Chapter 1: Data Collection

1. Data Collection

1.1 Intro to the Practice of Statistics

• Statistical Thinking: Understanding large amounts of data and information by applying mathematical formulas.

  • Formulas help understand general tendencies but do not yield precise answers.

  • Statistics deals with approximations, not exact calculations.

• Four-Part Definition of Statistics:

  1. Collection of information.

  2. Organizing and summarizing that information.

  3. Drawing conclusions about that information.

  4. Providing a measure of confidence in any conclusion (do the numbers reflect reality).

• Correlation vs. Causation:

  • Correlation does not imply causation.

    • Example: Cell phone usage and brain tumors. More research is needed to draw conclusions about causation.

• Lurking Variables:

  • A missing variable that skews the data.

    • Example: Classical music during pregnancy and academic benefit for the child. The lurking variable could be other factors like socioeconomic status, parental involvement, etc.

• Data Collection:

  • When putting statistics to practice, consider the problem of data collection.

    • Example: Determining whether Denton is mostly Democratic or Republican.

  • Collecting a sample from the general population is more practical than asking every single resident.

Definitions

• Population: The entire group of individuals to be studied.

• Sample: A subset of the population.

• Individual: A single member of a population.

• Statistic: A numerical summary of a sample.

• Parameter: A numerical summary of a population.

• Descriptive Statistics: The process of analyzing data using numbers, tables, and graphs.

• Inferential Statistics: The process of extending the conclusions of the sample to the population with some measure of reliability.

• Example:

  • Sociologist wants to know the rate of recidivism of prison convicts from Huntsville prison released in 2011.

  • Population: Convicts from Huntsville prison released in 2011.

  • Sample: 20 convicts randomly selected.

  • 12 out of 20 return to prison.

  • Statistic: 12/20 = 60\%. Inference: We are 95% confident that the recidivism rate is between 55% and 72%.

• Variables: Characteristics of the individuals of the population

  • Examples: height, income, ethnicity, left or right-handed, etc.

Types of Variables

• Qualitative Variables: Allow for classification of individuals based on attributes or characteristics.

• Quantitative Variables: Numerical measures of individuals. Subtraction and addition can be applied to quantitative variables

• Examples:

  • Determine whether variable is qualitative or quantitative:

    • (a) weight - quantitative

    • (b) eye color - qualitative

    • (c) income bracket - qualitative

    • (d) gender - qualitative

    • (e) temperature - quantitative

    • (f) commute time - quantitative

    • (g) zip code - qualitative

    • (h) number of customers that use the drive through at a fast food restaurant - quantitative

• Focus mainly on quantitative variables.

Types of Quantitative Variables

• Discrete: Represents information which is countable (one by one).

  • Comes from the Latin "discretes" which means separated.

• Continuous: Represents information which can divided indefinitely, meaning uninterrupted change.

• Examples:

  • Determine whether variable is discrete or continuous:

    • (a) time - continuous

    • (b) temperature - continuous

    • (c) number of customers - discrete

    • (d) velocity - continuous

    • (e) number of houses sold each year - discrete

    • (f) bacteria population in a culture at any given time - continuous

    • (g) miles per gallon - continuous

Levels of Measurement of a Variable

1. Nominal Level of Measurement:

   • Variable used to name, label, or categorize without attention to rank or order.

2. Ordinal Level of Measurement:

   • Variable has properties of nominal level variables, but rank and order are important.

3. Interval Level of Measurement:

   • Variable has properties of ordinal level variables, but addition and subtraction can be performed on the variables.

4. Ratio Level of Measurement:

   • Variable has properties of ordinal level variables, but ratios and percentages have meaning.

   • Multiplication and division can be performed on the variables.

• Examples:

  • Name the level of measurement for each variable:

    • (a) Nationality - Nominal

    • (b) Letter grade - Ordinal

    • (c) Time - Ratio

    • (d) Crime rates - Ratio

Practice Problems

1. The legal profession conducted a study to determine the percentage of cardiologists who had been sued for malpractice in the last ten years. The sample was randomly chosen from a national directory of doctors. Identify the individuals in the study.

   • A) each cardiologist selected from the directory

2. In a survey conducted in the town of Atherton, 22% of adult respondents reported that they had been involved in at least one car accident in the past ten years.

   • B) statistic

3. 26.2% of the mayors of cities in a certain state are from minority groups.

   • B) parameter

4. A study of 1600 college students in the city of Pemblington found that 10% had been victims of violent crimes.

   • B) statistic

5. The number of seats in a school auditorium

   • A) quantitative

6. The numbers on the shirts of a boy's football team

   • B) qualitative

7. The low temperature in degrees Fahrenheit on January 1st in Cheyenne, Wyoming

   • B) continuous

8. The number of pills in an aspirin bottle

   • B) discrete

9. The medal received (gold, silver, bronze) by an Olympic gymnast

   • B) ordinal

10. The musical instrument played by a music student

    • B) nominal

11. The year of manufacture of a car

    • A) ratio

12. Weight of rice bought by a customer

    • A) ratio

Homework

p. 11 #1-50, 57, 60