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 10 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 an α of 0.05?

                     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 29 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

a)

Answer: two-way ANOVA

Explanation: Since we want test the hypothesis whether impact of factual and thought provoking questions is more effective  before or after the corresponding passage, the two independent variables position of question (before vs. after the passage) and type of question (factual vs. thought provoking) are being compared. Hence two factor ANOVA with replication analysis is performed here to test the hypothesis.

b)
Answer:

Type: critical value = 4.3512 ; test statistic = 0.7120
Decision: Fail to reject H0

Position: critical value = 4.3512; test statistic = 14.9290
Decision:  ---Select--- Reject H0

Interaction: critical value = 4.3512 ; test statistic = 8.3333
Decision:  ---Select--- Reject H0.

Explanation:

The two factor ANOVA test three null hypothesis as shown below,

The Null and Alternative Hypothesis are,

H₀₁: There is no difference in the means of factor A

H_A1: There is a significant difference in the means of factor A

H₀₂: There is no difference in means of factor B

H_A2: There is a significant difference in means of factor B

H₀₃: There is no interaction between factors A and B

H_A3: There is a significant interaction between factors A and B

Where, factor A is the Type of questions , factor B is the Position of question.

The test is performed in excel by using following steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > ANOVA: Two Factor With Replication > OK.  The screenshot is shown below,

Step 3: Select Input Range: All the data values column, Rows per Sample: 6, Alpha = 0.05. The screenshot is shown below,

The result is obtained.  The screenshot is shown below,

Results of the study

Source of Variation	F		F crit	Significance?
Type of questions	0.712032	<	4.351244	Not significant
Position of questions	14.92899	>	4.351244	Significant
Interaction	8.333333	>	4.351244	Significant

c)

Type: η² = 0.0162; small effect
Position: η² = 0.395; large effect
Interaction: η² = 0.1895 ; large effect

Explanation:

The effect size is obtained as follows,

For Type of questions,

If the effect size is 0.01, the effect is small

For Type of positions,

If the effect size is 0.14 or more, the effect is large

For interaction,

If the effect size is 0.14 or more, the effect is large

d)

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.