Using Stevenss four levels of measurement give an example of

Using Stevens\'s four levels of measurement, give an example of nominal, ordinal, interval, and ratio scales (do NOT use examples from the text or lecture).

Solution

1.Examples of nominal variables include yes/no questions, gender, ethnicity, geographical region, religious affiliation, and other types of non-ordered demographic survey questions.

First Chloe collects information about the different types of flowers she\'s growing, and the colors of each. She counts 4 roses, 6 daisies, 3 sunflowers, and 4 lilies. The colors of the flowers are 3 red, 4 yellow, and 10 white. She decides to assign a code to each type and color of flower to keep track of this information in her records.

According to this table, a red rose would have the numerical code 15, with the first number representing the flower type and the second number representing the color. As far as the data is concerned, the number 15 does not need to be added, subtracted, multiplied, divided, or ordered in any way. It does not have a value of 15; it is simply a code to indicate a red rose. This is an example of nominal data, or categorical data that assigns numerical values as an attribute to an object, animal, person or any other non-number. This is similar to the numbers that are given to horses during a race. The number\'s themselves have no value, they simply identify the horses.

2.  Chloe has entered her roses into a local gardening competition. She had one rose get 4th place, one got 7th place, and one got 2nd place. These rankings are an example of ordinal data, which is data that can be ordered and ranked, but not measured, such as levels of achievement, prizes, rankings, and placements.

3.

Chloe has entered another rose competition. This time, her flowers have to fit in certain categories. As she is filling out the paper work, she notices some unusual questions. Take a look.

The second question represents a form of measurement called interval measurement, which is data that is grouped in evenly distributed values and measured based on the group to which the variable is attributed. In other words, interval data is measured in groups, rather than individually. For example, Chloe can measure the distance between each leaf and come up with .7. However, if the competition managers are trying to collect and group data in a more manageable way, then they will ask her to circle the option that is .5-1 inch. If you are collecting this information, you can really get a good visual representation by using a bar graph to display the data like this.

4. The next question asks about how many petals there are on Chloe\'s flower. You can take data like this and make a comparison. For example, what if the competition managers wanted to know how many flower petals there are in comparison to the leaves? They can learn this by using another form of measurement called aratio, which is a mathematical comparison between two numbers. This can be represented with a colon; however, we can take a ratio and manipulate it to gather more information about our data. For example, if Chloe has 6 leaves and 12 petals, then we could write that ratio like this: 6:12. We can also easily see from this that there are twice as many petals as there are leaves.