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Inquiry 1 written and oral reports are due in lab the week of 9/29. Today: More Statistics outliers and R 2. Outliers… 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7, 121, 130 Median = 4 Mean = 18. Is there a numerical way to determine the accuracy of our analysis? - PowerPoint PPT Presentation
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Inquiry 1 written and oral reports are due in lab the week of 9/29.
Today: More Statisticsoutliers and R2
Is there a numerical way to determine the accuracy of our analysis?
2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7, 121, 130
Mean = 18
Standard deviation = 40.5
Standard deviation is a measure of variability.
Outliers: When is data invalid?
Not simply when you want it to be.
Dixon’s Q test can determine if a value is statistically an outlier.
Dixon’s Q test can determine if a value is statistically an outlier.
|(suspect value – nearest value)|Q = |(largest value – smallest value)|
Dixon’s Q test can determine if a value is statistically an outlier.
|(suspect value – nearest value)|Q = |(largest value – smallest value)|
Example: results from a blood test…789, 700, 772, 766, 777
Dixon’s Q test can determine if a value is statistically an outlier.
|(suspect value – nearest value)|Q = |(largest value – smallest value)|
Example: results from a blood test…789, 700, 772, 766, 777
Dixon’s Q test can determine if a value is statistically an outlier.
|(suspect value – nearest value)|Q = |(largest value – smallest value)|
Example: results from a blood test…789, 700, 772, 766, 777
Q=|(700 – 766)| ÷ |(789 – 700)|
Dixon’s Q test can determine if a value is statistically an outlier.
|(suspect value – nearest value)|Q = |(largest value – smallest value)|
Example: results from a blood test…789, 700, 772, 766, 777
Q =|(700 – 766)| ÷ |(789 – 700)| = 0.742
Dixon’s Q test can determine if a value is statistically an outlier.
|(suspect value – nearest value)|Q = |(largest value – smallest value)|
Example: results from a blood test…789, 700, 772, 766, 777
Q =|(700 – 766)| ÷ |(789 – 700)| = 0.742 So?
You need the critical values for Q table:Sample # Q critical value
3 0.970
4 0.831
5 0.717
6 0.621
7 0.568
10 0.466
12 0.426
15 0.384
20 0.342
25 0.317
30 0.298
If Q calc > Q critrejected
From: E.P. King, J. Am. Statist. Assoc. 48: 531 (1958)
You need the critical values for Q table:Sample # Q critical value
3 0.970
4 0.831
5 0.717
6 0.621
7 0.568
10 0.466
12 0.426
15 0.384
20 0.342
25 0.317
30 0.298
If Q calc > Q critthan the outlier can be rejected
Q calc = 0.742
Q crit = 0.717
= rejection
From: E.P. King, J. Am. Statist. Assoc. 48: 531 (1958)
Outliers can lead to important and fascinating discoveries.
Transposons “jumping genes” were discovered because they did not fit known modes of inheritance.
Is there a numerical way to determine the accuracy of our analysis?
2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7, 121, 130
Mean = 18
Standard deviation = 40.5
Standard deviation is a measure of variability.
What about relating 2 variables?
R2 gives a measure of fit to a line.
If R2 = 1 the data fits perfectly to a straight line
If R2 = 0 there is no correlation between the data
Bradford Assay 3-7-05
R2 = 0.9917
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.140
0.160
0 0.5 1 1.5 2 2.5
ug protein
OD595
Protein quantity vs absorbance
We will practice T-test, outliers, and R2 in lab.
Also, you will have time to begin forming groups for Inquiry 2.