Question

In a study of memory process, rats were first presented with a fear-inducing stimulus on a learning task as soon as they stepped across a line in a test chamber. Afterwards, the rats were divided and given electrical stimulation either 50 or 150 milliseconds after crossing the line. In addition, the rats differed in terms of the area in which the stimulation electrodes were implanted in their brains (Neutral Area, Area A, or Area B). Researchers were interested in the time it took the animals to re-cross the line on a subsequent learning task. The idea is that stimulation of certain areas in the brain would interfere with memory and hence delay learning to avoid the line on the subsequent learning task. The data on time to re-cross the line are below. What can be concluded with α = 0.05?

                     Area

Time	neutral	A	B
50	26 31 36 41 21	12 19 25 16 15	24 31 19 29 24
150	26 29 24 18 33	26 31 38 30 24	27 20 29 29 22

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

Area: 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).
Time: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Area: 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 time difference in the time it took to step across the line.There is no time difference in the time it took to step across the line.    

There is an area difference in the time it took to step across the line.There is no area difference in the time it took to step across the line.    

There is a time by area interaction in the time it took to step across the line.There is no time by area interaction in the time it took to step across the line.    

Answer 1

a) What is the appropriate test statistic?
-Ans: The appropriate test statistic is two-way ANOVA.

Calculation:

Two-way ANOVA: Y versus Time, Area

Source	DF	SS	MS	F	P
Time	1	45.63	45.633	1.46	0.238
Area	2	122.87	61.433	1.97	0.161
Interaction	2	401.27	200.633	6.43	0.006
Error	24	748.40	31.183
Total	29	1318.17

S = 5.584 R-Sq = 43.22% R-Sq(adj) = 31.40%

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Time: critical value =4.26 ; test statistic =  1.46
Decision: Fail to reject H0

Area: critical value = 3.40 ; test statistic =  1.97
Decision: Fail to reject H0

Interaction: critical value = 3.40 ; test statistic =  6.43
Decision: Reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Time: η² =45.63/1318.17=0.034 ; small effect
Area: η² =122.87/1318.17=0.0932 ;  medium effect
Interaction: η² =401.27/1318.17=0.3044 ; large effect


d) Make an interpretation based on the results.

There is no time difference in the time it took to step across the line.    

There is no area difference in the time it took to step across the line.    

There is a time by area interaction in the time it took to step across the line.