1. Students
Get handout - Chi-square statistical
Genetics Problems – due tomorrow
Sickle cell video worksheet – due Friday
Tomorrow – Genetics of corn
Make-up – Friday at 7AM or 3:15PM
PSAT skipping #s??
Cell phones in bin…off or muted…please & thank you

2. Chi-square (Χ2) Statistical Analysis
Used to determine if observed data are close enough to expected/predicted data
Example
P: Gg x Gg expect 3:1 G = green
g = albino
Table 7.3 12 gg
Albino 72
GG or Gg
Green
(o – e)
Expected
# Observed
Genotype
Phenotype
Total = 63 21 84 9 -9
There is a small difference between observed & expected.
Is it close enough to say this is a 3:1 or is there too much variance????
We use the Chi-square test to determine this.

3. Chi-square (Χ2)
Used to determine if the observed data fall within acceptable limits & tests the
validity of a null hypothesis
Null hypothesis – states there is NO statistically significant difference between
the observed & expected values
You MUST write this down EVERY time you do a X2 test!
Χ2 = Σ
(o – e)2 e
o = observed
e = expected
Σ = sum of values

4. Χ2 = Σ Table 7.4 Phenotype observed (o) expected (e) (o – e) (o – e)2
Green 72 63 9
White 12 21 -9 81
1.29 81
3.86
Χ2 = Σ
(o – e)2 e =
We now compare our calculated Χ2 value with the Critical Values Table
Remember: null hypothesis says there is NO significant difference between
the observed & expected data.

5. Degrees of Freedom (df)
Critical Values of the Chi-Square Distribution
Probability (p)
Degrees of Freedom (df) 1 2 3 4 5
0.05
3.84
5.99
7.82
9.49
11.1
0.01
6.64
9.21
11.3
13.2
15.1
0.001
10.8
13.8
16.3
18.5
20.5
df = categories – 1 categories = phenotypes
= 2 – 1
df = 1
2. p value
p = 0.05 for science
3. Compare calculated Χ2 to table
5.15 > 3.84
REJECT null hypothesis…..observed data are not the same as expected
Observed data are not a 3:1

6. Your turn to calculate Chi-square
Complete “Color of Candy”
Guesstimate the %ages of each color & fill in “Percentage Expected”
must = 100%
3. Now complete “Number Observed” (o)
4. Now complete last column (e)…do NOT round, keep the decimal
Transfer your answers to Table 2 & calculate chi-square
Omit #3 of “Procedure”
Complete ALL questions on both sheets & staple into Lab Notebook
In future chi-square problems…
you may find it easier to work across the row instead of column