2Student T-testStudent t-tests are used when we are testing the difference between 2 samplesIt can only be used when using interval or ratio dataThe Null hypothesis is always that the 2 means are the sameThe alternative hypothesis is always that they are different, or that one is greater than the other
4Worked exampleA researcher wants to find out the difference between birth rates of more developed countries and less developed countriesWrite down the null hypothesis and the alternative hypothesis
5Worked exampleNull hypothesis: There is no difference between the mean birth rates of more and less developed countriesAlternative hypothesis: There is a difference between the mean birth rates of more and less developed countries
6Step 1On your copy of the statistics table, calculate the mean of column 1 and 4.= 14= 40
7Step 2 Calculate the standard deviation for group x and group y
8Step 3 Calculate the standard error for group x and y SE of x= 0.786 SE of y= 2.910
10The value of t can be either positive or negative so we can ignore the sign.
11Calculating 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
12Critical valuesLook up the critical values for 16 degrees of freedom on the tableThe critical value from the table for 0.05 (95%) is 2.12T= -8.26Do we accept or reject the NH?
13ResultsAs t(-8.625) is greater than the critical value (2.12) we can reject the NH and accept the AHIf t is smaller than the critical value, we have to accept the NH (‘There is no evidence to support the AH’)
15One-tailed testsWhen the hypothesis you wish to test is framed so that the direction is clearE.g. AH: Men are taller than womenSeparate table are used for critical valuesWe will only be using two-tailed tests
16Two-tailed testsFor when you are interested in whether a difference exists in any directionE.g. AH: Men are a different height from womenThe null hypothesis is the same for both tests
17Your turn… Complete tasks on worksheet A5 using the student t-test Answers:Degrees of freedom – 22T =