Ten cards, in the order an intro statistics or research-methods course usually takes them. Read each term in plain words, then follow the worked examples. Jump to the card you need:
Study card 1
Qualitative vs quantitative
Qualitative data put each person or thing into a category, usually with words. Quantitative data are numbers that come from counting or measuring. The fast check: could you take a meaningful average of it? A mean blood type makes no sense (qualitative); a mean pulse rate does (quantitative).
The terms
Qualitative (categorical) data
Labels that sort things into groups: words, or numbers used only as labels.
Example: Blood type, hair color, zip code, the make of a car, yes or no.
Quantitative data
Numbers from counting or measuring, where arithmetic makes sense.
Example: Pulse rate, weight, dollars spent, number of children.
Quantitative discrete
Counted: only certain values are possible.
Example: Number of phone calls in a day: 0, 1, 2, never 2.5.
Quantitative continuous
Measured: any value in a range is possible, including decimals.
Example: Length of a call in minutes, body weight, time to finish a task.
Qualitative vs quantitative research
The same words describe whole studies. A qualitative study collects words (interviews, open answers, field notes) and looks for themes. A quantitative study collects numbers and analyzes them with statistics. Some studies combine the two (mixed methods).
Example: Interviews about what makes a shift feel safe (qualitative); the number of falls per 1,000 patient days before and after a change (quantitative).
The four levels of measurement
A finer sort, from least to most information. It decides which statistics make sense: you can rank ordinal data but not average it.
Nominal
Categories with no order.
Example: Favorite food, yes or no, blood type.
Ordinal
Can be ranked, but the gaps between ranks are not measured amounts.
Example: A five-point agreement scale (strongly disagree, disagree, neutral, agree, strongly agree: a Likert scale), a top-five ranking.
Interval
Numbers with meaningful differences but no true zero, so ratios mean nothing.
Example: Temperature in degrees Fahrenheit or Celsius: 0° is not "no temperature," and 40° is not twice as hot as 20°.
Ratio
Numbers with a true zero, so ratios make sense.
Example: Scores out of 100, weight, time: 80 is four times 20.
Worked examples
Sort these: blood type, number of ER visits last year, satisfaction rated 1 to 5, body temperature
- Blood type is a label: qualitative (nominal).
- Number of ER visits is counted: quantitative, discrete.
- A 1-to-5 rating is ranked but the gaps are not fixed amounts: ordinal. Many courses treat it as qualitative data.
- Body temperature is measured: quantitative, continuous (interval level in degrees).
Answer: Qualitative; discrete; ordinal; continuous
Is a zip code quantitative?
- It is written with digits, but it only labels a place.
- Adding two zip codes or averaging them means nothing.
Answer: No: qualitative (nominal). A number used as a label is still a label.
Watch out: Numbers are not automatically quantitative. Jersey numbers, zip codes and ID numbers are labels. Ask what the number does: counts or measures (quantitative) or names (qualitative).
Study card 2
Independent vs dependent variables
In an experiment the researcher changes one thing on purpose and measures what happens to another. The thing changed is the independent variable; the thing measured is the dependent variable. Statistics courses call the same pair the explanatory variable and the response variable.
The terms
Independent variable (IV)
What the researcher manipulates or sets: the suspected cause. Its different settings are called levels or treatments.
Example: Study method: flashcards vs rereading.
Dependent variable (DV)
What is measured to see the effect. It "depends on" the independent variable.
Example: Score on the next exam.
Experimental group
The group that gets the treatment or change being studied.
Example: Units that start hourly rounding.
Control group
The comparison group that gets no treatment, the usual routine, or a placebo. Without it you cannot tell whether the change did anything.
Example: Units that keep their usual routine.
Placebo
An inactive treatment that looks like the real one, so expectations alone can be separated from the treatment’s effect.
Example: A sugar pill in a medication study.
Random assignment
Putting participants into groups by chance (a coin flip, a random-number list). It spreads hidden differences evenly, so a difference at the end can be credited to the treatment.
Example: Each volunteer lands in a group by a random-number list.
