# Statistics I. Tamás Dusek Széchenyi István University 2016 Historical meaning of statistics

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## Example

• Discrete
• The number of eggs that hens lay; for example, 3 eggs a day.
• The number of cars in a parking lot.
• Number of the inhabitants of a town.
• Continuous
• The amounts of milk that cows produce; for example, 8.343115 liter a day.
• The temperature.
• Age of a person.
• Example: Identify each of the following as examples of qualitative or numerical variables:
• 1. The temperature in Győr, Hungary at 12:00 pm on any
• given day.
• 2. Whether or not a 6 volt lantern battery is defective.
• 3. The weight of a lead pencil.
• 4. The length of time billed for a long distance telephone call.
• 5. The brand of cereal children eat for breakfast.
• 6. The type of book taken out of the library by an adult.

## Levels of measurement

• 1 Nominal
• 1A Coding
• 1B Qualitativ data, categorical data (gender, nationality, ethnicity, language, genre, style, biological species)
• 2 Ordinal – rank order
• 3 Interval - degree of difference; however zero is arbitrary
• 4 Ratio
• 4A continuous quantity with true zero
• 4B discrete quantity

## Importance of the levels of measurement

• Helps you decide what statistical analysis is appropriate on the values that were assigned
• Helps you decide how to interpret the data from that variable
• Dangers to Avoid
• 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.
• Other

## Surveys

• Surveys may be administered in a variety of ways, e.g.
• Personal Interview,
• Telephone Interview,
• Internet
• Questionnaire design principles:
• Keep the questionnaire as short as possible.
• Ask short, simple, and clearly worded questions.
• Use dichotomous (yes|no) and multiple choice questions.
• Use open-ended questions cautiously.
• Pretest a questionnaire on a small number of people.
• Think about the way you intend to use the collected data when preparing the questionnaire.

## Not everything that counts can be counted

• 5 (Quantity) Happy (Quality) Kids

## Univariate descriptive statistics

• After collecting data, the first task is to organize and simplify the data so that it is possible to get a general overview of the results.
• This is the goal of descriptive statistical techniques.
• One method for simplifying and organizing data is to present them in graphical way