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
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
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
Step 1 On your copy of the statistics table, calculate the mean of column 1 and 4. = 14 = 40
Step 2 Calculate the standard deviation for group x and group y σ x = 2.36 σ y = 8.73
Step 3 Calculate the standard error for group x and y SE of x= SE of y= 2.910
Step 4 Calculate t using the formula
T= The value of t can be either positive or negative so we can ignore the sign.
Calculating degrees of freedom Calculate degrees of freedom using the number of data for each set. [(n x -1)+(n y -1)] [(9-1)+(9-1)] Degrees of freedom = 16
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= Do we accept or reject the NH?
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)
One and two-tailed tests
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
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
Your turn… Complete tasks on worksheet A 5 using the student t-test Answers: Degrees of freedom – 22 T =