Question

1. (18 pts) Use the “Car Filter.sav” (SPSS) dataset (located below) to perform a Two-Way ANOVA. This dataset contains noise level readings taken from inside different sized cars equipped with different sized filters. Write your findings using the format presented in the class slides.
   1. (2 pts) What is the mean and standard deviation of each filter’s noise level?
2. 2. (2 pts) Based on the means and standard deviations calculated above for each filter, do you believe the mean noise levels are statistically equal across the two filter types? Please provide a thorough response.
3. 3. (3 pt) State your null and alternative hypotheses of the Two-Way ANOVA test. Assume that you do want to test for interaction between the two independent variables.
4. 4. (4 pts) Conduct a Two-Way ANOVA test (factorial analysis) between the two independent variables and the dependent variable. Be sure to include descriptive statistics of each variable (select the “EM Means” button in the “Univariate” box) and include “plots” of the two independent variables
5. 5. (3 pts) What is your response to the null hypothesis following your Two-Way ANOVA? Please provide a thorough response. Do the model’s assumptions hold?
6. 6. (4 pts) Conduct a non-parametric alternative to the Two-Way ANOVA you performed in part (c). Attach a copy of your results and interpret your findings. Please provide a thorough response. Are the results similar to the Two-Way ANOVA? Will this always be the case? Please provide a thorough response.

Noise	Car	Filter
810.00	1.00	1.00
820.00	1.00	1.00
820.00	1.00	1.00
840.00	2.00	1.00
840.00	2.00	1.00
845.00	2.00	1.00
785.00	3.00	1.00
790.00	3.00	1.00
785.00	3.00	1.00
835.00	1.00	1.00
835.00	1.00	1.00
835.00	1.00	1.00
845.00	2.00	1.00
855.00	2.00	1.00
850.00	2.00	1.00
760.00	3.00	1.00
760.00	3.00	1.00
770.00	3.00	1.00
820.00	1.00	2.00
820.00	1.00	2.00
820.00	1.00	2.00
820.00	2.00	2.00
820.00	2.00	2.00
825.00	2.00	2.00
775.00	3.00	2.00
775.00	3.00	2.00
775.00	3.00	2.00
825.00	1.00	2.00
825.00	1.00	2.00
825.00	1.00	2.00
815.00	2.00	2.00
825.00	2.00	2.00
825.00	2.00	2.00
770.00	3.00	2.00
760.00	3.00	2.00
765.00	3.00	2.00

Answer 1

1. (2 pts) What is the mean and standard deviation of each filter’s noise level?

Car	N	Mean
2	12	833.750
1	12	824.167
3	12	772.500

Filter	N	Mean
1	18	815.556
2	18	804.722

1. (2 pts) Based on the means and standard deviations calculated above for each filter, do you believe the mean noise levels are statistically equal across the two filter types? Please provide a thorough response.

Since the third means is different, we can say that the means are not statistically equal.

1. (3 pt) State your null and alternative hypotheses of the Two-Way ANOVA test. Assume that you do want to test for interaction between the two independent variables.

The hypothesis being tested is:

H₀: There is no main effect of Car

H_a: There is a main effect of Car

The hypothesis being tested is:

H₀: There is no main effect of Filter

H_a: There is a main effect of Filter

The hypothesis being tested is:

H₀: There is no interaction effect

H_a: There is an interaction effect  

1. (4 pts) Conduct a Two-Way ANOVA test (factorial analysis) between the two independent variables and the dependent variable. Be sure to include descriptive statistics of each variable (select the “EM Means” button in the “Univariate” box) and include “plots” of the two independent variables

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Car	2	26051.4	13025.7	199.12	0.000
Filter	1	1056.3	1056.3	16.15	0.000
Car*Filter	2	804.2	402.1	6.15	0.006
Error	30	1962.5	65.4
Total	35	29874.3

1. (3 pts) What is your response to the null hypothesis following your Two-Way ANOVA? Please provide a thorough response. Do the model’s assumptions hold?

There is a main effect of Car. (p < .05)

There is a main effect of Filter. (p < .05)

There is an interaction effect. (p < .05)

All the assumptions hold.

1. (4 pts) Conduct a non-parametric alternative to the Two-Way ANOVA you performed in part (c). Attach a copy of your results and interpret your findings. Please provide a thorough response. Are the results similar to the Two-Way ANOVA? Will this always be the case? Please provide a thorough response.

The results are similar to the Two-Way ANOVA.