SAT Math

Statistical Inference and Study Design flashcards

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Sample size and biasPopulations, Samples, and Representative Sampling
More of the wrong sampling method is still the wrong sampling method.
When should I use population and sample?Populations, Samples, and Representative Sampling
Distinguish the target group from observed participants.
What method supports sample size and bias?Populations, Samples, and Representative Sampling
size reduces random variation, not systematic selection bias
Representative selectionPopulations, Samples, and Representative Sampling
Random selection from the right list is more useful than an easy-to-reach crowd.
Population and samplePopulations, Samples, and Representative Sampling
Population is everyone you want to know about; sample is whom you observed.
What must I check in populations, samples, and representative sampling?Populations, Samples, and Representative Sampling
A large sample does not repair a systematically biased selection method
What method supports representative selection?Populations, Samples, and Representative Sampling
random sampling supports population generalization
What method supports population and sample?Populations, Samples, and Representative Sampling
sample ⊆ target population
When should I use sample size and bias?Populations, Samples, and Representative Sampling
Explain why selection method matters even for large samples.
When should I use representative selection?Populations, Samples, and Representative Sampling
Choose a method that gives the target group a fair opportunity for inclusion.
Rescale an estimated proportionEstimating Population Counts, Means, and Proportions
Scale only when the new group matches the population you sampled.
When should I use estimate a population count?Estimating Population Counts, Means, and Proportions
Scale a sample proportion to a known population size.
What method supports rescale an estimated proportion?Estimating Population Counts, Means, and Proportions
estimated affected count=proportion×group size
Estimate a population totalEstimating Population Counts, Means, and Proportions
Estimated average times population count gives an estimated total.
Estimate a population countEstimating Population Counts, Means, and Proportions
Apply the sample share to the full population.
What must I check in estimating population counts, means, and proportions?Estimating Population Counts, Means, and Proportions
Population estimates inherit sample uncertainty; use an appropriate representative sample from the target population
What method supports estimate a population total?Estimating Population Counts, Means, and Proportions
estimated total=N·sample mean
What method supports estimate a population count?Estimating Population Counts, Means, and Proportions
estimated count=N·x/n
When should I use rescale an estimated proportion?Estimating Population Counts, Means, and Proportions
Translate a rate estimate into a comparable group count.
When should I use estimate a population total?Estimating Population Counts, Means, and Proportions
Use a sample mean to estimate a total quantity.
Compare estimates with uncertaintyMargin of Error and Sample Size
Do not treat two estimated percentages as exact facts.
When should I use margin-of-error interval?Margin of Error and Sample Size
Form an interval around a stated estimate.
What method supports compare estimates with uncertainty?Margin of Error and Sample Size
compatible interval endpoint = estimate ± reported margin
Sample size and precisionMargin of Error and Sample Size
More random observations usually narrow sampling uncertainty.
Margin-of-error intervalMargin of Error and Sample Size
Subtract the margin for the low end and add it for the high end.
What must I check in margin of error and sample size?Margin of Error and Sample Size
A reported margin of error describes sampling uncertainty under stated conditions, not every source of error or an individual-outcome range
What method supports sample size and precision?Margin of Error and Sample Size
rough scaling: margin ∝ 1/√n under comparable conditions
What method supports margin-of-error interval?Margin of Error and Sample Size
interval=[estimate−margin, estimate+margin]
When should I use compare estimates with uncertainty?Margin of Error and Sample Size
Use reported intervals to judge whether a claimed difference is supported by the supplied information.
When should I use sample size and precision?Margin of Error and Sample Size
Identify the effect of a larger random sample under similar conditions.
Control and comparisonObservational Studies versus Experiments
A comparison group helps distinguish the treatment from what would happen anyway.
When should I use observational studies?Observational Studies versus Experiments
Recognize when researchers measure existing conditions.
What method supports control and comparison?Observational Studies versus Experiments
treatment effect is assessed by comparing group outcomes
ExperimentsObservational Studies versus Experiments
Researchers choose which condition each participant receives.
Observational studiesObservational Studies versus Experiments
Researchers watch what already happens.
What must I check in observational studies versus experiments?Observational Studies versus Experiments
Observing existing behavior differs from assigning treatments; causal conclusions depend on study design
What method supports experiments?Observational Studies versus Experiments
assigned treatment + randomized groups supports causal comparison
What method supports observational studies?Observational Studies versus Experiments
no assigned treatment ⇒ observational design
When should I use control and comparison?Observational Studies versus Experiments
Identify a comparison group’s role in an experiment.
When should I use experiments?Observational Studies versus Experiments
Recognize assigned explanatory conditions.
Both design featuresRandom Sampling versus Random Assignment
Selection and treatment randomization answer different questions together.
When should I use sampling purpose?Random Sampling versus Random Assignment
Connect random selection to population inference.
What method supports both design features?Random Sampling versus Random Assignment
random sampling + random assignment → potential generalization and causation
Assignment purposeRandom Sampling versus Random Assignment
Assignment chooses what happens to each participant.
Sampling purposeRandom Sampling versus Random Assignment
Sampling chooses who joins the study.
What must I check in random sampling versus random assignment?Random Sampling versus Random Assignment
Random sampling supports generalization; random assignment supports causal treatment comparison; neither substitutes for the other
What method supports assignment purpose?Random Sampling versus Random Assignment
random assignment → causal treatment comparison
What method supports sampling purpose?Random Sampling versus Random Assignment
random sample → population generalization
When should I use both design features?Random Sampling versus Random Assignment
Evaluate a study that uses random sampling and random assignment.
When should I use assignment purpose?Random Sampling versus Random Assignment
Connect randomized treatment allocation to causal evidence.
Bounded conclusionsBias, Generalization, Association, and Causation
Match both the claim type and its population to the evidence.
When should I use selection bias?Bias, Generalization, Association, and Causation
Identify a mismatch between a sample source and target population.
What method supports bounded conclusions?Bias, Generalization, Association, and Causation
claim strength ≤ design support
Confounding and causeBias, Generalization, Association, and Causation
A third factor can move both variables together.
Selection biasBias, Generalization, Association, and Causation
Check who had a real chance to be included.
What must I check in bias, generalization, association, and causation?Bias, Generalization, Association, and Causation
Limit conclusions to the target population and design; a strong association alone does not prove cause
What method supports confounding and cause?Bias, Generalization, Association, and Causation
an alternative shared cause can explain association
What method supports selection bias?Bias, Generalization, Association, and Causation
representative inference requires an appropriate sampling frame
When should I use bounded conclusions?Bias, Generalization, Association, and Causation
Choose a conclusion consistent with sampling and treatment design.
When should I use confounding and cause?Bias, Generalization, Association, and Causation
Explain how a third factor can produce an observed association.