Confounding (lurking) variable
A third factor that changes along with the independent variable and could explain the result instead.
Example: People who choose to take vitamin E may also exercise more.
Operational definition
The exact way a variable will be measured, so someone else could repeat the study.
Example: "Stress" = the score on a 10-item stress scale, not a feeling.
Worked examples
Does a 10-minute breathing exercise before a skills check-off lower anxiety? Name the variables.
- What the researcher controls: whether the student does the exercise. That is the independent variable.
- What is measured afterward: the anxiety score. That is the dependent variable.
- Groups: breathing exercise (experimental) vs no exercise (control).
Answer: IV = breathing exercise or not; DV = anxiety score
Two units record call-light use. One starts hourly rounding. What is being measured?
- Hourly rounding is the change the unit makes: the independent variable.
- The number of call-light uses is what is counted to see the effect: the dependent variable.
Answer: DV = number of call-light uses
A study compares reaction time after 0 mg, 100 mg and 200 mg of caffeine.
- Caffeine dose is set by the researcher: the independent variable, with three levels.
- Reaction time is measured: the dependent variable.
Answer: IV = caffeine dose (three levels); DV = reaction time
Watch out: Write the study as "the effect of ___ on ___." The first blank is the independent variable, the second the dependent variable. If the researcher only observes a variable instead of setting it (age, sex, smoking status), the study is not a true experiment and cannot prove cause.
Study card 3
Mean, median, mode and range by hand
Three ways to say where the middle of a data set is, and one quick way to say how spread out it is. Always sort the values from smallest to largest first: the median and the range depend on it, and the mode is easier to spot.
The terms
Mean
Add every value, then divide by how many there are. The everyday "average." The symbol x̄ (x-bar) is a sample mean; μ (mu) is a population mean.
Example: 3, 7, 7, 9, 14: sum 40 ÷ 5 = 8
Median
The middle value of the sorted list. With an even count, the average of the two middle values. Its position is (n + 1) ÷ 2.
Example: 3, 7, 7, 9, 14: the 3rd value, 7
Mode
The value that appears most often. A set can have two modes (bimodal) or none at all. It is the only one of the three that works for categories too.
Example: 3, 7, 7, 9, 14: 7
Range
Largest value minus smallest value. A quick, rough measure of spread that only looks at the two ends.
Example: 3, 7, 7, 9, 14: 14 − 3 = 11
Outlier
A value far from the rest. It pulls the mean toward it but barely moves the median, which is why the median is the better "typical" value for skewed data such as incomes or wait times.
Example: Incomes of 30k, 32k, 35k, 40k and 5 million: median 35k, mean over 1 million
Worked examples
Find the mean, median, mode and range of 6, 2, 9, 2, 11, 6, 6
- Sort: 2, 2, 6, 6, 6, 9, 11 (n = 7).
- Mean: 2 + 2 + 6 + 6 + 6 + 9 + 11 = 42, and 42 ÷ 7 = 6.
- Median: position (7 + 1) ÷ 2 = 4, and the 4th value is 6.
- Mode: 6 appears three times.
- Range: 11 − 2 = 9.
Answer: Mean 6, median 6, mode 6, range 9
Median of an even count: 12, 3, 8, 5, 20, 7
- Sort: 3, 5, 7, 8, 12, 20 (n = 6).
- Position (6 + 1) ÷ 2 = 3.5, so halfway between the 3rd and 4th values.
- (7 + 8) ÷ 2 = 7.5.
Answer: Median 7.5
Shift lengths in hours: 8, 8, 8, 8, 12. Mean vs median
- Mean: 44 ÷ 5 = 8.8 hours.
- Median: the 3rd of 5 sorted values, 8 hours.
- The one 12-hour shift pulls the mean up; the median still says a typical shift is 8 hours.
Answer: Mean 8.8, median 8
Mode of 4, 4, 7, 9, 9, 10
- 4 appears twice and 9 appears twice; nothing appears more.
- Two modes: the set is bimodal.
