Inquiry 1 written AND oral reports
due 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
More stats... Chi2, R2, and sample size
http://mathworld.wolfram.com/Chi-SquaredDistribution.html
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
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
Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display
1.06

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
Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display
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.
birth month vs birth day
4
11
6
12
2
6
3
17
14
7
17
13
21
21
birth month vs birth day
30
R² = 0.01
25
Birth Day
20
15
10
5
0
1
3
5
7
Birth Month
9
11
Protein quantity vs absorbance
Bradford Assay 3-7-05
0.160
2
R = 0.9917
0.140
0.120
0.100
0.080
OD595
0.060
0.040
0.020
0.000
0
0.5
1
1.5
ug protein
2
2.5
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 populations
Population- everything or everyone about
which information is sought
Sample- a subset of a population (that is
hopefully representative of the population)
population
sample
Population-
Sample-
• U.S. census
• Travis county
• Dogs
• Poodles
• 1 – infinity
• 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.