Statistics & Probability Study Design & Sampling Syllabus

Study Design & Sampling syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Study Design & Sampling in Statistics & Probability, not a summary of it.

1. 1

   Sampling Methods

   4 topics

   • Simple Random Sampling
   • Stratified and Cluster Sampling
   • Systematic Sampling
   • Convenience and Non-Probability Sampling
2. 2

   Experimental Design

   4 topics

   • Randomization and Control
   • Blinding and Placebo
   • Blocking and Factorial Designs
   • Confounding Variables
3. 3

   Observational Studies

   3 topics

   • Cohort vs Case-Control Studies
   • Cross-Sectional Studies
   • Bias in Observational Research
4. 4

   Sources of Bias and Error

   4 topics

   • Sampling vs Non-Sampling Error
   • Survey and Response Bias
   • Survivorship Bias
   • Reproducibility and Replication

Study Design & Sampling flashcards for Statistics & Probability

23 of 50 cards from the Study Design & Sampling deck — real questions with worked answers.

1. What is a simple random sample (SRS) of size $n$?

   A sample of $n$ individuals chosen so that every possible group of $n$ members of the population has an equal chance of being selected (and every individual has an equal probability of inclusion).

2. In simple random sampling without replacement from a population of size $N$, what is the probability that any specific individual is included in a sample of size $n$?

   $P = \frac{n}{N}$.

3. What is stratified random sampling?

   The population is divided into non-overlapping homogeneous groups (strata), and a separate simple random sample is drawn from each stratum, then combined.

4. In proportional stratified sampling, how many units $n_h$ are drawn from stratum $h$?

   $n_h = n \cdot \frac{N_h}{N}$, where $N_h$ is the stratum size, $N$ the population size, and $n$ the total sample size.

5. What is cluster sampling?

   The population is divided into groups (clusters), a random sample of whole clusters is selected, and all (or a random subsample of) members within chosen clusters are studied.

6. State one key difference between strata and clusters in sampling design.

   Strata are internally homogeneous and you sample from every stratum; clusters are ideally internally heterogeneous (mini-populations) and you sample only some clusters, not all.

7. What is systematic sampling with interval $k$?

   Order the population, choose a random start between $1$ and $k$, then select every $k$-th element thereafter.

8. How is the sampling interval $k$ computed in systematic sampling?

   $k = \frac{N}{n}$ (population size divided by desired sample size, rounded to a whole number).

9. What is the main risk that can bias a systematic sample?

   Periodicity: if the ordered list has a repeating pattern whose period coincides with (or is a multiple of) the interval $k$, the sample becomes unrepresentative.

10. What is convenience sampling?

    A non-probability method that selects individuals who are easiest to reach or most readily available, rather than by random chance.

11. Define non-probability sampling and name why it limits inference.

    Sampling in which some members have unknown or zero probability of selection; because selection probabilities are not known, results cannot be validly generalized to the population and standard error/margin-of-error theory does not apply.

12. Name three common non-probability sampling methods.

    Convenience sampling, voluntary response sampling, and quota (or purposive/judgment/snowball) sampling.

13. What is voluntary response sampling and its typical bias?

    People self-select into the sample by choosing to respond; it tends to over-represent those with strong (often negative) opinions, creating voluntary-response bias.

14. What is randomization in an experiment and why is it used?

    Randomly assigning subjects to treatment groups; it balances both known and unknown confounding variables across groups on average, so differences in outcome can be attributed to the treatment.

15. What is the purpose of a control group in an experiment?

    It provides a baseline comparison (receiving no treatment or a standard/placebo treatment) so the effect of the experimental treatment can be isolated.

16. What are the three core principles of experimental design?

    Control (of outside variables), Randomization (of assignment), and Replication (enough experimental units / repeating the experiment).

17. What is blinding in an experiment?

    Keeping subjects and/or those measuring outcomes unaware of which treatment was assigned, to prevent expectation from influencing behavior or measurement.

18. Distinguish single-blind from double-blind design.

    Single-blind: only the subjects (or only the assessors) are unaware of the treatment assignment. Double-blind: both the subjects and the researchers administering/measuring are unaware.

19. What is a placebo and the placebo effect?

    A placebo is an inert treatment indistinguishable from the real one. The placebo effect is a response to receiving a treatment caused by the expectation of an effect rather than the treatment itself.

20. What is blocking in experimental design?

    Grouping experimental units into blocks that are similar with respect to a known nuisance variable, then randomizing treatments within each block to remove that variable's variability.

21. State the design principle summarized as 'block what you can, randomize what you cannot.'

    Use blocking to control the effect of variables you can identify and measure; use randomization to average out the effect of variables you cannot identify or control.

22. In a factorial design, what does a $2 \times 3$ design mean and how many treatment combinations does it have?

    Two factors, one with $2$ levels and one with $3$ levels; it has $2 \times 3 = 6$ treatment combinations.

23. What key advantage do factorial designs offer over one-factor-at-a-time experiments?

    They allow estimation of interaction effects between factors (and efficiently estimate main effects) using the same experimental units.

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