Answer: Modes 4 and 9
Watch out: Forgetting to sort is the number-one median mistake: the median of 12, 3, 8 is 8 (sorted 3, 8, 12), not 3. And the mean of a list with repeats counts every repeat: 8, 8, 8, 8, 12 has five values, so divide by 5.
Study card 4
Percent change formula
Percent change compares a change with where it started: how big the move is relative to the original amount. Research results, budgets and lab values all report it, and the one rule that matters is to divide by the original value, never the new one.
The terms
Percent change
Percent change = (new − original) ÷ original × 100. Positive means an increase, negative a decrease.
Example: 40 → 50: (50 − 40) ÷ 40 = 0.25 = 25% increase
Percent decrease
Same formula; the result comes out negative. Report it as "a 20% decrease" or "−20%."
Example: 50 → 40: (40 − 50) ÷ 50 = −0.20 = 20% decrease
New amount from a percent
Original × (1 + rate) for an increase, original × (1 − rate) for a decrease.
Example: 40 up 15%: 40 × 1.15 = 46
Percentage points
The plain difference between two percents. Not the same as percent change.
Example: 10% → 15% is 5 percentage points, but a 50% increase
Worked examples
A clinic’s average wait falls from 60 minutes to 45. Percent change?
- Change: 45 − 60 = −15.
- Divide by the original: −15 ÷ 60 = −0.25.
- Times 100: −25%.
Answer: A 25% decrease
Enrollment grows from 80 to 100.
- Change: 100 − 80 = 20.
- 20 ÷ 80 = 0.25.
- A 25% increase.
Answer: +25%
Why is 40 → 50 a 25% increase but 50 → 40 only a 20% decrease?
- Both changes are 10.
- Up from 40: 10 ÷ 40 = 25%. Down from 50: 10 ÷ 50 = 20%.
- The original amount is different, so the percent is different.
Answer: The denominator changed
A measure rises 15% from 40. New value?
- 15% of 40 = 0.15 × 40 = 6.
- 40 + 6 = 46 (or 40 × 1.15 in one step).
Answer: 46
Watch out: Dividing by the new value instead of the original is the classic slip: 60 → 45 is −25% (÷ 60), not −33% (÷ 45). And "the rate went from 10% to 15%" is a 5-point rise and a 50% increase; say which one you mean.
Study card 5
Population vs sample
A population is the whole group you want to know about. A sample is the smaller group you actually measure. Statistics exists because measuring everyone is usually impossible, so you measure a sample and use it to estimate the population.
The terms
Population
Every person or thing the question is about.
Example: All registered nurses in one state.
Sample
The part of the population you collect data from. It should look like the population (be representative).
Example: 400 of those nurses, chosen at random.
Parameter
A number that describes the population. Usually unknown; it is what you want to estimate.
Example: The mean age of all the nurses, μ.
Statistic
A number calculated from the sample. It estimates the parameter.
Example: The mean age of the 400, x̄ = 38.
Variable and data
The variable is the characteristic recorded for each member, such as age or blood type. Data are the actual values.
Example: X = years of experience; data: 2, 11, 7, …
Descriptive vs inferential
Descriptive statistics summarize the data you have (graphs, averages). Inferential statistics use a sample to draw conclusions about the population, with a stated level of confidence.
Example: "The 400 averaged 38" is descriptive; "we estimate all nurses average 36 to 40" is inferential.
Worked examples
A researcher surveys 200 of a hospital system’s 3,000 nurses about burnout. Label each piece.
- The 3,000 nurses: population.
- The 200 surveyed: sample.
- The average burnout score of the 200: a statistic.
- The average score of all 3,000, which no one measured: the parameter being estimated.
Answer: Population 3,000; sample 200; statistic from the sample; parameter for the population
Which is the parameter: the 52% of 1,000 polled adults who said yes, or the share of all adults who would say yes?
- The 52% comes from the sample: a statistic.
- The share of all adults is a population number: the parameter.
Answer: The share of all adults
Watch out: Same first letter: Population → Parameter, Sample → Statistic. A statistic changes from sample to sample; the parameter is one fixed (unknown) number.
