You are interested in whether effort and willingness to help were affected by th

Question

You are interested in whether effort and willingness to help were affected by the form and amount of payment offered in return for the effort. In your study, college students were asked to estimate another student's willingness to help load a sofa into a van in return for a cash payment or candy of equivalent value. Willingness to help was assessed using a 11-point scale ranging from "not at all likely" to "Will help for sure". Presented is the data collected:

Cash payment, low amount of $1: 4, 5, 6, 4

Cash payment, moderate amount of $5: 7, 8, 8, 7

Candy payment, low amount of $1: 6, 7, 5, 7

Candy payment, moderate amount of $5: 8, 6, 5, 5

A. What is the marginal mean for cash payment?

        i.            7.5

      ii.            6.125

    iii.            5.5

     iv.            6.75

B. What is the marginal mean for a moderate level of payment?

        i.            6.75

      ii.            5.5

    iii.            6

     iv.            6.125

C. Calculate MS(interaction). It is ...?

        i.            0

      ii.            1.042

    iii.            9

     iv.            6.25

D. Calculate MS(within). It is ...

        i.            12.5

      ii.            1.042

    iii.            0

     iv.            6.25

E. Calculate F(level of payment). It is ...

        i.            0

      ii.            8.64

    iii.            6

     iv.            1

F. Calculate F(interaction). It is ...

        i.            8.64

      ii.            6.0

    iii.            1.0

     iv.            0

G. What is the F(critical) value for this scenario, with alpha of .05?

3.18

4.75

9.33

3.89

H. What are the conclusions of the interaction effect?

I.                    Significant qualitative and quantitative interaction effects.

        i.            No significant interaction effects observed.

      ii.            Significant qualitative interaction effects.

    iii.            Significant quantitative interaction effects.

J. What is the effect size of the interaction?

        i.            .42

      ii.            0

    iii.            .32

     iv.            .33

K. What are the conclusion regarding the main effect of the level of payment?

        i.            There is a significant large effect

      ii.            There is a non-significant large effect

    iii.            There is a significant small effect

     iv.            There is a significant medium effect

Explanation / Answer

a) mean of cash = 6.125

b) mean of moderate = 6.75

c) MS interaction = 9

d) MS within = 1.042

e) F level of payment   = 6

f) F interaction = 8.64

g) F -critical = 4.75

Anova: Two-Factor With Replication SUMMARY low moderate Total cash Count 4 4 8 Sum 19 30 49 Average 4.75 7.5 6.125 Variance 0.916666667 0.333333333 2.696428571 candy Count 4 4 8 Sum 25 24 49 Average 6.25 6 6.125 Variance 0.916666667 2 1.267857143 Total Count 8 8 Sum 44 54 Average 5.5 6.75 Variance 1.428571429 1.642857143 ANOVA Source of Variation SS df MS F P-value F crit Sample 0 1 0 0 1 4.747225 Columns 6.25 1 6.25 6 0.030622 4.747225 Interaction 9 1 9 8.64 0.012386 4.747225 Within 12.5 12 1.041666667 Total 27.75 15

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