Inquiry 1 written AND oral reports due Th 9/24 or M 9/28.

Inquiry 1 written AND oral reportsdue Th 9/24 or M 9/28

During your presentation:•Look at your audience.

•Project your voice.

•Keep visuals simple and clear.

•Explain completely and clearly but concisely (5-7 min).

•Make sense.

The written report for your inquiries will be formatted similarly to a scientific research article.

•Title

•Abstract

•Introduction

•Results

•Discussion

•Materials and Methods

•References

http://mathworld.wolfram.com/Chi-SquaredDistribution.html

More stats... Chi2, R2, and sample size

The Chi Square Test

• A statistical method used to determine goodness of fit– Goodness of fit refers to how close the observed

data are to those predicted from a hypothesis

• Note:– The chi square test does not prove that a

hypothesis is correct• It evaluates whether or not the data and the hypothesis

have a good fit

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display

Two flies with different traits are bred together

Out of 352 offspring 193 straight wings, gray bodies 69 straight wings, ebony bodies 64 curved wings, gray bodies 26 curved wings, ebony bodies


According to our hypothesis, there should be a 9:3:3:1 ratio of fly offspring

Phenotype Expected probability

Expected number

straight wings, gray bodies

9/16 9/16 X 352 = 198

straight wings, ebony bodies

3/16 3/16 X 352 = 66

curved wings, gray bodies

3/16 3/16 X 352 = 66

curved wings, ebony bodies

1/16 1/16 X 352 = 22


Apply the chi2 formula


Interpret the chi square value The calculated chi square value can be used

to obtain probabilities, or P values, from a chi square table

These probabilities allow us to determine the likelihood that the observed deviations are due to random chance alone

If the chi square value results in a probability that is less than 0.05 (ie: less than 5%)

The hypothesis is rejected


Interpret the chi square value

Before we can use the chi square table, we have to determine the degrees of freedom (df)

The df is a measure of the number of categories that are independent of each other

df = n – 1 where n = total number of categories

In our experiment, there are four categories Therefore, df = 4 – 1 = 3


Interpret the chi square value With df = 3, the chi square value of 1.06 is

slightly greater than 1.005 (which corresponds to P= 0.80)

A P = 0.80 means that values equal to or greater than 1.005 are expected to occur 80% of the time based on random chance alone

Therefore, it is quite probable that the deviations between the observed and expected values in this experiment can be explained by random chance

Spreadsheet applications will compute chi2

Is the male:female ratio in the CNS different from the general population?

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


4 1711 146 7

12 172 136 213 21

birth month vs birth day

birth month vs birth day

1 3 5 7 9 110

5

10

15

20

25

30

R² = 0.00546238003477373

Birth Month

Bir

th D

ay

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


•To use R2 the data must be continually variable...


If R2 = 1 the data fits perfectly to a straight line

If R2 = 0 there is no correlation between the data

Samples vs populations

Samples vs populationsPopulation- everything or everyone about which information is soughtSample- a subset of a population (that is hopefully representative of the population)

population

sample

Population-

• U.S. census

• Dogs

• 1 – infinity

Sample-

• Travis county

• Poodles

• Prime numbers

Why use a sample instead of a population?


•Logistics


•Logistics

•Cost


•Logistics

•Cost

•Time

Samples:

Random- each member of population has an equal chance of being part of the sample.

or

Representative- ensuring that certain parameters of your sample match the population.

Replicates:

Technical vs Experimental

Technical replicate- one treatment is divided into multiple samples.

Experimental replicate- different, replicate, treatments are done to different samples.

Testing blood sugar levels after eating a Snickers:


Divide a participants blood into 3 samples and test blood sugar in each sample.

Technical or Experimental replicate?


Test 3 different people.



Test the same person on 3 different days.


What sample size do you need?


It depends on the error you expect.

To determine an appropriate sample size, you need to estimate a few parameters.•Means•Standard Deviation

•Power: The probability that an experiment will have a significant (positive) result, that is have a p-value of less than the specified significance level (usually 5%).

This calculator will help you determine the appropriate sample size:

http://www.stat.ubc.ca/~rollin/stats/ssize/n2.html


It depends on the error you expect.

(So it is impossible to predict with 100% accuracy before the experiment is carried out.)

Next lecture we will finish talking about setting appropriate sample sizes.

Inquiry 1 written AND oral reports due Th 9/24 or M 9/28.

Documents

Transcript of Inquiry 1 written AND oral reports due Th 9/24 or M 9/28.