differences
s Variance of the differences
df N
t t table df
If t t Treatment is Significant
If t t No Change