Study card 6
Sampling methods
How the sample is chosen decides whether it can stand in for the population. Random methods give every member a known chance of being picked; convenience methods do not, and they are where bias creeps in.
The terms
Simple random sample
Every group of the chosen size has the same chance of being picked: names from a hat or a random-number list.
Example: Number all 3,000 nurses, draw 200 numbers at random.
Stratified sample
Split the population into groups (strata) that matter, then randomly sample from every group in proportion.
Example: Day shift and night shift, random picks from each.
Cluster sample
Split the population into natural clusters, randomly pick some clusters, and include everyone in the chosen ones.
Example: Randomly choose 5 of 40 units and survey every nurse on those 5.
Systematic sample
Start at a random point on a list, then take every nth member.
Example: A random start, then every 15th name.
Convenience sample
Whoever is easy to reach. Not random, and often biased.
Example: Handing a survey to the people in the break room.
Sampling bias
Some members of the population had less chance of being chosen, so the sample leans one way. Self-selected samples (whoever answers a posted link) are a common case.
Example: A call-in poll only hears from people who feel strongly.
Sampling error
The natural gap between a sample statistic and the population parameter, just because a sample is not the whole population. Bigger samples shrink it; bias does not shrink with size.
Example: Two random samples of 50 give means of 37 and 39.
Worked examples
Name the method: a school picks every 20th student on an alphabetical list after a random start.
- A fixed interval along a list, with a random start.
Answer: Systematic
Name the method: a hospital divides staff into RNs, LPNs and aides, then randomly picks 30 from each group.
- The population was first divided into meaningful groups.
- A random sample was taken inside every group.
Answer: Stratified
Name the method: a researcher randomly selects 6 clinics and surveys every patient at those 6.
- Whole clinics were picked at random.
- Everyone inside the chosen clinics is included.
Answer: Cluster
A survey link posted on social media gets 2,000 answers. Can the results describe all adults?
- Only people who saw the link and chose to answer are in it: a self-selected convenience sample.
- Size does not fix bias: 2,000 biased answers are still biased.
Answer: No
Watch out: Stratified vs cluster: a stratified sample takes SOME members from EVERY group; a cluster sample takes ALL members from SOME groups.
Study card 7
P-values and hypotheses in plain words
Hypothesis testing starts by assuming nothing is going on (the null hypothesis), then asks how surprising the sample would be if that were true. The p-value is that surprise, as a probability. A small p-value means the data would be rare under "nothing is going on," so you reject that idea.
The terms
Null hypothesis (H₀)
The "no effect, no difference" statement: the treatment does nothing, the two groups have the same mean, the coin is fair. It is assumed true until the data say otherwise.
Example: H₀: mean recovery time is the same with or without the new protocol.
Alternative hypothesis (Hₐ)
What the researcher suspects instead: there is an effect or a difference.
Example: Hₐ: recovery time is shorter with the protocol.
P-value
The probability of getting a sample result at least as extreme as the one observed, if the null hypothesis were true. It is not the probability that the null hypothesis is true.
Example: p = 0.03: if the protocol did nothing, a difference at least this large would show up in about 3 of every 100 such studies.
Significance level (α, alpha)
The cut-off chosen before the study, usually 0.05. It is the chance of a false alarm you are willing to accept.
Example: α = 0.05 means a 5% risk of a Type I error.
The decision
If the p-value is less than α, reject H₀: the result is "statistically significant." If the p-value is α or larger, do not reject H₀: the data did not give enough evidence.
Example: p = 0.03 < 0.05: reject. p = 0.20: do not reject.
Type I error
Rejecting a true null hypothesis: a false alarm. Its probability is α.
Example: Concluding the protocol helps when it does not.
Type II error
Failing to reject a false null hypothesis: a miss. Its probability is β (beta); 1 − β is the power of the study.
Example: Missing a protocol that really helps, often because the sample was too small.
Worked examples
A study reports p = 0.03 at α = 0.05. What is the conclusion?
