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,
  • Self Administered Questionnaire, and
  • Internet
  • Questionnaire design principles:
  • Keep the questionnaire as short as possible.
  • Ask short, simple, and clearly worded questions.
  • Start with demographic questions to help respondents get started comfortably.
  • Use dichotomous (yes|no) and multiple choice questions.
  • Use open-ended questions cautiously.
  • Avoid using leading-questions.
  • 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

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