Triola Elementary Statistics · 11th Edition
Chapter 1: Introduction to Statistics
Every key formula from Triola Elementary Statistics Chapter 1, in one searchable page. Click a card to study it — worked examples included.
1.2 · STATISTICAL THINKING
Never blindly accept calculations. Statistical thinking means asking:
The 5 big-picture checks
Context · Source · Sampling method · Conclusions · Practical implications
What do the values mean? Who collected them? How were they obtained?
What can we conclude? What real-world action follows?
What can we conclude? What real-world action follows?
KEY NOTES
- Context first: numbers without context (like Table 1-1’s raw x, y values) tell you nothing.
- Common sense and practical considerations beat cookbook formulas.
- A bad sampling method poisons every calculation that follows.
Voluntary response sample
Subjects choose whether to respond — results are generally useless for inferring about the larger population.
1.3 · TYPES OF DATA
Parameter vs statistic
Parameter = number describing a population · Statistic = number describing a sample
55% of all 100 Senators ⇒ parameter; 57% of a 2.3M-person poll ⇒ statistic.
Quantitative vs categorical
Quantitative = counts or measurements · Categorical = names or labels
Basketball jersey numbers are categorical (substitutes for names) — never do arithmetic on them.
Discrete vs continuous
Discrete = finite or countable · Continuous = infinitely many, no gaps
Eggs laid ⇒ discrete (counts). Liters of milk ⇒ continuous (5678.1234 L is possible).
Fewer cans vs less cola — grammar follows the type.
Fewer cans vs less cola — grammar follows the type.
1.4 · SAMPLING METHODS
Systematic
Pick a starting point, then every kth element (every 50th).
Convenience
Use whatever results are easiest to get — risky.
Stratified
Split population into strata (gender, age), then sample from EVERY stratum.
Cluster
Divide into clusters, randomly pick some clusters, survey ALL members of the chosen clusters.
KEY NOTES
- Stratified vs cluster: stratified = some members from all groups; cluster = all members from some groups.
- Neither satisfies the simple-random-sample requirement — pollsters often weight/adjust the results.
1.3 · LEVELS OF MEASUREMENT
Nominal
Names, labels, categories only — no ordering.
Ex: yes/no/undecided, political party. (No averaging Social Security numbers!)
Ex: yes/no/undecided, political party. (No averaging Social Security numbers!)
Ordinal
Ordered, but differences are meaningless — usually no calculations.
Ex: course grades A–F (GPA is the famous exception).
Ex: course grades A–F (GPA is the famous exception).
Interval
Differences meaningful, but no natural zero — ratios are meaningless.
Ex: body temperatures (°F), calendar years.
Ex: body temperatures (°F), calendar years.
Ratio
Natural zero — differences and ratios are meaningful.
Ex: distances (400 km is twice 200 km). Test: 50°F is NOT twice as hot as 25°F.
Ex: distances (400 km is twice 200 km). Test: 50°F is NOT twice as hot as 25°F.
1.4 · OBSERVE vs EXPERIMENT
Observational study
Observe and measure, but do not modify the subjects. Ex: an election poll.
Experiment
Apply a treatment, then observe its effects. Subjects = experimental units.
Ex: Salk vaccine trial — 200,745 got the vaccine, 201,229 got a placebo.
Ex: Salk vaccine trial — 200,745 got the vaccine, 201,229 got a placebo.
Study designs
Cross-sectional: data collected at one point in time.
Retrospective (case-control): data from the past.
Prospective (longitudinal/cohort): data collected going forward.
Retrospective (case-control): data from the past.
Prospective (longitudinal/cohort): data collected going forward.
1.4 · COLLECTING SAMPLE DATA
Simple random sample
Every possible sample of size n has the same chance of being chosen.
Many procedures in this book require a simple random sample.
Random vs probability sample
Random sample: each individual has an equal chance of selection.
Probability sample: each member has a known (not necessarily equal) chance.
Probability sample: each member has a known (not necessarily equal) chance.
WORKED EXAMPLE
Pick 1 of 50 state cards; use that state’s 2 senators.
Random? Yes — each senator has a 1/50 chance.
Simple random? No — you can never pick 2 senators from different states.
Probability? Yes — each chance is known.
Random? Yes — each senator has a 1/50 chance.
Simple random? No — you can never pick 2 senators from different states.
Probability? Yes — each chance is known.
WATCH OUT!
Mistakes that cost points
- Never average categorical data (jersey numbers, SSNs)
- Ordinal data usually get no calculations — differences are meaningless
- “Twice as much” is meaningless without a natural zero (interval data)
- Random sample ≠ simple random sample — check the definition
- Cluster = all members of chosen clusters; stratified = some members of all strata
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