Question

A researcher is studying the effects of inserting questions into instructional material for learning. There is doubt whether these questions would be more effective before or after the corresponding passage. In addition, the researcher wants to know the impact of factual and thought provoking questions. Students are randomly assigned to one of each of the four combination: position of question (before vs. after the passage) and type of question (factual vs. thought provoking). After 20 hours of studying under these conditions, the students are given a test on the content of the instructional materials. The test scores are below. What can be concluded with α = 0.05? Please use 4 numbers after decimal

                     Position

Type	before	after
factual	21 31 32 25 28 19	29 24 33 20 25 30
thought	27 20 15 21 26 24	36 39 41 29 31 35

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Type: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Position: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Type: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Position: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is a question type difference in the test scores.There is no question type difference in the test scores.    

There is a question position difference in the test scores.There is no question position difference in the test scores.    

There is a question type by position interaction in the test scores.There is no question type by position interaction in the test scores.    

Answer 1

Two-way ANOVA: Score versus Type, Position

Source	DF	SS	MS	F	P
Type	1	30.375	30.375	1.34	0.261
Position	1	287.042	287.042	12.63	0.002
Interaction	1	222.042	222.042	9.77	0.005
Error	20	454.5	22.725
Total	23	993.958

S = 4.767 R-Sq = 54.27% R-Sq(adj) = 47.41%

a) What is the appropriate test statistic?
Ans: Two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Type: critical value = 4.35 ; test statistic =  1.34
Decision: Fail to reject H0

Position: critical value = 4.35 ; test statistic =  12.63
Decision: Reject H0

Interaction: critical value = 4.35 ; test statistic = 9.77
Decision:  Reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Type: η² =30.375/993.958=0.0306 ; small effect
Position: η² =287.042/993.958=0.2888 ; large effect
Interaction: η² = 222.042/993.958 =0.2234 ;  large effect


d) Make an interpretation based on the results.

There is no question type difference in the test scores.    

There is a question position difference in the test scores.

There is a question type by position interaction in the test scores.