1. Genetic Statistics

2. Probability Probability is measured from 0 to 1
0 = event will not occur
1 = event will occur (100%)
% vs probability: 0.75 = 75%

3. Multiplication Rule
Multiplication rule: multiply probability of an event by the probability of the other event

4. Ex A: Coin Toss
What is the probability of flipping a coin and it landing on ‘tails’?
What is the probability of flipping a coin twice and getting 2 tails? 3 tails?

5. Addition rule
Addition rule: probability that any one of two or more mutually exclusive vents will occur is calculated by adding their individual probabilities

6. Ex B. Coin Toss
What is the probability of tossing 1 head and 1 tail in that order?
What is the probability of tossing 1 head and 1 tail in ANY order?

7. Ex C. Gender What is the probability of getting girl? A boy?
What is the probability of getting 2 girls? 2 boys?
What is the probability of getting 1 boy then 1 girl?
What is the probability of getting 3 girls?
What is the probability of boy, then boy, then girl?
What is the probability of boy, girl, then boy?
What is the probability of getting 2 boys and 1 girl in any order?

9. Ex D. Hair color
Bb x Bb is crossed. What is the probability of getting a brown haired person? Blond?
What is the probability of getting 2 brown haired kids?
What is the probability of getting 2 blond haired kids?
What is the probability of getting first a blond then a brown haired kid?
What is the probability of getting first a brown then a blond haired kid?
What is the probability of getting 1 blond and 1 brown haired kid in any order?

11. Ex E. Hair color
Bb x bb is crossed. What is the probability of getting a brown haired person? Blond?
What is the probability of getting 2 brown haired kids?
What is the probability of getting 2 blond haired kids?
What is the probability of getting first a blond then a brown haired kid?
What is the probability of getting first a brown then a blond haired kid?
What is the probability of getting 1 blond and 1 brown haired kid in any order?

13. T= tall
t= short
R = round
r = wrinkled
A = axial
a = terminal

14. Ex F: Dihybrid Tt x Tt. What is the probability of
T= tall
t= short
R = round
r = wrinkled
Tt x Tt. What is the probability of
tall?
Short?
Rr x Rr. What is the probability of
round?
wrinkled?
TtRr x TtRr. What is the probability of
tall and round?
Tall and wrinkled?
Short and round?
Short and wrinkled?

15. Ex G: Dihybrid Tt x tt What is the probability of
T= tall
t= short
R = round
r = wrinkled
Tt x tt What is the probability of
tall?
Short?
Rr x Rr. What is the probability of
round?
wrinkled?
TtRr x ttRr. What is the probability of
tall and round?
Tall and wrinkled?
Short and round?
Short and wrinkled?

16. Ex H: Dihybrid Tt x tt What is the probability of
T= tall
t= short
R = round
r = wrinkled
Tt x tt What is the probability of
tall?
Short?
Rr x rr. What is the probability of
round?
wrinkled?
Ttrr x ttRr. What is the probability of
tall and round?
Tall and wrinkled?
Short and round?
Short and wrinkled?

17. Ex I: Dihybrid Tt x Tt What is the probability of tall? Short?
T= tall
t= short
R = round
r = wrinkled
A = axial
a = terminal
Ex I: Dihybrid
Tt x Tt What is the probability of tall? Short?
Rr x Rr. What is the probability of round? wrinkled?
Aa x Aa. What is the probability of Axial? Terminal?
TtRrAa x TtRrAa. What is the probability of
Tall, round, axial?
Tall, round, terminal?
Tall, wrinkled, axial?
Tall, wrinkled terminal?
Short round, axial?

18. Ex J: Dihybrid Tt x tt What is the probability of tall? Short?
T= tall
t= short
R = round
r = wrinkled
A = axial
a = terminal
Ex J: Dihybrid
Tt x tt What is the probability of tall? Short?
Rr x Rr. What is the probability of round? wrinkled?
Aa x aa. What is the probability of Axial? Terminal?
TtRraa x ttRrAa. What is the probability of
Tall, round, axial?
Tall, round, terminal?
Tall, wrinkled, axial?
Tall, wrinkled terminal?
Short round, axial?

