A webquest for the Analysis of Variance methods in Introductory Statistics

The 2004 Olympic games were held in August in Athens Greece. There are competitors from all over the world who gathered together to see who was the best in each sport.

Weightlifting involves lifting weights above your head in two events, the snatch and the clean and jerk. Furthermore, the men's division is broken down into weight classes so that you compete with other men who are of similar weights as yourself.

This is a group activity with up to three people in the group.

Your task is to gather the total weight lifted in each of the weight categories for the men's weightlifting competition at the 2004 Olympic games. Then you will perform a one-way analysis of variance to see if there is a difference in the mean weights lifted of the different weight classes. Perhaps there is no reason to divide into different weight classes.

Use the methods of the Analysis of Variance to answer the following questions.

- Is there a difference in the mean snatch weight that the different weight classes can lift?
- Is there a difference in the mean clean & jerk weight that the different weight classes can lift?
- Is there a difference in the mean weights that the different weight classes can lift?
- Is there a difference in the mean weights of the snatch and clean & jerk competitions?
- Is there any interaction between the weight class and the competition type?

Use a one-way ANOVA to answer questions 1 and 2 and a two-way ANOVA to answer questions 3-5 (all at once).

Complete the entire process and copy and paste output from Minitab into Word. Email the instructor the Word file when it is complete.

- Visit the Athens 2004 website
to gather the official data from the games.
- Choose Schedule - Results from the left menu bar
- Choose Weightlifting from the list of competitions
- Choose Men from the menu on the left under the Weightlifting category

- Click on one of the weight categories (56kg, 62kg, 69kg, 77kg, 85kg, 94kg,
105kg, and +105kg)
- In the "Available Information" list box, choose "Final Results"
- Click the >> box next to "Available Information"
- For each competitor who completed the competition, record the weight class, place, snatch result, clean & jerk result, and total.

- Click on Men from the left menu to return to the listing of weight categories.
- Repeat step 2 with a different weight class until all of the weight classes have been collected.

Your data should look something like this. The ... means that some data has been omitted (after all, it is your task to collect the data).

class | place | snatch | clean | total |
---|---|---|---|---|

56kg | 1 | 135.0 | 160.0 | 295.0 |

56kg | 2 | 130.0 | 157.5 | 287.5 |

56kg | ... | ... | ... | ... |

56kg | 11 | 102.5 | 130.0 | 232.5 |

62kg | 1 | 152.5 | 172.5 | 325.0 |

62kg | ... | ... | ... | ... |

62kg | 15 | 95.0 | 130.0 | 225.0 |

... | ... | ... | ... | ... |

+105kg | 14 | 155.0 | 192.5 | 347.5 |

There are 121 competitors. It took me about 20 minutes to collect the information using copy / paste and then selecting the columns I wanted from the table and pasting the information into Excel.

Enter all the data into Minitab so we can analyze it.

The grade that you receive for the project will be based on the following rubric. This 25 point portion of the grade is based on the group effort. Each member of the group will receive an identical score.

Goal | Excellent (5 points) | Average (3 points) | Poor (1 point) |
---|---|---|---|

Identification | The full name of each group member is given and correctly spelt | At least one full name is missing or spelt incorrectly |
The first names of the group members are given |

Organization | Each question is identified by the question number and the text of the question. | Each question is identified by the question number | Questions are not identified |

Annotation | Each output (text or graph) from Minitab has an explanation | One or more outputs have no description | Only the output from Minitab is given, there are no explanations |

Completeness | Each question is fully answered | One question is completely missing or parts of a question are not answered | More than one question is not answered |

Correctness | There are 0 or 1 errors in the output or descriptions | There are 2 to 3 errors in the output or descriptions | There are more than 3 errors in the output or descriptions |

The project will lose 10% of its value for each class period it is late. If you earn a 23 but it is two days late, then your grade will be 23(0.8) = 18.4 or 18 points.

Instructions given are for Minitab version 14. The menu choices may be slightly different on other versions or in other software packages.

These questions are fairly straight forward. Use the one-way ANOVA methods from Minitab. The response variable is either snatch or clean (depending on your question) and the factor is the class.

Okay, this is a bit trickier as Minitab will only do a balanced design and our design isn't balanced as the number of competitors varies from 11 to 21. So, to balance our design, we're only going to take the top 10 competitors from each weight class. Yes, I know we could do 11, but this helps rule out some of the weaker ones and should reduce the variation within each class.

Follow these steps in Minitab to massage the data into a useable format.

- Choose Data / Subset worksheet
- Give it a useful name like "Top 10"
- Click on Condition
- type: place <= 10
- Click OK

- Click OK

Minitab requires categorical data for the factors when you're doing a two-way ANOVA. Unfortunately, our data is in two different columns, one for snatch and one for clean.

There are a couple of ways to accomplish this. I'm going to give you what I feel is the easiest way. Start off with the "Top 10" worksheet you just created.

- Choose Data / Stack / Columns
- Stack the snatch and clean columns
- Name the worksheet something like "twoway".
- Be sure to check the box that says use variable names in subscript column
- Click OK. When you do this, you'll now be in the "twoway" worksheet. Stay there.

- Rename the "Subscripts" column (C1) to be "event" and label the second column as "weight"
- Label a blank column as "class"
- Choose Calc / Make patterned data / Text values
- Store the patterned data in "class"
- The text values are "56kg 62kg 69kg 77kg 85kg 94kg 105kg +105kg". Make sure each one is separated by a space and that there are no spaces between the number and the kg.
- List each value 10 times (there are 10 places)
- List the whole sequence 2 times (there are 2 variables, snatch and clean)
- Click OK

Okay, now you can use the "twoway" worksheet and conduct your two-way analysis of variance. The factors are class and event and the response variable is weight.

Now that you have completed this webquest you should have accomplished the following items.

- Be able to go to the Web and gather data
- Arrange the data in a format suitable for data analysis
- Use technology to conduct a one-way ANOVA and a two-way ANOVA
- Interpret the results of the ANOVA
- Draw conclusions from the data

The data here comes from Athens 2004, the official website of the 2004 Summer Olympics.