Intro to Statistics and Collecting Data

Statistics: Definition and Scope

Statistics is the science of collecting, organizing, analyzing, and interpreting data to make informed decisions. It involves working with data sets that represent information gathered from counting, measuring, or collecting responses.

• Data: Information collected from observations, measurements, or responses.

• Population: The entire set of individuals or items of interest ("every," "each").

• Sample: A subset of the population, selected for analysis.

• Parameter: A numerical value that describes a characteristic of a population.

• Statistic: A numerical value that describes a characteristic of a sample.

Example: If you measure the salary of every employee at a marketing firm, you are working with a population and the average salary is a parameter. If you measure the salary of 12 out of 100 employees, you have a sample and the average salary is a statistic.

Practice: Identifying Populations, Samples, Parameters, and Statistics

• Collecting test scores from every other student in a class: Sample

• 46.5% of all registered voters are registered democrats: Parameter

• Amount spent by each customer in a grocery store: Population

• Average workout duration from a survey of 40 gym members: Statistic

Types of Data

Qualitative vs. Quantitative Data

Data can be categorized as either qualitative or quantitative, each with distinct characteristics and uses.

• Qualitative Data: Describes qualities or categories (e.g., favorite color, eye color).

• Quantitative Data: Represents quantities and can be measured numerically.

  • Discrete: Countable values (e.g., number of students, dice rolls).

  • Continuous: Measurable values that can take any value within a range (e.g., time, temperature).

Example: Surveying nationalities is qualitative; measuring distances walked is quantitative and continuous.

Practice: Data Types

• Brands of smartphones: Qualitative

• Number of goals scored in a match: Quantitative; Discrete

• Time to complete a lap: Quantitative; Continuous

Levels of Measurement

Understanding Levels of Measurement

Levels of measurement describe the nature of information within the values assigned to variables. They determine what kinds of statistical analysis are appropriate.

Example: Birth years are interval; satisfaction ratings are ordinal; working hours are ratio; favorite music genre is nominal.

Practice: Levels of Measurement

• Symptoms rated as mild, moderate, severe: Ordinal

• Birth weights of newborns: Ratio

• Favorite menu item: Nominal

• Dates of establishment: Interval

Example: Temperature data is interval; saying 80°F is twice as hot as 40°F is incorrect because the interval scale lacks a true zero.

Collecting Data: Observational Studies vs. Experiments

Methods of Data Collection

There are two main ways to collect data in statistics:

• Experiment: Researchers apply a treatment and measure its effects. Causation can be inferred.

• Observational Study: Researchers observe and measure characteristics without influencing them. Causation cannot be inferred.

Example: Giving a medication to one group and a placebo to another is an experiment. Surveying students about sleep habits is an observational study.

Practice: Identifying Study Types

• Surveying customers about a product: Observational Study; cannot infer causation.

• Testing a new app for fitness: Experiment is needed to infer causation.

Sampling Methods

Simple Random Sampling (SRS)

Sampling is the process of selecting a subset (sample) from a population for analysis. A representative sample accurately reflects the characteristics of the population.

• Simple Random Sampling (SRS): Every subject and every possible group of subjects is equally likely to be selected.

Example: Randomly selecting marbles from a bag or using a random number generator to select gym members.

Other Sampling Methods

• Systematic Sampling: Select every nth subject from the population.

• Cluster Sampling: Divide the population into groups (clusters), randomly select clusters, and include all members from selected clusters.

• Stratified Sampling: Divide the population into strata (groups with shared characteristics), then randomly sample from each stratum.

Example: Testing every 12th cookie (systematic), surveying random undergrads and grad students (stratified), or selecting random classes (cluster).

Practice: Sampling Methods

• Testing every tenth unit: Systematic Sampling

• Randomly selecting units: Simple Random Sampling

• Sampling from each machine: Stratified Sampling

• Randomly selecting cases: Cluster Sampling

Summary Table: Sampling Methods