Question

Provide formula for effect sizes and step-by-step solution by hand or software.

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 15 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 = 0.01?

                     Position

Type	before	after
factual	21 31 32 25 28 19	29 24 33 26 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

Using Minitab software, (Stat -> ANOVA-> General Linear Model), we get the following output :

a) The appropriate test statistic -  two-way ANOVA

b) Testing the significance of Type,

The value of test statistic F_obs = 0.91

and critical value

Since F_obs = 0.91 F_critical = 4.35124, so we fail to reject H₀ at 5% level of significance.

Decision - Fail to reject H0

Testing the significance of Position,

The value of test statistic F_obs = 16.40

and critical value

Since F_obs = 16.40 > F_critical = 4.35124, so we reject H₀ at 5% level of significance.

Decision - Reject H0

Testing the significance of Interaction,

The value of test statistic F_obs = 9.29

and critical value

Since F_obs = 9.29 > F_critical = 4.35124, so we reject H₀ at 5% level of significance.

Decision - Reject H0

c) Calculating effect sizes,

For Type, effect size, small

For Position, effect size, large

For Interaction, effect size, large

d) Interpretation :

i) here is no question type difference in the test scores.    

ii) There is a question position difference in the test scores.

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