Research Methods and Statistics for Psychology: practice problems and exam questions

Research designs, validity and reliability, descriptive statistics, probability and hypothesis testing for social science students.

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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. Research methods in psychologykey terms and facts · applying the concepts · cases and analysismultiple choice
  2. Descriptive statisticsmean and median · standard deviation · normal distributioncalculations
  3. Probabilityequally likely outcomes · counting and complements · binomial distributioncalculations
  4. Normal distributionarea in one tail · area between two values · percentilescalculations
  5. Confidence intervalsz interval · t interval · sample sizecalculations
  6. Hypothesis tests & confidence intervalsz statistic · t statistic · confidence intervalscalculations
  7. Linear regression & correlationslope and intercept · correlation coefficient · predictioncalculations
  8. Chi-square testsgoodness of fit · test of independence · critical value decisioncalculations

Exam tips for Research Methods and Statistics for Psychology

  • Correlation does not imply causation; only an experiment with random assignment shows cause.
  • A p-value is the probability of data at least this extreme if the null hypothesis is true.
  • Use the sample standard deviation (divide by n − 1) unless the question says population.

Worked examples

Research methods in psychologyEasy

A study that follows the same participants over a long period of time is called:

  1. AA longitudinal study
  2. BA cross-sectional study
  3. CA case study
  4. DA pilot study
Show hints
  1. Think "long" in time.
  2. Two wrong answers are now crossed out. One of the remaining two is right.
Show the answer and explanation

Why this is the answer

Longitudinal studies measure the same people repeatedly, showing change within individuals, but they are costly and suffer from participant drop-out.

Answer

A · A longitudinal study
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

Z-score and normal probability calculatorConfidence interval calculatorSample size calculatorMean, median and standard deviation calculatorLinear regression calculatorChi-square goodness-of-fit calculatorNormal distribution calculatorBinomial distribution calculatorPoisson distribution calculatorPermutation and combination calculator (nPr and nCr)t-test calculatorP-value calculatorCorrelation coefficient calculator (Pearson and Spearman)One-way ANOVA calculatorExpected value and variance calculatorSignificant figures calculator (count, round and calculate)Percent error calculator (and percent difference)

Related courses

AP Statistics practice problemsIntroductory StatisticsCFA Level I quantitative methods and fixed income practiceStatistics 2: Statistical InferenceEngineering MathematicsEvidence-Based PracticeFE Civil exam practiceIntroduction to Psychology
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