뒤로Introduction to Statistics and Collecting Data: Mini-Textbook Study Notes
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Intro to Statistics and Collecting Data
Introduction to Statistics
Statistics is the science of collecting, organizing, analyzing, and interpreting data to make informed decisions. Understanding the difference between populations and samples, as well as parameters and statistics, is foundational in statistical analysis.
Data: Information gathered from counting, measuring, or collecting responses.
Population: The entire set containing all data points 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: The salary of every employee at a marketing firm is a population; the average salary of all employees is a parameter. The salaries of 12 out of 100 employees is a sample; the average salary of those 12 is a statistic.
Practice: Population vs. Sample and Parameter vs. Statistic
Collecting test scores of 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 qualitative or quantitative, and quantitative data can be further classified as discrete or continuous.
Qualitative Data: Describes qualities or categories (e.g., favorite color, eye color).
Quantitative Data: Describes quantities or amounts and can be measured.
Discrete: Countable values that cannot be broken down further (e.g., dice roll, number of students).
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: Types of Data
Brands of smartphones owned: Qualitative
Number of goals scored in a match: Quantitative; Discrete
Time to complete a lap: Quantitative; Continuous
Levels of Measurement
Overview of Levels
Levels of measurement describe the nature of information within the values assigned to variables. They determine what kinds of statistical analysis are appropriate.
Level | Description | Qualitative/Quantitative | Example |
|---|---|---|---|
Nominal | Categories, names, or labels; no order or calculations | Either | Hair color |
Ordinal | Ordered categories; differences not meaningful | Either | Letter grades |
Interval | Ordered, meaningful differences; no true zero | Quantitative | Temperature |
Ratio | Ordered, meaningful differences; true zero exists | Quantitative | Heights, distances |
Example: Birth years (interval), satisfaction ratings (ordinal), working hours (ratio), favorite music genre (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 does not have a true zero.
Collecting Data
Observational Studies vs. Experiments
There are two main ways to collect data: observational studies and experiments. The method chosen affects whether causation can be inferred.
Experiment: Apply a treatment and measure its effects; causation can be inferred.
Observational Study: Observe and measure characteristics without intervention; causation cannot be inferred.
Example: Testing a medication with a placebo group is an experiment; surveying students about sleep habits is an observational study.
Practice: Data Collection Methods
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 larger group (population). A representative sample accurately reflects the characteristics of the population. In SRS, each subject and each possible group are equally likely to be chosen.
Representative Sample: Has the same proportions of characteristics as the population.
Simple Random Sample: Each member and group has an equal chance of selection.
Example: Randomly selecting 3 marbles from a bag is SRS; surveying only undergrads and grads in the same proportion as the population is representative.
Other Sampling Methods
When SRS is not practical, other sampling methods are used:
Systematic Sampling: Select every k-th subject from the population.
Cluster Sampling: Divide the population into groups (clusters), then randomly select entire clusters.
Stratified Sampling: Divide the population into groups (strata) based on shared characteristics, then randomly sample from each stratum.
Example: Testing every 12th cookie is systematic sampling; surveying 50 undergrads and 50 grads is stratified sampling; randomly selecting one class per grade is cluster sampling.
Practice: Sampling Methods
Selecting every tenth unit for inspection: Systematic Sampling
Randomly selecting 100 out of 1500 units: Simple Random Sampling
Taking 10 random units from each of 10 machines: Stratified Sampling
Summary Table: Sampling Methods
Method | Description | Example |
|---|---|---|
Simple Random | Each subject/group equally likely | Randomly select 15 employees |
Systematic | Select every k-th subject | Test every 12th cookie |
Cluster | Randomly select entire groups | Survey all students in one class per grade |
Stratified | Sample from each subgroup | Survey 50 undergrads & 50 grads |
Additional info: These foundational concepts are essential for understanding more advanced topics in statistics, such as probability, hypothesis testing, and inferential statistics.
