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What are the differences between bias and variability?
Bias: Accuracy, systematic error | Variability: Precision, spread of estimates
Differentiate between low bias/high variability and high bias/low variability.
Low Bias/High Variability: Accurate on average, inconsistent | High Bias/Low Variability: Inaccurate, but consistent
What are the differences between a biased estimator and an unbiased estimator?
Biased Estimator: Consistently over or underestimates the population parameter | Unbiased Estimator: Accurately estimates the population parameter on average.
Compare the effects of increasing sample size on bias and variability.
Bias: Increasing sample size does not reduce bias | Variability: Increasing sample size reduces variability.
What are the differences between random sampling and non-random sampling?
Random Sampling: Each member of the population has an equal chance of being selected, reduces bias | Non-Random Sampling: Not all members have an equal chance, increases bias.
Explain the concept of minimum variability.
A sampling distribution has minimum variability when sample statistics are very close to each other.
Explain why larger sample sizes reduce variability.
Larger samples provide more information about the population, leading to more stable and consistent estimates.
Explain the impact of bias on a sample.
Bias shifts the entire sampling distribution away from the true population parameter, leading to inaccurate estimates.
Explain the bullseye analogy for bias and variability.
The bullseye represents the true population parameter. Bias is how far the shots are from the center, and variability is how spread out the shots are.
Explain the effect of random sampling.
Random sampling helps ensure the sample is representative of the population, reducing potential bias.
What is an unbiased estimator?
An estimator whose average value across many samples equals the true population parameter.
Define sampling distribution.
The distribution of a statistic (e.g., sample mean) calculated from multiple samples of the same population.
What is bias in statistics?
Systematic deviation of the sample statistic from the true population parameter.
Define variability in the context of sampling distributions.
The spread or dispersion of sample statistics in a sampling distribution.
What does skewness measure?
Skewness measures the asymmetry of a probability distribution.