A6. The Chi-Squared Test

Question 1

Formula

Answer 1

Question 2

Example

Answer 2

Question 3

Maths example

Answer 3

Question 4

Critical Value example

Answer 4

Question 5

Comparing the x² value to the critical value
If your x^2 value is __________than (or equal to) the critical value, then there is a significant difference between the observed and expected results i.e. something other than chance is causing the difference. This means the null hypothesis can be rejected. If your x^2 value is ___________than the critical value, then there is no significant difference between the observed and expected results — the null hypothesis can’t be rejected.

Answer 5

Comparing the x² value to the critical value
your x2 value is larger than (or equal to) the critical value, then there is a significant difference between the observed and expected results i.e. something other than chance is causing the difference. This means the null hypothesis can be rejected. If your x2 value is smaller than the critical value, then there is no significant difference between the observed and expected results — the null hypothesis can’t be rejected.

Question 6

Possible outcomes of a chi-squared test

Answer 6

x² value > critical value = reject the null hypothesis

x² value <critical value = fail to reject the null hypothesis

Question 7

Comparing the x² value to the critical value example

Answer 7

The chi-squared value of 2.7 is smaller than the critical value of 3.84. This means that there’s no significant difference between the observed and expected results. We’ve failed to reject the null hypothesis — so the theory that wing length in fruit flies is controlled by monohybrid inheritance is supported.

Question 8

Degrees of freedom is…

Answer 8

n-1

n = number of participants