Section1.3
Chapter 1: Introduction to Statistics
Overview
Textbook: Elementary Statistics, Fourteenth Edition
Publisher: Pearson Education, Inc.
Years of Publication: 2022, 2018, 2014
1-1 Statistical and Critical Thinking
Importance of statistical and critical thinking in understanding data and making informed decisions.
1-2 Types of Data
Distinction between different types of data (nominal, ordinal, interval, ratio) and their implications for analysis.
1-3 Collecting Sample Data
Emphasis on using appropriate methods for collecting sample data.
Simple random sample is crucial for valid conclusions.
Poor sampling methods can render data unusable, resisting attempts at statistical manipulation.
Key Concept
Sample Data Collection:
Use appropriate methods to avoid useless data.
Simple Random Sample is particularly emphasized.
The Gold Standard
Randomness in Placebo/Treatment Groups:
Effective method referred to as the “gold standard.”
Placebo: A non-effective pill or procedure used for psychological or comparative purposes.
Example: Sugar pill has no medicinal effect but serves as a control in experiments.
Basics of Collecting Data
Data collection methods:
Observational Studies: Collect data without altering the subjects.
Experiments: Involve applying treatments and observing effects.
Experiment vs Observational Study
Experiment
Definition: Applying treatment and observing its effects on subjects (individuals in experiments).
Observational Study
Definition: Observing specific characteristics without modifying the participants.
Example of Misinterpretation
Ice Cream and Drownings (Observational Study):
Confusion arises when correlating ice cream sales with drownings.
Failure to recognize temperature as a lurking variable affecting both.
Improved Analysis through Experiments
Ice Cream and Drownings (Experiment):
Ice cream consumption does not affect drowning rates if appropriately tested with control groups.
Design of Experiments
Key Concepts
Replication: Repeating experiments with sufficient sample size to observe treatment effects.
Blinding: Ensuring subjects are unaware of receiving treatment vs placebo (reduces placebo effect).
Double-Blind: Both subjects and experimenters are unaware of assignments.
Randomization: Subjects randomly assigned to groups to ensure similarity.
Types of Sampling
Simple Random Sample
Definition: Selection where each sample has an equal chance of selection.
Systematic Sampling
Definition: Selecting every kth element from a starting point.
Convenience Sampling
Definition: Using readily available data.
Stratified Sampling
Definition: Dividing population into strata and sampling from each.
Cluster Sampling
Definition: Dividing population into clusters, randomly selecting some, and sampling all members.
Multistage Sampling
Definition: Using combination methods of basic sampling techniques.
Types of Observational Studies
Cross-sectional: Data is collected at a single point in time.
Retrospective (Case Control): Data is collected from past records and interviews.
Prospective (Cohort): Data is collected in the future from common factor groups.
Confounding
Definition: Unable to identify the specific cause of an observed effect.
Importance of planning to prevent confounding effects in experiments.
Controlling Effects of Variables
Randomized Designs
Completely Randomized Experimental Design: Random selection for treatment groups.
Randomized Block Design: Grouping similar subjects and randomly assigning treatments within blocks.
Matched Pairs Design: Comparing treatment groups with matched subjects.
Rigorously Controlled Design: Carefully assigning subjects to maintain similarity in important factors.
Sampling Errors
Types of Errors
Sampling Error: Discrepancies between sample results and true population results due to chance.
Nonsampling Error: Result from human error, biased data, improper statistical application.
Nonrandom Sampling Error: Use of non-random sampling methods leading to biased results.