1. Naked mole rats are a burrowing rodent
native to parts of East Africa. They have a
complex social structure in which only one
female (the queen) and one to three males
reproduce, while the rest of the members of the colony function as workers.
Mammal ecologists suspected that they had an unusual male to female ratio. They counted the numbers of each sex in one colony.
Sex
 Number of animals
Female
 52
Male
 34

2. State the Null hypothesis
There is no difference in the numbers of male and female naked mole rats.
Which statistical test do we use to analyse the data?
Ratio of male to female naked mole rats.
Two categories, frequencies of each.

3. χ2 Chi Squared Test
Used to test if your results fit the pattern you expected.
Check if any differences seen between the predicted results and the actual results are due to chance (so don’t matter) or show a significant difference.

4. What to actually do... Step 1: Work out the expected results (E)
Step 2: Collect data from real situation (O)
Step 3: Work out the difference (O-E)
Step 4: Square these results, this gets rid of an negative values. (O-E)2
Step 5: Divide by the expected value ((O-E)2 /E)
Step 6: Add up all these values ∑ ((O-E)2 /E)
Step 7: Compare this result with the χ2 table.
Degrees of Freedom
P= 0.05 1
3.84 2
5.99 3
7.81 4
9.49 5
11.07 6
12.59 7
14.07 8
15.51 9
16.92 10
18.31
Degrees of freedom = classes -1
Probability above 0.05 results ok
Probability below 0.05 no significant differences

5. Remember – there were 52 females and 34 males
Calculate the expected results
Expected results = = 86 = 43
Remember – there were 52 females and 34 males
Calculate the chi-squared value
 Sex
 Observed
 Expected
 O - E
 (O – E)2
 (O – E)2/E
Female
 52 43 9 81
1.88
Male
 34
 TOTAL
3.76

6. What are the degrees of freedom?
DF = n – 1 = 2 – 1 = 1
Male and female
Compare the calculated value with the critical value
 Degrees of freedom
 Significance level
 5% (0.05)
2% (0.02)
1% (0.01)  1
 3.84
5.41
6.64  2
5.99
7.82
9.21

7. Our calculated value is 3.76
 Degrees of freedom
 Significance level
 5% (0.05)
2% (0.02)
1% (0.01)  1
 3.84
5.41
6.64  2
5.99
7.82
9.21
The critical value of Chi-squared at 5% significance and 1 degree of freedom is 3.84
Our calculated value is 3.76
The calculated value is smaller than the critical value at the 5% level of probability.
Make a conclusion
We can accept the null hypothesis because our X2 value is below 3.84, so there is not a significant difference between the observed and expected results at the 5% level of probability.
In doing this we are saying that the naked mole rates do not have a significantly larger female population in comparison with the male population.

8. Example taken from turn alteration in maggots EMPA (do maggots turn left or right in a chamber)