What is the "population" (Grundgesamtheit) in statistics?
The complete set of objects, people, or things you want to gain information about.
Why does your choice of population matter for interpreting results?
It determines how generalizable (broadly applicable) your results are.
How does a sample (Stichprobe) relate to the population?
A sample is a subset of the relevant population.
What is "sample size" (Stichprobengröße)?
The number of objects to be studied within the sample.
What three factors influence how large a sample size should be?
Cost, the nature of the study, and the desired precision in describing the population.
What is meant by "sampling" (Stichprobenziehung)?
The method used to select which objects from the population make up the sample.
What defines a random sample?
A sample in which objects are chosen purely by chance.
Why choose objects randomly rather than through some other method?
To avoid systematic error (bias) in how the sample is composed
Why are random samples generally considered representative?
Because every member of the population has an equal chance of being included.
Does random sampling guarantee a representative sample?
No — no method can guarantee this. Randomness reduces the risk of bias but doesn't eliminate the possibility of an unrepresentative sample.
What does sampling theory provide?
A set of methods for drawing samples while avoiding systematic error.
What's the first step in stratified sampling?
The population is divided into groups called strata (e.g., low-income vs. high-income).
What happens after the strata are defined in stratified sampling?
Random individuals are selected from within each stratum.
What must be accounted for when analyzing results from a stratified sample?
The known proportion of each stratum within the overall population.
What should each cluster resemble in cluster sampling?
A small-scale mirror of the entire population — not a group sharing one characteristic.
What's the key difference between cluster sampling and stratified sampling?
In cluster sampling, whole clusters (each representative of the population) are selected for study; in stratified sampling, individuals are drawn from within distinct subgroups.
What does quota sampling fix in advance?
Specific quotas for the sample's composition (e.g., a set number of men and women).
What is the main risk of quota sampling?
Since selection isn't random and not all relevant characteristics can be controlled, the sample can still end up unrepresentative even when the quotas are met.
What is an "outcome" in the context of causal inference?
A measure (variable) that we're interested in studying, whose value may be affected by treatment.
What role does "treatment" play in causal inference?
The treatment is what determines the causal effect observed on the outcome.
What is the "treatment group" in a causal study?
The people who receive the treatment.
What is the "control group" in a causal study?
The people who do not receive the treatment.
What makes a control group a "good" one?
It reveals the fate of the treated individuals in a counterfactual world where they had not been treated.
How many potential outcomes does each person have in a potential outcomes framework, and how many are actually observed?
Each person has two potential outcomes — with treatment and without treatment — but only one of the two is ever observed for that person.
In potential-outcomes notation, what does Y₁ᵢ represent?
The outcome for person i if they receive treatment.
In potential-outcomes notation, what does Y₀ᵢ represent?
The outcome for person i if they do not receive treatment.
How is the individual causal (treatment) effect for person i defined?
As Y₁ᵢ − Y₀ᵢ, the difference between their outcome with treatment and their outcome without treatment.
Why does comparing the outcome of one treated person to a different untreated person tell us little about a true causal effect?
Because the difference reflects not just the treatment's effect, but also that the two people may have differed from each other even without treatment.
How can the difference between a treated person 1 and an untreated person 2 be decomposed?
Y₁ − Y₀ = {Y₁₁ − Y₀₁} + {Y₀₁ − Y₀₂}, where Y₁₁ is person 1's observed outcome with treatment and Y₀₁, Y₀₂ are the (mostly hypothetical) outcomes without treatment for persons 1 and 2.
What does the term {Y₁₁ − Y₀₁} represent in this decomposition: Y₁ − Y₀ = {Y₁₁ − Y₀₁} + {Y₀₁ − Y₀₂}?
The causal effect of the treatment on person 1.
What does the term {Y₀₁ − Y₀₂} represent in this decomposition: Y₁ − Y₀ = {Y₁₁ − Y₀₁} + {Y₀₁ − Y₀₂}, and what is it called?
The difference between person 1 and person 2's outcomes if neither were treated — this is called selection bias.
How is the average causal effect across a group of n people written?
Eₙ[Y₁ᵢ − Y₀ᵢ] = (1/n)Σ(Y₁ᵢ − Y₀ᵢ) = (1/n)ΣY₁ᵢ − (1/n)ΣY₀ᵢ
What hypothetical scenario does the average causal effect represent?
The average outcome in a scenario where everyone in the group receives treatment, compared to a scenario where nobody in the group receives treatment.
In the potential outcome framework, what does the indicator variable Dᵢ represent?
Whether person i received treatment: Dᵢ = 1 if treated, Dᵢ = 0 otherwise.
What does E[Yᵢ | Dᵢ=1] in a potential outcomes framework represent, and what does it fail to tell us?
The average observed outcome among the treated. It contains no information about Y₀ᵢ (what those same people's outcomes would have been without treatment).
What does E[Yᵢ | Dᵢ=0] represent in a potential outcomes framework, and what does it fail to tell us?
The average observed outcome among the untreated. It contains no information about Y₁ᵢ (what those same people's outcomes would have been with treatment).
How is the "difference in group means" expressed using conditional expectations in a potential outcome framework?
E[Yᵢ|Dᵢ=1] − E[Yᵢ|Dᵢ=0] = E[Y₁ᵢ|Dᵢ=1] − E[Y₀ᵢ|Dᵢ=0]
What does the "constant-effect assumption" in a potential outcome framework state?
That the treatment affects every person's outcome by the same fixed amount, κ.
How is the constant-effect assumption in the potential outcome framework written, and what does it imply?
Y₁ᵢ = Y₀ᵢ + κ, which means Y₁ᵢ − Y₀ᵢ = κ — i.e., under this assumption, the individual causal effect equals the average causal effect for everyone.
Under the constant-effect assumption in the potential outcome framework, how does the difference in group means decompose?
E[Y₁ᵢ|Dᵢ=1] − E[Y₀ᵢ|Dᵢ=0] = κ + {E[Y₀ᵢ|Dᵢ=1] − E[Y₀ᵢ|Dᵢ=0]}
What do the two terms in this decomposition E[Y₁ᵢ|Dᵢ=1] − E[Y₀ᵢ|Dᵢ=0] = κ + {E[Y₀ᵢ|Dᵢ=1] − E[Y₀ᵢ|Dᵢ=0]}represent?
κ is the causal effect of interest; the bracketed term is the selection bias — the difference in the (untreated) potential outcome Y₀ᵢ between the treated and untreated groups.
In the potential outcome framework, what does "selection bias" capture conceptually?
Everything about person i that's related to the outcome other than the treatment itself — i.e., pre-existing differences between the groups.
Under what condition can selection bias be corrected for?
If the only source of selection bias is a set of observed and measurable differences in characteristics between the groups.
Last changed11 days ago