19. Ex K: Dihybrid Ttrraa x ttRrAa. What is the probability of
T= tall
t= short
R = round
r = wrinkled
A = axial
a = terminal
Ex K: Dihybrid
Ttrraa x ttRrAa. What is the probability of
Tall, round, axial?
Tall, round, terminal?
Tall, wrinkled, axial?
Tall, wrinkled terminal?
Short, round, axial?
Short, wrinkled, terminal

21. Chi-squared analysis Chi-squared analysis
Data collected rarely conform exactly to prediction, so its important to determine if the deviation between expected values (based on the hypothesis) and the actual results (based on your experiment) are significant enough to discredit the original hypothesis.
Chi-Squared analysis: (χ2) purpose is to determine if the actual results are different enough from expected results to suggest that the experimental hypothesis is not correct.

22. Null Hypothesis (H0): says that:
Want evidence to show your null hypothesis is incorrect. If null is incorrect, it means there IS a difference.
Experimental hypothesis (H1): says there will be a difference between the experimental group and control group
Null Hypothesis (H0): says that:
The treatment will have no effect
There will be no difference between the treatment and control
No difference between observed and expected values
Ex.
Experimental hypothesis: Acid rain is killing white pine trees.
Null hypothesis:
Acid rain is not killing white pine trees
There will be no difference in white pine trees in normal water and acid rain.

23. Ex L. In hospital A, 6 babies were boys, 4 were girls.
Data Table 1
boys
girls
Total
Observed
Expected
(Observed – expected) expected
χ2= _________

24. P-value
Probability table: p-value: Shows the percentage of time that your data was due to random chance. Ranges from 0 to 1. values over 0.05 mean that your data could have occurred due to chance.
A p-value less than or equal to 0.05:
reject null hypothesis
Experimental hypothesis is supported
Was a difference in treatment and control
Significant difference between treatment and control
Significant difference between observed and expected values

25. A p-value greater than 0.05:
Accept null hypothesis
Experimental hypothesis is NOT supported
No effect or difference in treatment and control
No significant difference between treatment and control
The results are due to chance
No difference in observed and expected values

26. To calculate p-value you need:
Chi-squared value
Degrees of freedom reflect the number of independent and dependent variables in your experiment:
df= number of categories - 1

27. Accept the null hypothesis←
Not significant
→ Reject the null hypothesis, significant
Degrees of Freedom
Probability
0.90
0.50
0.25
0.10
0.05
0.01 1
0.016
0.46
1.32
2.71
3.84
6.64 2
0.21
1.39
2.77
4.61
5.99
9.21 3
0.58
2.37
4.11
6.25
7.82
11.35 4
1.06
3.36
5.39
7.78
9.49
13.28 5
1.61
4.35
6.63
9.24
11.07
15.09
What is the p-value for a χ2 of 2.71 and 1 df? Accept or reject null hypothesis?
What is the p-value for a χ2 of 11.4 and 4 df? Accept or reject the null hypothesis?

28. Ex. In hospital B, 43 babies were boys, 37 were girls.
Df =__________ P-value= _________ Null hypothesis: Result:
Data Table 1
boys
girls
Total
Observed
Expected
(Observed – expected) expected
χ2= _________

29. Ex. Bb x Bb What percent will be brown haired?
What percent will be blond haired?
If 50 babies were born:
How many should be brown haired?
How many blond haired?
If 75 babies were born:

30. Ex. 50 kids were born, 30 had brown hair, 20 had blond hair
Ex. 50 kids were born, 30 had brown hair, 20 had blond hair. Was this a fair example?
Df =__________ P-value= _________ Null hypothesis: Result:
Data Table 1
brown
blond
Total
Observed
Expected
(Observed – expected) expected
χ2= _________

31. Ex. 50 kids were born, 30 had brown hair, 20 had blond hair
Ex. 50 kids were born, 30 had brown hair, 20 had blond hair. Was this a fair example of Bb x Bb?
Df =__________ P-value= _________ Null hypothesis: Result:
Data Table 1
brown
blond
Total
Observed
Expected
(Observed – expected) expected
χ2= _________

32. Ex. 50 kids were born, 30 had brown hair, 20 had blond hair
Ex. 50 kids were born, 30 had brown hair, 20 had blond hair. Was this a fair example of Bb x bb?
Df =__________ P-value= _________ Null hypothesis: Result:
Data Table 1
brown
blond
Total
Observed
Expected
(Observed – expected) expected
χ2= _________