Transcript Chi Square Analysis

Chi Square Analysis
• The chi square analysis allows you to
use statistics to determine if your data
“good” or not.
• In our fruit fly labs we are using laws of
probability to determine possible
outcomes for genetic crosses.
• How will we know if our fruit fly data is
“good”?
• The following formula is used
If your hypothesis is true, then the squared deviations
between the observed and expected values will most
likely be small and so will the test statistic.
If your hypothesis is false, then the squared
deviations between the observed and expected
values will most likely be large and so will the test
statistic.
• The test statistic is compared to a
theoretical probability distribution
• In order to use this distribution properly
you need to determine the degrees of
freedom
• Degrees of freedom is the number of
phenotypic possibilities in your cross
minus one.
• If the level of significance read from the
table is greater than .05 or 5% then your
hypothesis is accepted and the data is
useful
• The hypothesis is termed the null
hypothesis which states that there is no
substantial statistical deviation between
observed and expected data.
Let’s look at a fruit fly cross
x
Black body, eyeless
F1: all wild
wild
F1 x F1
5610
1881
622
1896
Analysis of the results
• Once the numbers are in, you have to
determine the cross that you were
using.
• What is the expected outcome of this
cross?
• 9/16 wild type: 3/16 normal body
eyeless: 3/16 black body wild eyes: 1/16
black body eyeless.
Now Conduct the Analysis:
Phenotype
Observed
Wild
5610
Eyeless
1881
Black body
1896
Eyeless, black body
622
Total
10009
Hypothesis
To compute the hypothesis value take
10009/16 = 626
Now Conduct the Analysis:
Phenotype
Observed
Hypothesis
Wild
5610
5634
Eyeless
1881
1878
Black body
1896
1878
Eyeless, black body
622
626
Total
10009
To compute the hypothesis value take
10009/16 = 626
• Using the chi square formula compute the chi
square total for this cross:
• (5610 - 5634)2/ 5634 = .07
• (1881 - 1877)2/ 1877 = .01
• (1896 - 1877 )2/ 1877 = .20
• (622 - 626) 2/ 626 = .02
•  2= .30
• How many degrees of freedom?
• Using the chi square formula compute the chi
square total for this cross:
• (5610 - 5634)2/ 5634 = .07
• (1881 - 1877)2/ 1877 = .01
• (1896 - 1877 )2/ 1877 = .20
• (622 - 626) 2/ 626 = .02
•  2= .30
• How many degrees of freedom? 3
• Looking this statistic up on the chi
square distribution table tells us the
following:
• the P value read off the table places our
chi square number of .30 close to .95
or 95%
• This means that 95% of the time when
our observed data is this close to our
expected data, this deviation is due to
random chance.
• We therefore accept our null
hypothesis.
• What is the critical value at which we
would reject the null hypothesis?
• For three degrees of freedom this value
for our chi square is > 7.815
• What if our chi square value was 8.0
with 4 degrees of freedom, do we
accept or reject the null hypothesis?
• Accept, since the critical value is >9.48
with 4 degrees of freedom.
• How can we use the chi square test in a
different sort of lab?
• If we were testing the effect of light on
plant growth, how could the chi square
analysis be used?
• In this case our experimental group is
plants grown in the dark and the control
plants are grown in the light.
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What would your expected data be?
Control plants grown in the light.
What would your observed group be?
Plants grown in the dark.
Do you expect to accept or reject the
null hypothesis?
• reject