Statistical Studies &
Sampling Methods

Key word: "monitors" and "no dietary changes suggested." In an observational study, researchers record what is already happening without assigning any treatment. If the nutritionist had told some people to change their diet, it would be an experiment. The fact that participants are already eating a certain way (already "affected") and nothing is changed makes this observational.

This is a Sample Survey because parents are being asked questions (no treatment assigned). The sampling method is Self-Selected because parents choose whether to respond. This creates extreme bias — only parents with strong opinions (usually those who strongly oppose or strongly support) tend to respond. Don't confuse this with Convenience sampling, which is about proximity, not voluntary participation.

The control group does not receive the real treatment — it's the baseline for comparison. Group B (placebo) is the control group. Group A is the experimental group. Note: the control group doesn't have to receive "nothing" — a placebo counts. The purpose is to isolate whether the treatment (drug) caused any difference by comparing to a group without it.

This mirrors the wildlife researcher example exactly. Key signals: recording/counting natural behavior, no intervention, subjects (birds) are already behaving naturally. The researcher is purely observing. This is a classic Observational Study.

This is one of the most important concepts: observational studies show association, not causation. The doctor observed a pattern but didn't randomly assign coffee consumption — maybe anxious people drink more coffee, or a third factor (like work stress) causes both. Only a randomized experiment can establish cause-and-effect. This is why experiments are the gold standard in research.

Simple Random Sampling: assigning a number to everyone and using a random generator is the textbook definition. Every individual has an equal probability of selection. Don't confuse "using numbers" with Systematic — Systematic requires a fixed interval rule (like every 5th person). Here, the selection is purely random with no interval pattern.

Stratified vs. Cluster is the most commonly confused pair. The key: in Stratified, you divide by a characteristic (age, gender, grade) and pick some individuals from each group. In Cluster, you pick entire groups at random. Here: age groups are formed → individuals randomly selected from each → Stratified. ✓

Cluster: the schools are the "clusters." The key word is "every student" in the selected schools — the entire cluster is included, not a random sample from each. If the researchers had surveyed only some students from each of the 5 schools, it might be Stratified. But including ALL students from randomly chosen schools = Cluster.

Systematic sampling = random start + fixed interval rule. The random start (product #7) ensures the beginning isn't biased, but after that, a rule takes over: check #7, #17, #27, #37… This is NOT Simple Random because the remaining selections are not random — they're determined by the rule once the start is set.

Convenience sampling: surveying whoever is easy to access. The bias: people near city hall likely work in government or have strong opinions about it — not representative of the whole city. This is different from Self-Selected because the reporter is doing the selecting (approaching people), not participants volunteering themselves.

This is question wording bias. The phrase "Don't you agree..." is a leading question — it implies the "correct" answer is yes. Bias in surveys can arise not just from who you ask, but how you ask it. A neutral version: "Do you support extending the lunch period?" Both the sample selection AND the question design can create bias.

Self-selected sampling = greatest chance of biased results. People who feel strongly (e.g., drivers who hate lower speed limits) are far more motivated to respond than those who are indifferent. The 10,000 responses sound impressive but represent a biased subset, not the general population. Larger sample size does NOT fix selection bias.

Even though lying is a valid concern, the primary statistical reason is that surveys/observational studies cannot establish causation. A confounding variable (like study habits, stress level, or socioeconomic status) might cause both better sleep and better scores. To prove causation, you'd need a randomized experiment where sleep amount is actually controlled and randomly assigned.

Surveying everyone in a conveniently accessible group (ICU on Tuesday) is Convenience sampling. ICU patients are seriously ill and have a very different care experience than other patients. The sample misrepresents the population (all hospital patients). Even if 100% of ICU patients respond, the sample itself is biased — coverage bias, not response bias.

Ultimate Stratified vs. Cluster test:
Stratified → divide into groups, select some from each group.
Cluster → select entire groups at random, include everyone.
Here: 5 ZIP codes chosen at random, ALL households included → Cluster. The "randomly chosen" ZIP codes are clusters, not strata.

Random assignment is what makes an experiment powerful. If subjects chose their own group, healthier/more motivated people might choose the treatment — making it look like the treatment works when it's actually just healthier people doing better. Random assignment spreads unknown confounders (age, health, lifestyle) approximately equally, isolating the treatment effect.

Students in the library during 3rd period are selected because they are accessible, not because of any random process. This is Convenience sampling. The bias: library students during class time likely have stronger study habits than the average student — severely misrepresenting the school population. It's also a survey (asking questions), not an observational study (just watching).

This IS an experiment (treatment is assigned), and there IS a control group (old plan). But the assignment is NOT random. Alphabetical order can correlate with cultural background, which may relate to baseline fitness, diet, or other factors. For a valid experiment, groups must be formed by true random assignment, not any systematic method that could correlate with the outcome.

This is an example of coverage bias — the sampling method systematically excludes certain groups. Young adults (especially college students and 18–35 age group) predominantly use mobile phones and don't have landlines. This skews survey results toward older demographics. This is why modern surveys must use multiple contact methods or random digit dialing including mobile numbers.

The hardest question! Here's the key: neighborhoods are used as strata (groups defined by a geographic characteristic). From each selected stratum (neighborhood), a random sample of individuals is taken — NOT all residents. This is Stratified sampling. If she had included ALL 50,000 residents of each selected neighborhood, it would be Cluster. The partial selection within each group = Stratified. ✓