m) interpret the findings. n) construct an ANOVA summary table O) Caclulate w2 a

Question

m) interpret the findings.

n) construct an ANOVA summary table

O) Caclulate w2 and interpret

P) conduct protected t tests if necessary

study guide

194 3. You observe that people seem to be happier when they are wearing a new article of clothing. You also would like to test whether level of happiness depends on the particular type of new clothing worn. To test this, you provide a random sample of fivef your classmates with-new T-shirts and five with new shoes, and instruct them to wear the articles of clothing all day. At the end of the day, you ask these subjects to rate, on a 10-point scale, how happy they are. A control group of five classmates is also asked for this self-rating, but without the experimental manipulation. Ratings for each subject are reported below. Higher scores indicate greater happiness. Conduct a one-way ANOVA on these data. New T-shirt Group 6 6 7 5 New Shoes Group 8 Control Group 6 5 10 a. State Ho and H. b. Calculate SSea- c. Calculate sS d. Calculate ss. e. Calculate dfea f. Calculate dfv g. calculate df h. Calculate MSBG . Calculate MSW j. Compute the E ratio. K. What is Ecrit for = .05? 1. Reject Ho? m. Interpret the findings.

Explanation / Answer

Step 1

Null Hypothesis Ho : µ1 =µ2 =µ3

Alternative Hypothesis :µ1 µ2 µ3

Step 2

Degrees of freedom between = k - 1 = 3 - 1 = 2

Degrees of freedom Within = n - k = 15 - 3 = 12

Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.885

Step 3

Grand Mean = G / N = 6.4+8.2+4.6 / 3 = 6.4

SST = ( Xi - GrandMean)^2 = (6-6.4)^2 + (6-6.4)^2 + (7-6.4)^2 + ……..& so on = 49.6

SS Within = (Xi - Mean of Xi ) ^2 =,(6-6.4)^2 + (6-6.4)^2 + (7-6.4)^2 + ……..& so on = 17.2

SS Between = SST - SS Within = 49.6 - 17.2 = 32.4

Step 4

Mean Square Between = SS Between / df Between = 32.4/2 = 16.2

Mean Square Within = SS Within / df Within = 17.2/12 = 1.433

Step 5

F Cal = MS Between / Ms Within = 16.2/1.433 = 11.302

We got |F cal| = 11.302 & |F Crit| =3.885

MAKE DECISION

Hence Value of |F cal| > |F Crit|and Here We Reject Ho

Treatments ONE WAY ANOVA Mean = X /n New T Shirt Group 6 6 7 5 8 6.4 New Shoes Group 8 7 9 7 10 8.2 Control Group 4 6 5 3 5 4.6

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