Introduction to Statistics

Introduction to Statistics

• Data is information from observations, counts, measurements, or responses.
• Examples: People eating three daily servings of whole grains reduce stroke risk by 37%. 70% of 1500 spinal cord injuries to minors result from vehicle accidents, and 68% were not wearing seatbelts.
• Statistics is the science of collecting, organizing, analyzing, and interpreting data to make decisions.

What is Data?

• Data consists of information from observations, counts, measurements, or responses.

Data Sets

• Population: The collection of all possible outcomes, responses, measurements, or counts of interest.
• Sample: A subset of the population.

Parameter and Statistic

• Parameter: A number describing a population characteristic.
• Example: Average age of all people in a country.
• Statistic: A number describing a sample characteristic.
• Example: Average age of people from a sample of three states.

Example: Identifying Data Sets

• Population: Responses of all adults in the U.S.
• Sample: Responses of 1708 adults in the U.S. survey.
• Data Set: 939 "yes" and 769 "no" responses.

Example: Distinguish Parameter and Statistic

• Parameter: A recent survey of MBAs reported that the average salary for an MBA is over $82,000.
• This is a sample statistic, as it is based on a subset of the MBA population.

Branches of Statistics

• Descriptive Statistics: Organizing, summarizing, and displaying data (e.g., tables, charts, averages).
• Inferential Statistics: Using sample data to draw conclusions about a population.

Example: Descriptive and Inferential Statistics

• Descriptive: For unmarried men, approximately 70% were alive at age 65. For married men, 90% were alive at age 65.
• Inferential: Being married is associated with longer life for men.

Types of Data

• Qualitative Data: Attributes, labels, or non-numerical entries (e.g., place of birth, eye color).
• Quantitative Data: Numerical measurements or counts (e.g., age, weight, temperature).

Example: Classifying Data by Type

• Qualitative Data: Model names (e.g., Fusion 14 S, F-150 XL).
• Quantitative Data: Base prices of vehicles.

Levels of Measurement

• Nominal Level: Categorized using names, labels, or qualities (e.g., names of network affiliates, categories of survey responses).
• Ordinal Level: Qualitative or quantitative data that can be arranged in order (e.g., ranking of TV programs, socioeconomic levels).
• Interval Level: Quantitative data where differences between data entries are meaningful; zero does not imply none (e.g., temperatures in Celsius or Fahrenheit).
• Ratio Level: Quantitative data where differences between data entries are meaningful; zero does imply none and ratios are meaningful (e.g., height, weight, age, income, etc).

Example: Classifying Data by Level

• Nominal: Network affiliates for top five TV programs
• Ordinal: Ranking of five TV programs.

Levels of Measurement (Ratio)

• Similar to interval level
• Zero entry is inherent zero
• Ratio of two data values can be formed
• One data value can be expressed as a multiple of another

Example: Classifying Data by Level (Interval/Ratio)

• Interval: Home run totals by team
• Ratio: World Series victories by year

Designing a Statistical Study

• Identify variables of interest and the population.
• Develop a data collection plan (e.g., sample vs. population).
• Collect data.
• Describe data with descriptive stats.
• Interpret data with inferential stats.

Data Collection

• Observational Study: Observing and measuring characteristics of a population.
• Experiment: Applying a treatment to part of the population and observing responses.
• Simulation: Using a model to reproduce conditions of a situation or process.

Example: Methods of Data Collection

• Survey: Investigation of population characteristics.
• Observation: Measuring characteristics without intervention.
• Experiment: Applying a treatment and observing responses.
• Simulation: Using a mathematical/physical model (e.g. crash testing).

Key Elements of Experimental Design

• Control: Controlling for other effects not related to the treatment.
• Randomization: Randomly assigning subjects to treatment or control groups.
• Replication: Repeating the experiment with a large enough sample.
• Confounding Variables: Variables whose effects cannot be separated.

Key Elements of Experimental Design (Cont.)

• Placebos: A treatment with no active effect given to subjects in a control group.
• Blinding: Keeping subjects unaware of who is receiving treatment or a placebo.
• Double-Blind Experiment: Neither the subjects nor the experimenters know the treatment status.

Key Elements of Experimental Design (Replication)

• Replication: Repeating an experiment using a large sample size (e.g., an experiment testing a vaccine by giving it and a placebo to 2 groups of 10,000 people).

Example: Experimental Design

• A gum company wants to test its effectiveness for quitting smoking. The company identifies smokers and puts them into male and female groups. It is important to note that the sample size of one thousand is small. In this example the males and females are not considered similar enough. The company could divide smokers into groups based on health issues, habits, and other variables before assigning them or testing them.

Sampling Techniques

• Simple Random Sample: Every member of a population has an equal chance of being selected.

Example: Simple Random Sample

• Assign numbers to all members of the population. Randomly choose numbers for the sample.

Other Sampling Techniques

• Stratified Sample: Divide the population into subgroups (strata) and collect a random sample from each stratum.
• Cluster Sample: Divide population into groups and randomly select some of these groups to collect the sample data.
• Systematic Sample: Select members at regular intervals from a sorted list.

Example: Identifying Sampling Techniques

• Stratified: Dividing students by major before selecting a sample.
• Simple Random: Randomly selecting students from a numbered list.