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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

Inquiry 1 written and oral reports are due in lab the week of 9/29

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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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Page 1: Inquiry 1 written and oral reports are due in lab the week of 9/29

Inquiry 1 written and oral reports are due in lab the week of 9/29.

Today: More Statisticsoutliers and R2

Page 2: Inquiry 1 written and oral reports are due in lab the week of 9/29

Outliers…

2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7, 121, 130

Median = 4

Mean = 18

Page 3: Inquiry 1 written and oral reports are due in lab the week of 9/29

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.

Page 4: Inquiry 1 written and oral reports are due in lab the week of 9/29

Outliers: When is data invalid?

Page 5: Inquiry 1 written and oral reports are due in lab the week of 9/29

Outliers: When is data invalid?

Not simply when you want it to be.

Page 6: Inquiry 1 written and oral reports are due in lab the week of 9/29

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.

Page 7: Inquiry 1 written and oral reports are due in lab the week of 9/29

Dixon’s Q test can determine if a value is statistically an outlier.

|(suspect value – nearest value)|Q = |(largest value – smallest value)|

Page 8: Inquiry 1 written and oral reports are due in lab the week of 9/29

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

Page 9: Inquiry 1 written and oral reports are due in lab the week of 9/29

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

Page 10: Inquiry 1 written and oral reports are due in lab the week of 9/29

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)|

Page 11: Inquiry 1 written and oral reports are due in lab the week of 9/29

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

Page 12: Inquiry 1 written and oral reports are due in lab the week of 9/29

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?

Page 13: Inquiry 1 written and oral reports are due in lab the week of 9/29

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)

Page 14: Inquiry 1 written and oral reports are due in lab the week of 9/29

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)

Page 15: Inquiry 1 written and oral reports are due in lab the week of 9/29

What can outliers tell us?

Page 16: Inquiry 1 written and oral reports are due in lab the week of 9/29

If you made a mistake, you should have already accounted for that.

Page 17: Inquiry 1 written and oral reports are due in lab the week of 9/29

Outliers can lead to important and fascinating discoveries.

Transposons “jumping genes” were discovered because they did not fit known modes of inheritance.

Page 18: Inquiry 1 written and oral reports are due in lab the week of 9/29

What about relating 2 variables?

Page 19: Inquiry 1 written and oral reports are due in lab the week of 9/29

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.

Page 20: Inquiry 1 written and oral reports are due in lab the week of 9/29

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

Page 21: Inquiry 1 written and oral reports are due in lab the week of 9/29

R2 gives a measure of fit to a line.

4 1711 146 7

12 172 136 213 21

birth month vs birth day

Page 22: Inquiry 1 written and oral reports are due in lab the week of 9/29

birth month

Birth day

birth month vs birth day

R2 = 0.0055

0

5

10

15

20

25

0 2 4 6 8 10 12 14

Page 23: Inquiry 1 written and oral reports are due in lab the week of 9/29

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

Page 24: Inquiry 1 written and oral reports are due in lab the week of 9/29

We will practice T-test, outliers, and R2 in lab.

Also, you will have time to begin forming groups for Inquiry 2.

Page 25: Inquiry 1 written and oral reports are due in lab the week of 9/29

Inquiry 1 written and oral reports are due in lab the week of 9/29.

Today: More Statisticsoutliers and R2