Planning a Study: Data Collection & Random Sampling

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Questions and Answers

Considering a scenario where a sample is selected from a population with replacement, and given the complexities introduced by non-constant probabilities of selection, which of the following methods is MOST effective for minimizing bias in statistical inference?

Employing a Horvitz-Thompson estimator, appropriately weighted by the inverse of inclusion probabilities, especially when dealing with unequal selection probabilities to ensure unbiased estimation of population parameters. (correct)
Applying a stratified sampling technique to create homogeneous subgroups to reduce variability, followed by equal probability sampling within each stratum, and then aggregating the results.
Using a cluster sampling approach with a large number of small, heterogeneous clusters to mimic the population's variability and minimize the impact of intra-cluster correlation.
Implementing a systematic sampling method with a randomly selected starting point to ensure uniform coverage across the population and reduce the risk of selection bias.

In experimental design, the deliberate introduction of a confounding variable post hoc is an acceptable strategy to discern causal relationships more accurately, especially when initial analyses are inconclusive.

False (B)

Describe a sophisticated methodology beyond simple random sampling that significantly improves the precision of estimating population parameters in a heterogeneous population, justifying its effectiveness through the lens of variance reduction. How do you ensure that your choice avoids introducing bias related to cluster effects or stratification?

Employ stratified sampling with optimal allocation, where strata are formed based on auxiliary information highly correlated with the outcome variable. Allocate sample sizes to each stratum inversely proportional to the square root of the within-stratum variance and proportional to stratum size, minimizing the overall variance of the estimator. In order to avoid bias, perform appropriate weighting based on sampling fractions. Furthermore, this needs to be compared to other methods, such as simple random sampling.

In the context of experimental design, the process of ________ is employed to mitigate the effects of unknown confounding variables by ensuring that, on average, treatment groups are balanced with respect to these variables, thereby strengthening causal inferences.

random assignment Signup and view all the answers

Match the following statistical study types with their appropriate definitions:

Observational Study = A study in which individuals are observed, and variables of interest are measured, without any attempt to influence the responses; treatments are not imposed. Experimental Study = A study in which a treatment is deliberately imposed on individuals in order to observe their responses. Retrospective Study = An observational study that examines existing data for a sample of individuals. Prospective Study = An observational study that tracks individuals into the future to collect data as it unfolds. Signup and view all the answers

In the realm of probabilistic inference, consider a scenario where the occurrence of event A provides absolutely no incremental information regarding the likelihood of event B, and vice versa. Given this condition, and assuming that both events A and B have non-zero probabilities, which of the following statements MUST invariably hold true?

$P(A \cup B) = P(A) + P(B) - P(A) \times P(B)$ and $P(A \cap B) = P(A) \times P(B)$, satisfying both the addition rule for the union of independent events and the multiplication rule for their intersection. (D) Signup and view all the answers

In the context of statistical simulations designed to approximate complex stochastic processes, augmenting the number of iterations ad infinitum reliably guarantees convergence to the true probability, irrespective of the inherent biases embedded within the generative model itself.

False (B) Signup and view all the answers

Propose a stratified sampling strategy that optimizes estimation precision given a fixed budget and a population with known auxiliary variables correlated with the outcome, detailing how to balance stratum sizes and sample allocation to minimize variance while accounting for sampling costs and potential non-response bias.

Implement Neyman allocation within strata defined by auxiliary variables highly correlated with the outcome. Adjust sample sizes in each stratum proportional to stratum size and inversely proportional to the square root of within-stratum variance, factoring in stratum-specific sampling costs. Furthermore, address potential non-response by oversampling in strata with higher non-response rates and implement weighting adjustments using propensity scores. Signup and view all the answers

In hypothesis testing, the ________ represents the probability of observing a test statistic as extreme as, or more extreme than, the statistic obtained from a sample, assuming that the null hypothesis is true.

p-value Signup and view all the answers

Match the following statistical biases with their definitions:

Voluntary Response Bias = Bias arising when individuals self-select to participate in a study, leading to a sample that is not representative of the population. Undercoverage Bias = Bias resulting from some members of the population being inadequately represented in the sample. Non-response Bias = Bias that occurs when a significant number of people in the selected sample do not respond to the survey, and these non-respondents differ in important ways from those who do respond. Response Bias = Bias resulting from inaccurate or untruthful answers provided by respondents. Signup and view all the answers

Flashcards

Population

The entire group of individuals about which we want information.

Sample

A subset of individuals selected from a population to collect data.