Genetics and Statistics
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A Tale of Two Hypotheses
Why Statistics Matter… “The Quicker Picker Upper”
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Your 6th grade brother is doing a project for the science fair. He decides he wants to compare the absorbances of different brands of paper towels. He thinks the premium brand (Bounty) will absorb more.
What is the hypothesis?
How would you set up this experiment?
What is the independent variable and the dependent variables?
How will you collect data?
Based on the data, what is your conclusion?
How different are these numbers? Are they different enough? To find out - we’ll learn how to use statistics!
Bounty Great Value Sparkle Lab
Consider this story....
Two tigers at a zoo are bred together and they have four cubs.
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Two of the four cubs are white (leucistic) tigers. Based on that, Kristin hypothesizes that both of the parents must be carrying a recessive gene for albinism. The cross would look like:
A a x A a
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Who fell into the bleach?
At least they have a future in the circus.....
Don't hate me because I'm beautiful!
If Kristin's hypothesis is accurate the punnett square would look like…
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| A | a |
A | | |
a | | |
Your friend, Emily is unconvinced.
If your hypothesis is correct, then only ONE of the four cubs should be an albino.
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But isn't 1/4 pretty close to 2/4 ...maybe the difference is just due to chance....
Once I flipped a coin four times I got heads 3 times. Sometimes it just happens that way. Maybe you just got lucky and got an extra white kitten.
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The only way to solve this problem and the argument is to do a statistical analysis.
We call this type of analysis a CHI SQUARE
The purpose is to determine whether the results are statistically significant.
What are the odds that your tigers are Aa x Aa?
Are the results likely due to random chance?
Or could other factors be at work here?
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Here's how to do a chi square.
Summed for all classes means that you are looking at all the traits you observed. In this case, orange and white.
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I do not like math!
To apply the formula, plug in your "observed" and "expected" numbers....this will give you
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= 1.33
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To determine if this number is good or not, you must look at a chi square chart.
"Degrees of freedom" is one less than the original number of classes ovserved, which was 2 (orange & white)
So we will look at the first row (DoF = 1)
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1.33 is between the 20% and 30% columns
Basically this means that the difference you observed between orange and white cubs can be expected to occur more than 20% of the time, just due to chance. Anything lower than 5% suggests the the differences are probably due to something other than chance.
Results are always better with a large sample size.
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If you find that you have a "poor fit", then you should reject your hypothesis.
p value = the probability that the difference between the observed and the expected values could be due to chance.
a statistical hypothesis test that determines if observed sample data matches an expected theoretical distribution. It measures how well a model fits data by comparing observed frequencies with expected frequencies
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Emily thinks she gets it now. So she looks at another case. She breeds two black mice together and finds that over the course of 3 years, the parents produce 230 brown mice, and 710 black mice. She hypothesizes that the parents are Bb (heterozygous). Bb x Bb
Poor fit
| Observed | Expected |
Black | 710 | 705 |
Brown | 230 | 235 |
Total | 940 | |
A chart can make this easier.
(710-705) 2 / 705 = .035
(230 - 235) 2 / 235 = .106
X2 = .141
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H0: There will be no difference in the observed and expected values other than those due to random chance.
Your chi square value supports this (good fit), then you fail to reject the H0 .
It’s either reject (poor fit), or fail to reject (good fit).
HYPOTHESIS HA and the NULL HYPOTHESIS H0
Online Chi Square Calculator at http://www.graphpad.com/quickcalcs/chisquared1.cfm
-- just plug in the observed and expected values
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Practice with Cards
Use a deck of cards to model chi square analysis.
It is -expected- that you have half black and half red cards in a deck.
Draw 10 cards at random and determine the x2 value.
Do you support or reject the hypothesis that half the cards are black and half are red?
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| Observed | Expected |
Black | | |
Red | | |
Total | | |
Degrees of freedom =
Chi Square =
Support or Reject?