Question

The following data represent the results from an independent-measures experiment comparing three treatment conditions with n = 4 in each sample. Conduct an analysis of variance with α = 0.05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments. Treatment A Treatment B Treatment C 18 20 22 19 18 20 18 20 19 21 22 23 F-ratio = p-value = Conclusion: There is a significant difference between treatments These data do not provide evidence of a difference between the treatments η 2 = To calculate η 2 you can find the directions in the Learning Activities for Module 16. The directions are within the paragraph that starts with "Another value that sometimes gets calculated..." The results above were obtained because the sample means are close together. To construct the data set below, the same scores from above were used, then the size of the mean differences were increased. In particular, the first treatment scores were lowered by 2 points, and the third treatment scores were raised by 2 points. As a result, the three sample means are now much more spread out. Before you begin the calculation, predict how the changes in the data should influence the outcome of the analysis. That is, how will the F-ratio for these data compare with the F-ratio from above? Treatment A Treatment B Treatment C 16 20 24 17 18 22 16 20 21 19 22 25 F-ratio = p-value = Conclusion: There is a significant difference between treatments These data do not provide evidence of a difference between the treatments η 2 =

The allo ng da a re resent the results frorn an ın ependern measures ex er ment com arır ulficient to condlude that there are significant differennces between the treatments three treatmen candions with n 4 n each sam e. Contua an an sis af variance wth α 5 10 determine hether these data are Treatment A Treatment B Treatment C 23 Fratio- value O There is a significarn difference between treatments O These data do not provide evidence of a difference between the treatmerS To calculate you can find the directions in the Learring Acivities for Module 16. The directions are within the paragraph that starts with "Another value that sometimes gets calculated... The res ts a 0 e were ob ned because the羔r le means are dose 19 e er. To construci e data set below, the same scores rom above ere use the n scores were lowered by 2 points, and the third treatment scores were raised by 2 points. As a result, the three sample means are now much more spread ou. e sue a the mean articular, Lhe first treatmen erences were ıncrease n Defore you begin the cakulation predict how the changes in the data should inlluence the outcome of the analysis. That is, how will the Fratio for these dala compare with the Fratio from above? Fratio- value Condlusiort O There is a significarn difference between treatments O These data do no provide evidence of a dilference between the treatmenns

Answer 1

1)

applying one way ANOVA:

Source of Variation	SS	df	MS	F	P-value
Between Groups	8	2	4	1.5	0.2740
Within Groups	24	9	2.67
Total	32	11

F =1.5

p value =0.2740

these data do not provide,,,,,,,,,,,

η 2 = 8/32 =0.25

2)

Source of Variation	SS	df	MS	F	P-value
Between Groups	72	2	36	13.5	0.0020
Within Groups	24	9	2.67
Total	96	11

F =13.5

p value =0.0020

there is a significant,,,

η 2 = 72/96 =0.75