Students
- Get
-handout - Chi-square statistical
-Lab notebooks
-Get a 4 fcn calculator from the counter….if needed
-Sickle cell video worksheet – Q1 – 10 due Monday
-Cell phones in bin…off or muted…please & thank you
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
Phenotype Genotype # Observed Expected (o – e)
Green
GG or Gg
72
63
9
Albino
gg
12
21
-9
84
84
Total =
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.
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
(o – e)2
=Σ
e
o = observed
e = expected
Σ = sum of values
Table 7.4
expected (e) (o – e) (o – e)2 (o – e)2
e
Phenotype
observed (o)
Green
72
63
9
White
12
21
-9
Χ2
2
(o
–
e)
=Σ
=
e
Table 7.4
expected (e) (o – e) (o – e)2 (o – e)2
e
Phenotype
observed (o)
Green
72
63
9
81
1.29
White
12
21
-9
81
3.86
Χ2
2
(o
–
e)
=Σ
= 5.15
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.
Critical Values of the Chi-Square Distribution
Degrees of Freedom (df)
Probability (p)
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
1. 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
Your turn to calculate Chi-square
1. Complete “Color of Candy”
2. 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
5. Transfer your answers to Table 2 & calculate chi-square
6. Omit #3 of “Procedure”
7. Complete ALL questions on both sheets & staple into Lab Notebook