- Compare: 0.03 is less than 0.05.
- Reject the null hypothesis. The difference is statistically significant.
- Plain words: a difference at least this big would be unusual if the treatment did nothing.
Answer: Reject H₀; statistically significant
A study reports p = 0.20. Does that prove there is no effect?
- 0.20 is larger than 0.05, so do not reject the null hypothesis.
- "Do not reject" is not "prove." The study may simply have been too small to detect a real effect.
Answer: No: not enough evidence, which is different from evidence of no effect
p = 0.001. Is the effect large?
- A p-value measures surprise under the null hypothesis, not size.
- With a huge sample, a tiny, unimportant difference can get a tiny p-value. Look at the effect size and the confidence interval too.
Answer: Not necessarily
Watch out: Two things a p-value is not: the probability that H₀ is true, and a measure of how big or important the effect is. And "not significant" never means "no effect."
Study card 8
Correlation vs causation
Correlation means two variables move together. Causation means one of them makes the other change. A study can show the first without proving the second, and the gap between them is where most bad headlines come from.
The terms
Correlation coefficient (r)
A number from −1 to +1 that describes a straight-line relationship. The sign is the direction; the distance from 0 is the strength.
Example: r = 0.85 strong positive; r = −0.85 strong negative; r = 0.10 almost none
Positive correlation
As one variable goes up, the other tends to go up.
Example: Hours of sleep and alertness scores.
Negative correlation
As one goes up, the other tends to go down.
Example: Screen time before bed and hours of sleep.
r² (coefficient of determination)
r squared: the share of the variation in one variable that is explained by its straight-line link to the other.
Example: r = 0.60 → r² = 0.36, so 36% explained
Third-variable problem
A hidden factor drives both variables, so they move together without either causing the other.
Example: Ice cream sales and drownings both rise with summer heat.
Direction problem
Even when one does cause the other, a correlation cannot say which way.
Example: Does low mood reduce exercise, or does less exercise lower mood?
Illusory correlation
Seeing a link that is not there, because the matching cases are easier to remember.
Example: A full moon and a busy night on the unit.
Worked examples
Which is stronger, r = 0.30 or r = −0.65?
- Ignore the sign for strength and look at the distance from 0.
- 0.65 is farther from 0 than 0.30.
Answer: r = −0.65 (a stronger, negative relationship)
Cities with more hospitals have more deaths per year. Do hospitals cause deaths?
- A third variable: bigger cities have more people, so more hospitals and more deaths.
- The correlation is real; the causal story is not.
Answer: No: population size drives both
What kind of study could show that a new wound dressing speeds healing?
- Only an experiment: randomly assign patients to the new dressing or the usual one, then compare healing time.
- A survey of patients who happened to use each dressing would be a correlation, open to third variables (which patients got the new dressing?).
Answer: A randomized experiment
Watch out: Three questions for any "linked to" headline: Could a third thing drive both? Could the arrow point the other way? Was anything randomly assigned? Without random assignment, treat the finding as a correlation.
Study card 9
Types of studies
Research designs trade depth, realism, cost and the ability to prove cause. Descriptive and correlational designs describe and relate; only a true experiment, with a manipulated variable and random assignment, can support a cause-and-effect claim.
The terms
Case study (clinical study)
One person or a small group studied in depth.
Example: A detailed record of one patient with a rare condition.
Trade-off: Rich detail; hard to generalize, because the case is often unusual.
Naturalistic observation
Watching behavior where it normally happens, without interfering.
Example: Observing hand-washing at a sink on the unit.
Trade-off: Realistic; little control, and observers can be biased.
Survey
A list of questions given to many people.
Example: A burnout questionnaire sent to 2,000 nurses.
Trade-off: Large, diverse samples; shallow, and people may misremember or shade their answers.
Archival research
Analyzing records that already exist.
Example: Ten years of incident reports.
Trade-off: Cheap, no participant contact; you cannot control what was recorded.
Longitudinal
The same people measured repeatedly over months or years.
Example: One graduating class surveyed every five years.
