Did Mendel fake is data?
• Do a quick internet search and can you find
opinions that support or reject this point of
view.
• Does it matter? Should it matter?
Does the data fit?
• Problem: Does experimentally determined data
fits the results expected from theory (i.e.
Mendel’s laws as expressed in the Punnett square).
• Example:
– Expected 75% to 25% ratio
– Does an observed result of
78 to 22 fit?? 85 to 15?
The Chi Square Test
• A “Goodness of fit” test
• A statistical way to “Reject the Null
Hypothesis”
Null Hypothesis
A way to state expected outcome
• Example 1: Hybrid parents will produce a 3:1
genotypic ration (predicted values based on
punnett square analysis)
• Example 2: Flipping a coin should land on
heads 50% of the time.
**Chi-square is used to REJECT a hypothesis
not to PROVE it.
Coin Data
• If this coin is fair…then we would expect
the chi-square analysis to show us the
results are due only to chance and not due to
some other hypothesis.
• Let’s look how coin data either:
– Rejects a hypothesis that a coin is fair or
– Suggests that the hypothesis that a coin is fair is
likely.
The Formula
(obs - exp)
C =å
exp
2
2
Example
• Expected results of a coin toss (the Null
Hypothesis): 50 heads , 50 tails
• Observed results: 55 heads, 45 tails
• Now it's just a matter of plugging into the formula:
2 = (55 - 50)2 / 50 + (45 - 502 / 50
= (5)2 /50 + (-5)2 / 100
= 25 / 50 + 25 / 50
= 0.50 + 0.50
= 1.0
• This is our chi-square value: now we need to see
what it means and how to use it.
Chi-Square Table
Using the Table
• In our example of 55 heads to 45 tails, we
calculated a chi-square value of 1.0, with 1 degree
of freedom.
• Looking at the table, 1 d.f. is the first row, and p =
0.05 is the sixth column. Here we find the critical
chi-square value, 3.841.
• Since our calculated chi-square, 1.0, is less than
the critical value, 3.841, we “fail to reject” the
null hypothesis. Thus, an observed ratio of 55
heads to 45 tails is a good fit to 50:50 ratio.
Degrees of Freedom
• A critical factor in using the chi-square test is the
“degrees of freedom”, which is essentially the
number of independent random variables involved.
• Degrees of freedom is simply the number of
classes of offspring minus 1.
• For our example, there are 2 classes of offspring:
heads and tails. Thus, degrees of freedom (d.f.) =
2 -1 = 1.
Critical Chi-Square
• Critical values for chi-square are found on tables,
sorted by degrees of freedom and probability
levels. Science uses p = 0.05.
• If your calculated chi-square value is greater than
the critical value from the table, you “reject the
null hypothesis”.
• If your chi-square value is less than the critical
value, you “fail to reject” the null hypothesis (that
is, you accept that your genetic theory about the
expected ratio is correct).
Corn and Chi-Square for Real
• Question: Is this corn the result
of the following dihybrid cross:
PpSs X PpSs
-First do the Punnett Square
-Find the expected outcomes
-Compare actual to expected by
doing chi square. Share your
results with a nearby group.
Lab Notebook Expectations
Introduction: How does the dihybrid cross show
Mendel’s Law of Independent Assortment?
Identify the traits you will be looking at in the
corn.
Hypothesis: What do you expect from crossing
two heterozygotes—may show a Punnett
Square.
Methods: How did you count a random sample
of the corn? What does each kernel on the corn
represent?
Data and analysis:
-Chi-square analysis for your data.
-Chi-square analysis for another group’s data.
-Trend related to each chi-square analysis.
Conclusion:
-Explain how the chi-square analysis can confirm
Mendel’s Law of Independent Assortment.
-Discuss what genetic linkage is and why this would
cause you to reject the null hypothesis shown in a
dihybrid cross.
Practice
How can Chisquare be used to
analyze these
results?
Back to problem set #21
• Go back to the
genetic
recombination
problem…do a chisquare analysis as if
it was not linkage.
What does your
analysis tell you?
Do Mendel’s laws always apply?
• Dominance
• Segregation
• Independent Assortment
Questioning Mendel’s Peas
• If all his data made sense, what can we say
about the genes he looked at: were they on
the same chromosome or on different
chromosomes?
Does the location of a gene affect
inheritance patterns?
A quick review of genetic
material….
•Chromosome
•Chromatin
•DNA
•Gene
•Nucleotide
•Nuclear proteins?
Genes are
linked to
chromosomes
Crossing-over
• Cross-overs occur when tetrads form during
meiosis
• Recombination frequencies allow for the
creation of chromosome maps
Recombination due to cross-overs
Recombination frequencies
Chromosome map
Sex-link chromosomes
• Genes located on the X or Y chromosomes
are linked to gender
• What observation provide hints that a gene
is sex linked?
Example: Eye Color in Fruit Flies