Advanced Statistics Flashcards: Key Formulas and Concepts

Front

What is bias in an estimator?

Back

Bias is the difference between the expected value of an estimator and the true value of the parameter it is trying to estimate.

Front

What makes an estimator unbiased?

Back

An estimator is unbiased if its expected value equals the true parameter value, meaning it does not systematically overestimate or underestimate.

Front

What does the Central Limit Theorem state?

Back

The CLT states that the distribution of the sample mean approaches a normal distribution as the sample size becomes large, regardless of the population's original distribution.

Front

What is the standard error, and how is it related to the sample size?

Back

The standard error is the standard deviation of the sampling distribution of the sample mean. It decreases as the sample size increases, improving precision.

Front

How does increasing the sample size affect the sampling distribution?

Back

Increasing the sample size reduces the standard error, making the sampling distribution narrower and estimates more precise.

Front

Why is the Central Limit Theorem important in statistics?

Back

The CLT allows us to use the normal distribution to make inferences about the sample mean, even if the population distribution is not normal, as long as the sample size is large enough.

Front

What is a sampling distribution?

Back

A sampling distribution is the probability distribution of a given statistic based on a large number of samples drawn from the same population.

Front

How do you calculate the Z-score for a sample mean?

Back

Front

What is the formula for calculating the standard error of the sample mean?

Back

Front

What is the variance of the sample mean?

Back