Attaching unwarranted significance to aspects of the numbers that do not convey meaningful information

Failing to simply data when would easily do so

Manipulating our data in ways that destroy information

Performing meaningless statistical operations on the data

Nominal and ordinal measurement

Nominal measurement: not measurement in the everyday sense of the word; the value does not imply any ordering of the cases, for example, shirt numbers in football; Even though player 17 has higher number than player 7, you can’t say from the data that he’s greater than or more than the other.

When attributes can be rank-ordered

Distances between attributes do not have any meaning, for example, the distance between the winner of a sport competition and the second one, and between the second and third one

The Hierarchy of Levels

Nominal

Interval

Ratio

Attributes are only named; weakest

Attributes can be ordered

Distance is meaningful

Absolute zero

Ordinal

Types of data

Nominal and ordinal are qualitative (categorical) levels of measurement.

Interval and ratio are quantitative levels of measurement.

VARIABLES

QUANTITATIVE

QUALITATIVE

RATIO

Pulse rate

Height

INTERVAL

36o-38oC

ORDINAL

Social class

NOMINAL

Gender

Ethnicity

Example: Identify each of the following as examples of (1) nominal, (2) ordinal, (3) discrete, or (4) continuous variables:

1. The length of time until a pain reliever begins to work.

2. The number of chocolate chips in a cookie.

3. The number of colors used in a statistics textbook.

4. The brand of refrigerator in a home.

5. The overall satisfaction rating of a new car.

6. The number of files on a computer’s hard disk.

7. The pH level of the water in a swimming pool.

8. The number of staples in a stapler.

Measure and Variability

No matter what the response variable: there will always be variability in the data.

One of the primary objectives of statistics: measuring and characterizing variability.

Controlling (or reducing) variability in a manufacturing process: statistical process control.

Methods used to collect data

Census: A 100% survey. Every element of the population is listed. Seldom used: difficult and time-consuming to compile, and expensive.

Survey: Data are obtained by sampling some of the population of interest. The investigator does not modify the environment.

Experiment: The investigator controls or modifies the environment and observes the effect on the variable under study.

Administrative resources: The source of the data is an administrative activity.