2 X 2 Chi-Square Analysis
Chi-Square is a statistical test that can be used when looking at a single treatment (i.e. cross between green and albino
pea plants) or when comparing the results of two treatments (i.e. control vs. cells treated with caffeine). Lab 7 uses the
2X2 Chi-Square Analysis to compare various treatments. The following data set should be used for lab 7:
Root Tip
Treatment
Control
Interphase
460
43
Number of Cells
Metaphase
Ana/Telophase
Total
8
24
535
Lectin
417
117
51
41
626
1 mM caffeine
549
18
3
5
575
5 mM caffeine
449
11
2
7
469
10 mM
caffeine
100 mM
caffeine
330
9
3
0
342
Prophase
Cytotoxic------------------------------------------------------------
0
Class Example:
In the control treatment 86% of the cells where in interphase while 14% were in mitosis. In the 1mM caffeine treatment
95% of the cells were in interphase while 5% were in mitosis. Are the two treatments actually different or is this
difference due to chance? To find out conduct a 2X2 Chi-Square Analysis. First state the null hypothesis. The null
hypothesis (H0) is a hypothesis which the researcher tries to disprove, reject or nullify. Our null hypothesis is that the
control and the treatment are equal in their phase distributions (% of cells in interphase & % of cells in mitosis). If this
test tells us that the null hypothesis is not rejected, we can say that differences in our two groups (control vs. 1 mM
caffeine) are due to chance. If this tells us that the null hypothesis is rejected, then we can say the two groups are
statistically different from one another. In other words, 1mM caffeine impacts the cell cycle in a way that is different
from normal conditions.
Formula for Chi Square: 2 =  (o-e)2/e
Formula 2X2 degrees of Freedom: df = (# treatments – 1) ( #phase groups – 1)
Critical Value can be found using the Chi Square Critical Value Table:
Record data (from given data – or data that you may collect during an experiment) in a Table of Observed Values. The
table is set up as follows:
Control
Interphase
A
Mitosis
B
Total
A+B
Treatment
C
D
C+D
Total
A+C
B+D
A+B+C+D=N
Let’s practice comparing control to 1mM Caffeine from data on page 1.
Table of Observed Values (complete using data from 1st page Control vs 1mM Caffeine)
Interphase
Mitosis
Total
Control
A
B
A+B
Treatment
(1mM Caffeine)
C
D
C+D
A+C
B+D
A+B+C+D=N
Total
Use the values from your Table of Observed Values to calculate expected values. A Table of Expected Values is set up as
follows:
Group
Control
Treated
Interphase
(A + B) (A + C)
N
(C + D) (A + C)
N
Mitosis
(A + B) (B + D)
N
(C + D) (B + D)
N
Let’s practice using the Table of Observed Values.
Table of Expected Values (complete using you observed value data of Control vs. 1mM Caffeine)
Group
Control
Interphase
(A + B) (A + C)
N
Mitosis
(A + B) (B + D)
N
Treated
(C + D) (A + C)
N
(C + D) (B + D)
N
Now that we have observed and expected values we can use the Chi-Square Equation ( 2 =  (o-e)2/e ). Using your
calculated values either plug them into the Chi-Square Equation or use the table below. This table simply breaks the
equation down step by step to help you organize your calculations.
Group
Control
Interphase
Control Mitosis
Observed (o)
Expected (e)
o-e
(o-e)2
(o-e)2/e
Treated
Interphase
Treated Mitosis
Total of (o – e)2/e = X2
Once you calculate X2 value determine the degrees of freedom for your analysis. Use the following equation to do this
calculation: df = (# treatments – 1) ( #phase groups – 1)
Calculate the degrees of freedom for this comparison: df = ________________
After calculating the degrees of freedom find the critical value at p = 0.05 in the Chi-Square Critical Value table (1st page
of this packet or page S90 of lab manual). Critical Value = ________________
Last step – compare the critical value to the Chi-Square value. If X2 is greater than or equal to the critical value, the null
hypothesis is rejected. If the calculated X2 is less than the critical value, the null hypothesis is not rejected.
Reject H0 or not?
For Lab 7 part 2 use the data from the various treatments provided in this handout (1st page). In your lab notebook you
should record the following information:














State the Null Hypothesis comparing control and lectin data
Create a table of observed values comparing control and lectin
Create a table of expected values for control and lectin
Create a table of for calculation of Chi-Square Value
Record the degrees of freedom calculation
Record the critical value
State outcome of analysis – reject or not?
State the Null hypothesis comparing control and 5mM caffeine data
Create a table of observed values comparing control and 5mM caffeine
Create a table of expected values for control and 5mM caffeine
Create a table of for calculation of Chi-Square Value
Record the degrees of freedom calculation
Record the critical value
State outcome of analysis – reject or not?
*Note: ignore the “Using 84% I and 16% M” bullet from previous handout instructions