Page 1 of 49 11/6/2026, 2:14:38 AM Page 1
Introductory
Statistics |
Research Design,
Data Types, and
Statistical
Inference Study
Guide
Introductory Statistics _ Research
Introductory
Design, Data
Statistics
Types, _ Research
and Statistical
Design,
Inference
Data Types,
Study Guide.pdf
and Statistical Inference Study Guide 1 of 49
,Page 2 of 49 11/6/2026, 2:14:38 AM Page 2
Why we learn statistics
Statistics allows us to use data from a sample to learn about a larger population. It helps us
distinguish patterns supported by evidence from patterns that might occur by chance. For
example, if students who study more tend to earn higher grades, statistics helps us evaluate
how strong that relationship is and whether the observed pattern could reasonably be due
to chance.
Statistics
Methods for collecting, organizing, analyzing, and interpreting data
Population
The entire group we want to understand
Introductory Statistics_ Research Design, Data Types, and Inference.pdf
Introductory Statistics_ Research Design, Data Types, and Inference 2 of 49
,Page 3 of 49 11/6/2026, 2:14:38 AM Page 3
Sample
The subset of the population from which we collect data
Descriptive statistics
Methods used to summarize observed data
Inferential statistics
Methods used to draw conclusions about a population based on sample data
Introductory Statistics_ Research Design, Data Types, and Inference.pdf
Introductory Statistics_ Research Design, Data Types, and Inference 3 of 49
, Page 4 of 49 11/6/2026, 2:14:38 AM Page 4
Sampling error
The natural difference between a sample result and the corresponding population value
Simpson's paradox
A trend that appears in separate groups can reverse or disappear when the groups are
combined
Why intuition can be misleading
Human beings often see patterns in small samples, confuse correlation with causation, or
selectively notice evidence that supports existing beliefs. Statistics provides systematic
methods for evaluating those impressions. Consider a study finding that students who use a
tutoring service earn lower grades. Does tutoring cause lower grades? Not necessarily.
Students who are already struggling may be more likely to seek tutoring. This is an example
of why we must consider alternative explanations.
Introductory Statistics_ Research Design, Data Types, and Inference.pdf
Introductory Statistics_ Research Design, Data Types, and Inference 4 of 49
Introductory
Statistics |
Research Design,
Data Types, and
Statistical
Inference Study
Guide
Introductory Statistics _ Research
Introductory
Design, Data
Statistics
Types, _ Research
and Statistical
Design,
Inference
Data Types,
Study Guide.pdf
and Statistical Inference Study Guide 1 of 49
,Page 2 of 49 11/6/2026, 2:14:38 AM Page 2
Why we learn statistics
Statistics allows us to use data from a sample to learn about a larger population. It helps us
distinguish patterns supported by evidence from patterns that might occur by chance. For
example, if students who study more tend to earn higher grades, statistics helps us evaluate
how strong that relationship is and whether the observed pattern could reasonably be due
to chance.
Statistics
Methods for collecting, organizing, analyzing, and interpreting data
Population
The entire group we want to understand
Introductory Statistics_ Research Design, Data Types, and Inference.pdf
Introductory Statistics_ Research Design, Data Types, and Inference 2 of 49
,Page 3 of 49 11/6/2026, 2:14:38 AM Page 3
Sample
The subset of the population from which we collect data
Descriptive statistics
Methods used to summarize observed data
Inferential statistics
Methods used to draw conclusions about a population based on sample data
Introductory Statistics_ Research Design, Data Types, and Inference.pdf
Introductory Statistics_ Research Design, Data Types, and Inference 3 of 49
, Page 4 of 49 11/6/2026, 2:14:38 AM Page 4
Sampling error
The natural difference between a sample result and the corresponding population value
Simpson's paradox
A trend that appears in separate groups can reverse or disappear when the groups are
combined
Why intuition can be misleading
Human beings often see patterns in small samples, confuse correlation with causation, or
selectively notice evidence that supports existing beliefs. Statistics provides systematic
methods for evaluating those impressions. Consider a study finding that students who use a
tutoring service earn lower grades. Does tutoring cause lower grades? Not necessarily.
Students who are already struggling may be more likely to seek tutoring. This is an example
of why we must consider alternative explanations.
Introductory Statistics_ Research Design, Data Types, and Inference.pdf
Introductory Statistics_ Research Design, Data Types, and Inference 4 of 49
