##### Question

In: Statistics and Probability

# (18 pts) Use the “Car Filter.sav” (SPSS) dataset (located below) to perform a Two-Way ANOVA. This...

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?
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.
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.
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
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?
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.
 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

## Solutions

##### Expert Solution

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

Ha: There is a main effect of Car

The hypothesis being tested is:

H0: There is no main effect of Filter

Ha: There is a main effect of Filter

The hypothesis being tested is:

H0: There is no interaction effect

Ha: 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.

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