Question

A linguist is interested in knowing how best to learn a foreign language. The linguist develops a new way to learn a foreign language called Aural-Oral and wants to compare it to the traditional translation method. In a research study, students from a sample are randomly assigned to one of the methods: Aural-Oral, translation, and combination of both. In addition, the linguist wants to know if IQ is related to learning a foreign language, so the students are split into having a high or average IQ. After a year of studying a foreign language, the students are asked to take a vocabulary test on the foreign language. What can the linguist conclude with an α of 0.01?

	IQ
Method	high	average
aural-oral	31 24 20 25	32 19 37 28
translation	28 25 23 23	20 23 14 15
combined	17 28 21 18	26 27 32 27

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

b) Obtain/compute the appropriate values to make a decision about H₀.
IQ: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Method: 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).
IQ: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Method: 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 an IQ difference on vocabulary.There is no IQ difference on vocabulary.     

There is a method difference on vocabulary.There is no method difference on vocabulary.     

There is a method by IQ interaction on vocabulary.There is no method by IQ interaction on vocabulary.     

Answer 1

a) What is the appropriate test statistic?
two-way ANOVA

b) Obtain/compute the appropriate values to make a decision about H₀.
IQ: critical value =  8.285; test statistic =  0.538
Decision:  Fail to reject H0

Method: critical value = 6.013 ; test statistic =  2.840
Decision:  Fail to reject H0

Interaction: critical value = 6.013 ; test statistic =  4.672
Decision:  Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
IQ: η² = 0.016 ; trivial effect
Method: η² = 0.169 ; small effect
Interaction: η² = 0.278 ;  medium effect


d) Make an interpretation based on the results.

There is no IQ difference on vocabulary.     

There is no method difference on vocabulary.     

There is no method by IQ interaction on vocabulary.     

Source	SS	df	MS	F	p-value	F critical	n²
Method	127.08	2	63.542	2.840	.0847	6.013	0.169
IQ	12.04	1	12.042	0.538	.4726	8.285	0.016
Interaction	209.08	2	104.542	4.672	.0232	6.013	0.278
Error	402.75	18	22.375
Total	750.96	23