What methods did we employ in this experiment?

On each trial you rated the likeability of an individual based on a photo of their face. Many different factors contribute to likeability of a face, and one major effect is that people tend to give higher likeability ratings to people who are roughly the same age as themselves. In this study you saw faces from 32 young (ages 18-32) and 32 old (ages 50 and older) persons. The faces in each set were also half male and half female, but this is not a variable of interest in the current study.

The independent variable is the age of the face. The dependent variable is the likeability rating, with 0 indicating not likeable at all and 100 indicating very likeable. We will use a two-sample t-test to explore whether you show higher likeability ratings for the young faces than for the older faces.

What do we predict participants will do? Why?

Most college students are in the young age group, so we expect that they will give higher likeability ratings for the young faces than for the old faces. If you happen to be an older student, you might also show a bias toward higher likeability ratings for young faces, but it will not be as strong as for younger students.

The statistical analysis below guides you through a two-sample t-test. The null hypothesis is that the mean likeability rating is the same for young and old faces

H0: young -old = 0,

and the alternative hypothesis is that the mean likeability rating is different for young faces and old faces

Ha: young -old 0.

We will use = 0.05.

Formulas

To calculate the t test statistic, you need to first calculate the mean and variance of scores for each condition. This is done in the first four questions. Next, you need to pool the variances using the following formula

s2=(n11)s21+(n21)s22n1+n22,

where n1 and n2 are the sample sizes (number of trials) for the young and old face conditions. s21 and s22 are the variances for the young and old face conditions.

The pooled variance is used to calculate the standard error of the difference of means

sX1X2=s2(1n1+1n2).

Now compute the t test statistic

t=X1X2sX1X2,

which has degrees of freedom df=n1 + n2 -2.

Finally, you can calculate the p-value for the test statistic. This is most easily done with an online calculator. Be sure to use a two-tailed test.

Mean likeability for young faces:

(The difference between your answer and the correct value must be less than 0.01.)

Variance of the likeability for the young faces:

(The difference between your answer and the correct value must be less than 0.01.)

Mean likeability for old faces:

(The difference between your answer and the correct value must be less than 0.01.)

Variance of the likeability for the old faces:

(The difference between your answer and the correct value must be less than 0.01.)

Pooled variance:

(The difference between your answer and the correct value must be less than 0.01.)

Standard error of the difference of means:

(The difference between your answer and the correct value must be less than 0.01.)

t test statistic:

(The difference between your answer and the correct value must be less than 0.01.)

degrees of freedom:

(Your answer must exactly equal the correct value.)

p-value for a two-tailed test:

(The difference between your answer and the correct value must be less than 0.001.)

Do you reject the null hypothesis?:

Trial Age of face Sex of face Likeability rating

1 Young Male 44

2 Young Female 59

3 Young Female 59

4 Young Female 63

5 Old Female 39

6 Young Male 15

7 Young Male 42

8 Old Male 73

9 Old Male 75

10 Young Female 57

11 Young Female 41

12 Young Male 57

13 Young Female 31

14 Old Female 80

15 Old Male 70

16 Old Female 24

17 Old Male 30

18 Old Female 72

19 Old Male 78

20 Old Female 57

21 Old Male 18

22 Old Female 24

23 Young Female 36

24 Young Male 34

25 Young Male 82

26 Old Female 42

27 Old Female 68

28 Old Male 24

29 Young Female 66

30 Old Female 69

31 Young Male 25

32 Young Female 56

33 Young Male 37

34 Old Male 88

35 Young Male 71

36 Young Male 56

37 Old Female 61

38 Young Male 58

39 Old Male 75

40 Young Female 58

41 Young Male 70

42 Old Female 23

43 Young Female 41

44 Old Female 76

45 Old Male 56

46 Old Female 68

47 Young Male 30

48 Old Male 24

49 Young Male 31

50 Old Male 34

51 Young Male 60

52 Old Male 53

53 Young Female 59

54 Old Male 57

55 Old Male 29

56 Young Female 65

57 Young Male 62

58 Young Female 33

59 Young Female 71

60 Old Female 65

61 Old Male 71

62 Young Female 47

63 Old Female 21

64 Old Female 72