Trade-off: Shows change over time; slow, costly, and people drop out (attrition).
Cross-sectional
Different groups (often age groups) compared at one point in time.
Example: Comparing 25-, 45- and 65-year-olds this year.
Trade-off: Fast; generation (cohort) differences can look like age effects.
Correlational study
Two or more variables measured as they are, to see whether they move together.
Example: Sleep hours and medication errors over a month.
Trade-off: Finds relationships; cannot prove cause.
Experiment
The researcher manipulates the independent variable and randomly assigns people to groups, with a control group and often blinding.
Example: Patients randomly assigned to a new discharge checklist or usual care.
Trade-off: The only design that can show cause; not always possible or ethical.
Blinding
Single-blind: participants do not know which group they are in. Double-blind: neither do the staff who interact with them. Both guard against expectations shaping the result (the placebo effect and experimenter bias).
Example: Identical-looking pills, coded by someone outside the study.
Quasi-experiment
Groups compared on a variable that cannot be assigned, such as age or sex, so cause cannot be claimed.
Example: Comparing stress in nurses over and under 40.
Worked examples
Name the design: 300 people answer 40 questions about sleep habits online.
- A list of questions given to many people.
Answer: Survey (descriptive)
Name the design: the same 500 children are assessed at ages 5, 10 and 15.
- The same people, measured repeatedly over years.
Answer: Longitudinal
Name the design: patients are randomly assigned to a new pain protocol or the usual one, and pain scores are compared.
- A manipulated variable (the protocol) and random assignment.
- In healthcare research this design is usually called a randomized controlled trial (RCT).
Answer: Experiment
Name the design: a researcher reviews five years of discharge records to relate length of stay to readmission.
- Existing records, no new data collected, two variables related to each other.
Answer: Archival, correlational
Watch out: Measuring a variable is not manipulating it. A study that compares smokers with non-smokers did not assign anyone to smoke, so it is correlational no matter how large it is.
Study card 10
Standard deviation and z-scores in plain words
The mean says where the middle is; the standard deviation says how far values typically sit from it. A small standard deviation means the values cluster near the mean; a large one means they are spread out. A z-score uses it to say how unusual one value is.
The terms
Standard deviation (SD)
A number that measures how far data values are from their mean, in the same units as the data. Written s for a sample, σ (sigma) for a population.
Example: Mean 70, SD 10: a typical score sits about 10 points from 70.
Reading "mean ± SD"
Research tables often report a result as mean ± standard deviation; the column header or a table note says so (some tables use the standard error of the mean instead, a smaller number). When it is the SD, the second number describes the spread of the data, not a margin of error.
Example: "Age 38 ± 9 years" (mean ± SD) means a mean of 38 with values typically within about 9 years of it.
Variance
The standard deviation squared. The same idea, in squared units.
Example: SD 10 → variance 100
z-score
How many standard deviations a value is above (+) or below (−) the mean: z = (value − mean) ÷ SD.
Example: 85 with mean 70 and SD 10: (85 − 70) ÷ 10 = 1.5
The 68-95-99.7 rule
In bell-shaped data, about 68% of values fall within 1 SD of the mean, about 95% within 2 SD and about 99.7% within 3 SD, so a z-score beyond ±2 is unusual.
Example: z = 2.5 is rarer than z = 0.5
Worked examples
Mean 50, SD 5. z-score of 60?
- (60 − 50) ÷ 5 = 10 ÷ 5.
Answer: z = 2 (two standard deviations above the mean)
Mean 70, SD 10. z-score of 55?
- (55 − 70) ÷ 10 = −15 ÷ 10.
Answer: z = −1.5 (below the mean)
Two units report a mean wait of 20 minutes. Unit A has SD 2, unit B has SD 12. Which is more predictable?
- Same mean, different spread.
- A smaller SD means the waits cluster near 20 minutes.
Answer: Unit A
Watch out: A z-score of 0 is exactly the mean, not "no result." And a standard deviation is never negative: a minus sign belongs only to a z-score below the mean.