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A factor is a basis for categorizing data. For example, if you count the number of sit-ups individuals can do, one basis of categorization is age. For age, you might have the following levels.
|Level 0||6 years old to 10 years old|
|Level 1||11 years old to 15 years old|
|Level 2||16 years old to 20 years old|
Now, suppose that you make a series of observation to see how many sit-ups people can do. If you take a random sampling of five people, you might find the following results.
|Person 1||8 years old (level 0)||10 sit-ups|
|Person 2||12 years old (level 1)||15 sit-ups|
|Person 3||16 years old (level 2)||20 sit-ups|
|Person 4||20 years old (level 2)||25 sit-ups|
|Person 5||13 years old (level 1)||17 sit-ups|
Notice that you have made at least one observation per level. To perform an analysis of variance, you must make at least one observation per level.
To perform the analysis of variance, you specify an array of observations, with values 10, 15, 20, 25, and 17. levels specifies the level (or category) to which each observation applies. In this case, levels has the values 0, 1, 2, 2, and 1. Finally, there are three possible levels, so you pass in a value of 3 for the numberOfLevels parameter.