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

Today: More Statisticsoutliers and R2

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?

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?

Outliers: When is data invalid?

Not simply when you want it to be.

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)

What can outliers tell us?

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

Outliers can lead to important and fascinating discoveries.

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

What about relating 2 variables?

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

R2 gives a measure of fit to a line.

4 1711 146 7

12 172 136 213 21

birth month vs birth day

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

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.

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

Today: More Statisticsoutliers and R2