Last saved by: El Toro High School

Statistical Analysis:

	Probability & Genetics
Genetics & Probability
•	Mendel’s laws:
•	segregation 
•	independent assortment 
	reflect same laws of probability that apply to tossing coins or rolling dice
Probability & genetics
•	Calculating probability of making a specific gamete is just like calculating the probability in flipping a coin
•	probability of tossing heads? 50%
•	probability making a P gamete…
Probability & genetics
•	Outcome of 1 toss has no impact on the outcome of the next toss
•	probability of tossing heads each time?
•	probability making a P gamete each time?

Calculating probability
Pp   x   Pp
Calculating dihybrid probability
•	Rule of multiplication also applies to dihybrid crosses
•	heterozygous parents — YyRr
•	probability of producing yyrr?
•	probability of producing y gamete = 1/2
•	probability of producing r gamete = 1/2
•	probability of producing yr gamete = 
1/2 x 1/2 = 1/4
•	probability of producing a yyrr offspring =
1/4 x 1/4 = 1/16
The Chi-Square (X^2) Test is used to examine the difference between an actual sample and a hypothetical sample that would be expected due to chance. 
Using Chi-Square, it is possible to discern whether experimental results are valid, or whether they are probably due to chance alone.
The Chi-Square test compares two rival hypotheses (the null hypothesis and an alternative hypothesis) to see which hypothesis is best supported by the data.

Observed and Expected Results
•	Observed results are what you actually observed in your experiment.

•	Expected results are a theoretical prediction of what the data would look like if the experimental results are due only to chance.

How do you get expected results?
•	If you are working with a genetics problem, then use the Punnett square ratio as your expected result. 
•	(null hypothesis)
•	If you are working with a another type of problem, use probability.

Obtaining the X^2 value:
Example:   We flip a coin 200 times to determine if the coin is fair.
H0:  There is no statistically significant difference between our coin flips and what we would expect by chance.   (The coin is fair.)
HA: There is a statistically significant difference between our coin flips and what we would expect by chance.  (The coin is not fair.)

Critical Value Table
Now you need to look up your X 2 value in a critical value table to see if it is over a certain critical value.  

Typically, in biology we use the p = 0.05 confidence interval. 
	The p-value is a predetermined choice of how certain we are.  The smaller 	the p-value, the more confidence we can claim.  p = 0.05 means that we can 	claim 95% confidence.

Calculating Degrees of Freedom
	Degrees of Freedom = # classes -1
In our example experiment, the classes were heads and tails (2 classes).
Degrees of Freedom in our experiment would be: DF = 2 - 1 = 1

Accept or Reject the Null Hypothesis
•	If the X 2  value is less than the critical value, accept the null hypothesis. (The difference is not statistically significant.)
•	If the X 2  value is greater than or equal to the critical value, reject the null hypothesis.  (The difference is statistically significant.)

In our example, the X ^2  value we calculated was 1.28, which is less than the critical value of 3.84.  Therefore:
•	We accept our null hypothesis.
•	We reject our alternative hypothesis .
•	We determine that our coin is fair.