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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
Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display
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
Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display
Apply the chi2 formula
Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display
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
Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display
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
1.06
Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display
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?
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 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
What about relating 2 variables?
•To use R2 the data must be continually variable...
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
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?
Why use a sample instead of a population?
•Logistics
Why use a sample instead of a population?
•Logistics
•Cost
Why use a sample instead of a population?
•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:
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?
Testing blood sugar levels after eating a Snickers:
Test 3 different people.
Technical or Experimental replicate?
Testing blood sugar levels after eating a Snickers:
Test the same person on 3 different days.
Technical or Experimental replicate?
What sample size do you need?
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
What sample size do you need?
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.
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