1. Advanced Higher Geography
Section 3 – Student t-test

2. Student T-test
Student t-tests are used when we are testing the difference between 2 samples
It can only be used when using interval or ratio data
The Null hypothesis is always that the 2 means are the same
The alternative hypothesis is always that they are different, or that one is greater than the other

3. Formula

4. Worked example
A researcher wants to find out the difference between birth rates of more developed countries and less developed countries
Write down the null hypothesis and the alternative hypothesis

5. Worked example
Null hypothesis: There is no difference between the mean birth rates of more and less developed countries
Alternative hypothesis: There is a difference between the mean birth rates of more and less developed countries

6. Step 1
On your copy of the statistics table, calculate the mean of column 1 and 4.
= 14
= 40

7. Step 2 Calculate the standard deviation for group x and group y

8. Step 3 Calculate the standard error for group x and y SE of x= 0.786
SE of y= 2.910

9. Step 4
Calculate t using the formula

10. The value of t can be either positive or negative so we can ignore the sign.

11. Calculating degrees of freedom
Calculate degrees of freedom using the number of data for each set.
[(nx-1)+(ny-1)]
[(9-1)+(9-1)]
Degrees of freedom = 16

12. Critical values
Look up the critical values for 16 degrees of freedom on the table
The critical value from the table for 0.05 (95%) is 2.12
T= -8.26
Do we accept or reject the NH?

13. Results
As t(-8.625) is greater than the critical value (2.12) we can reject the NH and accept the AH
If t is smaller than the critical value, we have to accept the NH (‘There is no evidence to support the AH’)

14. One and two-tailed tests

15. One-tailed tests
When the hypothesis you wish to test is framed so that the direction is clear
E.g. AH: Men are taller than women
Separate table are used for critical values
We will only be using two-tailed tests

16. Two-tailed tests
For when you are interested in whether a difference exists in any direction
E.g. AH: Men are a different height from women
The null hypothesis is the same for both tests

17. Your turn… Complete tasks on worksheet A5 using the student t-test
Answers:
Degrees of freedom – 22
T =