Evidence-Based Practice: practice problems and exam questions

The statistics needed to read clinical research: 2 × 2 tables for diagnostic tests, predictive values and likelihood ratios, prevalence and incidence, relative and absolute risk, the number needed to treat, and the basics of confidence intervals and significance tests.

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Cram pack (PDF)Formula sheets, method steps and practice problems with full solutions, ready to print.

Topics in this course

  1. Evidence-based practice statistics2 × 2 tables, prevalence and incidence · likelihood ratios, risk measures and rates · predictive values, post-test probability and NNTcalculations
  2. Descriptive statisticsmean and median · standard deviation · normal distributioncalculations
  3. Confidence intervalsz interval · t interval · sample sizecalculations
  4. Hypothesis tests & confidence intervalsz statistic · t statistic · confidence intervalscalculations

Exam tips for Evidence-Based Practice

  • Label a, b, c and d in the 2 × 2 table before you calculate anything.
  • Sensitivity and specificity read down the columns, predictive values along the rows.
  • The NNT is 1/ARR, rounded up, and it depends on the baseline risk.

Worked examples

Evidence-based practice statisticsEasy
testdisease presentdisease absenttotalpositive324350674abnegative76780856cdtotal40011301530

Practice exercise (made-up values, not clinical guidance). A new test was compared with the reference standard in a study (see the 2 × 2 table). Find the sensitivity Se as a percentage. Round to one decimal place.

a = 324b = 350c = 76d = 780

Find Se (%)

Show hints
  1. Sensitivity: of everyone with the disease, how many test positive?
  2. Se = a/(a + c).
  3. 324/400.
Show the answer and the step-by-step solution

Diagnostic 2 × 2 table: a = true positives, b = false positives, c = false negatives, d = true negatives. Sensitivity = a/(a + c) (positives among those with the disease), specificity = d/(b + d), PPV = a/(a + b) (disease among those who test positive), NPV = d/(c + d), accuracy = (a + d)/total. Prevalence = existing cases/population; cumulative incidence = new cases/population at risk.

Formula

Se = a/(a + c)

Substitute

Se = 324/400 = 0.81 = 81%

Answer

Se = 81%
Descriptive statisticsMedium
152025303540455055

Find the sample standard deviation s of the data: 26, 57, 34, 22, 53, 13, 59.

n = 7

Find s

Show hints
  1. First find the mean.
  2. Square each deviation from the mean, add them, divide by n − 1 and take the square root.
  3. x̄ = 37.71.
Show the answer and the step-by-step solution

Descriptive statistics: the mean is the sum divided by n; the median is the middle value of the sorted data (the average of the two middle values when n is even). The sample standard deviation is s = √(Σ(x − x̄)²/(n − 1)). A z-score z = (x − μ)/σ says how many standard deviations a value lies from the mean.

Mean

x̄ = 264/7 = 37.71

Squared deviations

Σ(x − x̄)² = (−11.71)² + 19.29² + (−3.714)² + (−15.71)² + 15.29² + (−24.71)² + 21.29² = 2067

Standard deviation

s = √(2067/6) = 18.56

Answer

s = 18.56

How practising works

  • “Practise this course” mixes problems from all its topics, like a real exam.
  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Mock exams are timed and have no hints, and you get your score and a full review at the end.

Calculators for this course

Confidence interval calculatorSample size calculatorMean, median and standard deviation calculatort-test calculatorP-value calculatorOne-way ANOVA calculatorSensitivity, specificity, PPV and NPV calculator (2×2 table)NNT calculator (number needed to treat, ARR, RRR)Significant figures calculator (count, round and calculate)Percent error calculator (and percent difference)

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Research Methods and Statistics for PsychologyIntroductory StatisticsAP Statistics practice problemsCFA Level I quantitative methods and fixed income practiceStatistics 2: Statistical InferenceEngineering MathematicsMedical SciencesNursing Fundamentals and Clinical Practice
Practise this course for freePractise this courseTake a mock exam5 free problems every day. No card needed.