🧑‍⚕️ Data, samples and study design

Where the numbers come from decides what you are allowed to conclude from them.

⭐ The one idea

You can almost never measure everyone. So you measure a sample, describe it with statistics, and use those to estimate the parameters of the whole population. Every later chapter is about how far that estimate can be trusted.

Population → sample → back againPOPULATION · μ, σ, pSAMPLE (n = 8)x̄, s, p̂statistics — you measure theseestimate μ, σ, pparameters — you never see these
Population → sample. Greek letters (μ, σ, p) are parameters of the population. Roman letters (x̄, s, p̂) are statistics from the sample.

👥 Population, sample, parameter, statistic

🌎 Population

Everyone you want to know about. All patients admitted with sepsis in the US this year. Its size is N.

🔍 Sample

The part you actually measure. 200 sepsis charts pulled from three hospitals. Its size is n.

Π Parameter

A number that describes the population: mean μ, SD σ, proportion p. Usually unknown.

📊 Statistic

A number that describes the sample: mean , SD s, proportion . You compute it.

🧠 Memory hook: Parameter ↔ Population, Statistic ↔ Sample. Descriptive statistics describe the sample; inferential statistics infer about the population.

🧩 Kinds of data

Which kind of data?DATAone value per personQUALITATIVElabels, no arithmeticNominalblood type, unit, sexOrdinalpain 0–10, stage I–IVQUANTITATIVEcounts and measuresDiscretenumber of falls or medsContinuoustemp, weight, BP, timeDiscrete = you COUNT it.Continuous = you MEASURE it.
Qualitative data are labels; quantitative data are numbers you can average. Quantitative splits into discrete (counted) and continuous (measured).

🔢 Discrete

Counted. Whole numbers with gaps. Number of falls this month, number of meds on the MAR, number of children, number of patients on the unit.

Ask: could it be 2.5? If not, it is discrete.

🌡️ Continuous

Measured. Any value in a range. Temperature 98.63 °F, weight 72.4 kg, time to first dose 17.5 min, hemoglobin 11.8 g/dL.

The only limit is how precise your instrument is.

📏 Levels of measurement (NOIR)

LevelWhat you can doNursing exampleTrap
Nominalname / categorize onlyblood type, unit, diagnosis code, sexno order — O is not “less than” AB
Ordinalrank in orderpain 0–10, Braden score, cancer stage, triage levelthe gaps are not equal: pain 8 is not twice pain 4
Intervalorder + equal gaps, no true zerotemperature in °F or °C, calendar year0 °C is not “no heat”, so ratios are meaningless
Ratioeverything, true zeroweight, blood pressure, urine output, heart rate, dose0 mL really means none — 200 mL is twice 100 mL

🎲 How to pick a sample

Four ways to pick 6 from 36gold = the people who end up inthe studySimple randomevery group of 6 equally likelyStratifieda few from EVERY row (age band)Clusterpick one whole rowSystematicevery 6th one on the listConvenience sampling — whoeveris easiest to reach — is fastand biased.
Simple random, stratified, cluster and systematic sampling. Only the first four give every patient a known chance of being chosen; a convenience sample does not.
MethodHowExample
Simple randomevery set of n has the same chance (random number generator on the whole list)pick 50 MRNs at random from all 900 admissions
Stratifiedsplit into groups that matter, sample within each10 from each age band so every band is represented
Clustersplit into natural groups, pick whole groupsrandomly pick 3 units and survey everyone on them
Systematicevery k-th person from a random startevery 10th chart in the file
Conveniencewhoever is nearbythe patients you happen to have today — biased

🧪 Study design

Observational or experiment?Did the researcher act?that is the first questionNO → Observationaljust watch and recordRetrospectivelook back at chartsProspectivefollow forward in timeYES → Experimentassign a treatmentRandomisedcoin-flip who gets itBlinded / placebonobody knows who got itOnly a randomised experiment canshow cause.
The first question is always: did the researcher assign the treatment? If not, it is observational and can show association, not cause.

👀 Observational

Researchers watch and record; nobody is assigned anything. Chart review of pressure-injury rates by turning schedule. Shows association only.

Retrospective looks back at existing records. Prospective follows people forward. Cross-sectional is one snapshot in time.

💉 Experiment

Researchers assign the treatment. Randomize 200 post-op patients to ice packs vs no ice packs and compare pain scores. The only design that can show cause.

Explanatory variable = the treatment. Response variable = the outcome you measure.

🎲 Randomization

Coin-flip assignment spreads unknown differences evenly between groups, so the groups start alike.

👁️ Blinding & placebo

Single-blind: subjects do not know their group. Double-blind: neither do the people measuring them. A placebo (sugar pill, saline) hides who got the real thing.

⚠️ Where bias sneaks in

🚫 Selection bias

The sample was not picked the way the population looks. Surveying only day-shift nurses about fatigue.

🚫 Nonresponse bias

The people who answered differ from those who did not. Only the angriest patients return the satisfaction survey.

🚫 Response bias

People answer wrong on purpose or by accident. Patients under-report drinks per week.

🚫 Confounding (lurking variable)

A hidden third factor drives both things. Coffee drinkers have more heart disease — because more of them smoke.

📚 Choosing a source (week 2)

Peer-reviewed journal > professional guideline (CDC, AHA) > textbook > news article > blog. Ask: who collected the data, how big was the sample, was it random, who paid for it, and is the full method published? A survey on a company’s own website that sells the product is not evidence.

✅ Quick self-check

❓ “Number of IV attempts before success” — discrete or continuous?
Discrete. You count attempts; 2.5 attempts is impossible.
❓ A nurse surveys the 40 patients on her floor about hospital food. Population? Sample? Type of sampling?
Population: all patients in the hospital (or all patients, depending on the claim). Sample: those 40. Convenience sample — likely biased.
❓ The mean age of every registered nurse in Utah is 43.1 years. Parameter or statistic?
Parameter — it describes the whole population (every RN in Utah).
❓ Pain rated 0–10 is what level of measurement?
Ordinal. It is ordered, but the distance from 3 to 4 is not necessarily the same as from 8 to 9.
MAT 300 · built from your own course files (the statistics study guide, the Desmos guide, the formula sheet and the final-exam study questions) with nursing examples. Not a substitute for the textbook — check any number against your own notes before an exam.