2 Student 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
4 Worked 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
5 Worked 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
6 Step 1On 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
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 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?
13 ResultsAs 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’)
15 One-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
16 Two-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
17 Your turn… Complete tasks on worksheet A5 using the student t-test Answers:Degrees of freedom – 22T =