Day 8 Daily ANOVA Assumptions
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Apr 3, 2024
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Name: Jack Di Lorenzo
STAT 146
Daily 8
One Factor ANOVA with Testing Assumptions
Problem 1. A study measured the number of filtration systems that employees assembled each week using one of three different assembly methods. Are the methods different or do they result in essentially the same number of assembled filtration systems each week? In other words, is one method better than the others? The data is saved as FiltrationSystems.mtw. I produced the output that you will need. You should run the output to be sure you know how to obtain the correct output.
1a. Obtain descriptive (summary) statistics for the number of filtration systems assembled for each method.
1b. Rank the means.
B>A>C
1c. Is there evidence that one method is better than the others?
Show the complete testing process and Tukey’s comparisons, if needed. Form an overall conclusion that answers the question.
---show the complete test process here---
Population The response variable is the fill-amount in ounces.
The treatments are the five machines, which represent the different levels in the ANOVA.
Method
The null hypothesis (Ho) states that all machines have the same mean fill-amount (μA = μB = μC = μD = μE).
The alternative hypothesis (Ha) is that at least one machine has a different mean fill-amount.
The significance level (alpha) is set at 0.05.
Results from the ANOVA:
The F test statistic is 53.27 Df=4 The P-value is reported as very small.
Conclusion:
STAT 146 Intro to Stat II Daily 8
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Based on the F test statistic and the P-value, we reject the null hypothesis.
There is sufficient evidence at the 5% level of significance to conclude that at least one machine's mean fill-
amount differs from the others.
Do not forget to answer the original question and explain how you know: Is there evidence that one method is better than the others?
Yes, there is evidence that one method is better than the others. Specifically, Methods A and B are better than
Method C. There is no evidence to suggest a difference between Methods A and B, so we cannot conclude
that either is superior within that pair. However, since both are superior to C, we can say that Methods A and
B are the better methods overall.
1d. Check the assumptions for an ANOVA (Normality of the residuals and Levene’s test for equal variance). Be sure to summarize your overall findings.
We have met the assumptions of a one-way ANOVA since the residuals can be assumed to be normally
distributed and have constant variability across the different groups. This conclusion is based on the P-values
from the normality test and Levene’s test being higher than the significance level of 0.05, indicating that there
is no reason to reject the assumptions of normality and equal variances for the ANOVA model.
Problem 2. A local college now offers food trucks each day to supplement the lunch time food options on campus. A random sample of food truck customers were asked to provide an overall rating (1 – 10). The data can be found in the file Food Truck Ratings.mwx.
2a. Obtain descriptive (summary) statistics for the Rating for each food truck.
2b. Rank the means.
RCS>TW>RND>WOW>>RK
2c. Conduct the appropriate hypothesis test (Show the complete test process) to determine whether there is one food truck mean rating that stands out as better as the other food trucks. Use alpha = 0.05. Run Tukey’s comparisons, if needed. Form an overall conclusion that answers the question: Does one food truck mean rating stand out as better than the other food trucks? Explain how you know.
STAT 146 Intro to Stat II Daily 8
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---show the complete test process---
Population:
The response variable is the fill-amount in ounces.
The treatments are the outputs from the five machines, which are being compared.
Method:
The null hypothesis (Ho) is that all machines have the same mean fill-amount (μA = μB = μC = μD = μE).
The alternative hypothesis (Ha) is that at least one machine has a different mean fill-amount.
The significance level (alpha) is set at 0.05.
ANOVA Results:
The F test statistic is -53.27 df = 4 The P-value is reported as very small.
Conclusion:
With an F test statistic of -53.27 and a very small P-value, we reject the null hypothesis. This indicates that
there is significant evidence at the 5% level of significance to suggest that at least one machine's mean fill-
amount is different from the others.
STAT 146 Intro to Stat II Daily 8
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Be sure to answer the question: Does one food truck mean rating stand out as better than the other food
trucks? Explain how you know.
Yes, there is evidence that one or more food truck mean ratings stand out as better than the others. Roc City
Sammich and Tom Wahls have the highest mean ratings, which are not significantly different from each other
but are significantly higher than at least one other food truck (Robs Kabobs). Therefore, Roc City Sammich and
Tom Wahls can be considered the best-rated food trucks among the ones analyzed.
2d. Check the assumptions for an ANOVA (Normality of the residuals and Levene’s test for equal variance). Be sure to summarize your overall findings.
Levene’s Test for Equal Variances:
The null hypothesis of Levene's Test states that all variances are equal across groups.
The alternative hypothesis states that at least one group has a variance different from the others.
With a Levene's Test statistic of 1.27 and a P-value of 0.294, we fail to reject the null hypothesis at the alpha
level of 0.05. This means there is no statistically significant evidence to suggest that the variances are different
among the food trucks.
Conclusion: The assumption of equal variances is met for the ratings of the food trucks. This is evidenced by the high P-
value in Levene's test (greater than 0.05), indicating that the variances of ratings are not significantly different
across food trucks. The equality of variances across the groups suggests that it is appropriate to proceed with
the ANOVA analysis.
STAT 146 Intro to Stat II Daily 8
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