Explanatory vs. Response Variables
In a study testing whether energy gels make runners faster, what is the response variable?
Running speed (or time taken to run)
Is "types of ice-cream flavours" a categorical or quantitative variable?
Categorical
In an observational study, researchers collect data without directly interfering. True or False?
True
In a simple random sample, what is the key characteristic?
Every individual in the population has an equal chance of being selected
Name the four main principles of experimental design.
Control, Randomise, Replicate and Block
Which type of variable potentially has an effect on the other variable?
Explanatory variable
How many countries a student has visited would be classified as what type of variable?
Quantitative
Can an observational study establish causation between variables? (Yes or No)
No (only association or correlation)
Stratified sampling divides the population into similar groups called _______.
Strata
In a study testing a new study technique, why is it important to have a control group?
To compare the treatment effect against a baseline to see if the treatment actually makes a difference
A researcher investigates whether the number of hours spent training affects an athlete's final race time. Identify the response variable.
Final race time
A student's year level in primary school (Year 1, Year 2, etc.) is an example of which type of variable?
Categorical (ordinal categorical)
A researcher randomly assigns 100 participants to either drink green tea or water daily for 8 weeks, then measures their energy levels. What type of study is this?
Experiment
A town wants to survey 500 adults about a new shopping centre. They randomly select 50 streets, then survey all adults on those streets. What sampling method is this?
Cluster Sampling
A researcher tests a new training program on 30 athletes and finds it improves performance. Which principle of experimental design might be questioned here?
Replication (the sample size of 30 might be too small; the study should be replicated or conducted on a larger sample to ensure results are reliable)
In an investigation of whether caffeine consumption influences exam performance, which is the explanatory variable?
Caffeine consumption
Which of the following is quantitative: campus location, sleep hours, or dread level (1–5 scale)?
Sleep hours
A researcher reviews past medical records to study the relationship between smoking and lung disease. Is this prospective or retrospective?
Retrospective
Why might a researcher prefer cluster sampling over simple random sampling?
Economic efficiency – it's cheaper and more practical, especially for geographically dispersed populations
In a study examining whether light level and noise level affect exam performance, researchers believe these factors might have different effects on male and female students. Why should gender be treated as a blocking variable rather than an explanatory variable?
Gender is a characteristic students already have, not a condition the researcher imposes. Blocking controls for it to ensure both males and females are equally represented in each treatment group, rather than manipulating it as a treatment.
A study examines the relationship between daily water intake and recovery time after exercise. The researchers measure both variables for 100 athletes over a 12-week period. Identify both the explanatory and response variables, and explain why you classified them this way.
Explanatory = Daily water intake (the suspected cause); Response = recovery time after exercise (what the researchers are trying to measure/predict). Water intake is hypothesised to affect recovery, not the other way around.
The "dread" variable measured on a scale of 1–5 could be argued as both categorical and quantitative. Explain why and discuss which classification makes more sense for statistical analysis in an introductory statistics course.
It has ordered categories (1–5), making it ordinal categorical, but can be treated as quantitative for analysis purposes because we can calculate means and perform statistical tests. Quantitative is often more useful for analysis.
A researcher wants to determine whether attending peer-led study sessions causes students to improve their exam scores. Should this be an observational study or an experiment? Explain your reasoning and identify at least one confounding variable that could arise in an observational approach.
Should be an experiment – randomly assign students to attend or not attend study sessions to establish causation. In an observational study, confounding variables (e.g., motivated students naturally choose to attend sessions) would make it impossible to know if improved scores are due to the sessions or the students' motivation.
A university wants to survey 1,000 students about campus facilities. The student population includes: 400 first-year students, 300 second-year, 200 third-year, and 100 fourth-year students. Design a stratified sample of 1,000 students and explain why this method is better than simple random sampling for this scenario.
Select 400 first-year, 300 second-year, 200 third-year, and 100 fourth-year students (proportional to population). Stratified sampling ensures each year group is represented equally, capturing year-specific perspectives on facilities (which may differ significantly between cohorts), rather than risking under-representation of smaller year groups.
Design an experiment testing whether a new hybrid training program (combining endurance and strength training) improves performance in a simulated triathlon. Address all four principles of experimental design in your answer: Control, Randomize, Replicate, and Block. Identify your response and explanatory variables.
Explanatory variable = training program type (hybrid vs. standard); Response variable = triathlon performance (time or score). Control: Use a standard training program as control group. Randomise: Randomly assign athletes to hybrid or standard training. Replicate: Use a large sample (e.g., 100+ athletes) to ensure reliability. Block: Group athletes by experience level (beginner, intermediate, advanced) first, then randomly assign within each block to ensure experience is equally distributed between groups.