This problem is designed to help you see the effect of outliers can have on an ANOVA test. Students enrolled in developmental mathematics classes at a community college are encouraged to go to the Math Tutoring Center (MTC) for help with their homework. Some students schedule their time so that they go once or twice a week to focus on all of their math homework at once. Some students even start forming study groups and meet at the MTC to work together. The staff that run the MTC want to know if some classes are using their services more than others. They collect data from 5 classes and 17 students per class that attend the session at least once in the term. The dependent variable is the number of days a student visits the MTC during one academic term (about 12-13 weeks). Group 1 Group 2 Group 3 Group 4 Group 5 10 5 11 16 7 12 15 21 14 22 14 13 17 9 12 12 12 20 13 20 4 6 20 9 8 17 19 20 43 17 10 12 9 49 14 15 5 15 13 11 7 7 16 14 8 10 12 12 14 14 23 9 7 14 13 12 10 10 16 9 14 13 17 15 15 7 14 11 9 15 15 15 8 12 15 18 13 6 42 10 20 9 10 17 11 Conduct the one-factor fixed effect ANOVA with the data. Report the requested sample statistics: 1.) MSbetween= (report answer accurate to 3 decimal places) F-ratio = ________ (report answer accurate to 3 decimal places) P-value = _______ (report answer accurate to 4 decimal places) 2.) What is the conclusion about groups, on average, using the MTC to equal amounts (α=0.05)? There is not enough evidence to suggest the averages of daily visits to the MTC are different. The evidence suggests the averages of daily visists to the MTC are not all the same.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
This problem is designed to help you see the effect of outliers can have on an ANOVA test.
Students enrolled in developmental mathematics classes at a community college are encouraged to go to the Math Tutoring Center (MTC) for help with their homework. Some students schedule their time so that they go once or twice a week to focus on all of their math homework at once. Some students even start forming study groups and meet at the MTC to work together. The staff that run the MTC want to know if some classes are using their services more than others. They collect data from 5 classes and 17 students per class that attend the session at least once in the term. The dependent variable is the number of days a student visits the MTC during one academic term (about 12-13 weeks).
| Group 1 | Group 2 | Group 3 | Group 4 | Group 5 |
|---|---|---|---|---|
| 10 | 5 | 11 | 16 | 7 |
| 12 | 15 | 21 | 14 | 22 |
| 14 | 13 | 17 | 9 | 12 |
| 12 | 12 | 20 | 13 | 20 |
| 4 | 6 | 20 | 9 | 8 |
| 17 | 19 | 20 | 43 | 17 |
| 10 | 12 | 9 | 49 | 14 |
| 15 | 5 | 15 | 13 | 11 |
| 7 | 7 | 16 | 14 | 8 |
| 10 | 12 | 12 | 14 | 14 |
| 23 | 9 | 7 | 14 | 13 |
| 12 | 10 | 10 | 16 | 9 |
| 14 | 13 | 17 | 15 | 15 |
| 7 | 14 | 11 | 9 | 15 |
| 15 | 15 | 8 | 12 | 15 |
| 18 | 13 | 6 | 42 | 10 |
| 20 | 9 | 10 | 17 | 11 |
Conduct the one-factor fixed effect ANOVA with the data. Report the requested sample statistics:
1.)
MSbetween=
(report answer accurate to 3 decimal places)
F-ratio = ________
(report answer accurate to 3 decimal places)
P-value = _______ (report answer accurate to 4 decimal places)
2.)
What is the conclusion about groups, on average, using the MTC to equal amounts (α=0.05)?
- There is not enough evidence to suggest the averages of daily visits to the MTC are different.
- The evidence suggests the averages of daily visists to the MTC are not all the same.
3.)
For any group with extreme outliers, delete these values and rerun the ANOVA. Report the requested new sample statistics:
MSbetween= _______
(report answer accurate to 3 decimal places)
F-ratio = ________
(report answer accurate to 3 decimal places)
P-value = _________ (report answer accurate to 4 decimal places)
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