In: Math
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 α = 0.05?
IQ
Method | High | Average |
---|---|---|
Aural-Oral | 31 24 20 25 |
32 19 37 28 |
Translation | 28 25 31 20 |
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) Compute the appropriate test statistic(s) to
make a decision about H0.
Method: critical value = ; test
statistic =
Decision: ---Select--- Reject H0 Fail to reject H0
IQ: 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).
Mehotd: η2
= ; ---Select--- na trivial effect small
effect medium effect large effect
IQ: 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.
a) What is the appropriate test statistic?
Two-Way ANOVA
b) Compute the appropriate test statistic(s) to make a decision
about H0.
Method: critical value = 3.555 ; test statistic = 1.991
Decision: Fail to reject H0
IQ: critical value = 4.414 ; test statistic = 0.239
Decision: Fail to reject H0
Interaction: critical value = 3.555 ; test statistic =
5.018
Decision: Reject H0
c) Compute the corresponding effect size(s) and indicate
magnitude(s).
Mehotd: η2 = 0.181 ; small effect
IQ: η2 = 0.013 ; small effect
Interaction: η2 = 0.358 ; large 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 a method by IQ interaction on vocabulary.