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.