Sampling distributions arise because samples ____________. Each random sample will have different cases and, so, a different value of the statistic. Although we can always simulate a sampling distribution, the Central Limit Theorem saves us the trouble for means and proportions. The Process Going Into the Sampling Distribution Model What Can Go Wrong? Don’t confuse the sampling distribution with the distribution of the sample. When you take a sample, you look at the distribution of the values, usually with a histogram, and you may calculate summary statistics. The sampling distribution is an imaginary collection of the values that a statistic might have taken for all random samples—the one you got and the ones you didn’t get. Beware of observations that are not independent. The CLT depends crucially on the assumption of independence. You can’t check this with your data—you have to think about how the data were gathered. Watch out for small samples from skewed populations. The more skewed the distribution, the larger the sample size we need for the CLT to work.
Sampling distributions arise because samples ____________. Each random sample will have different cases and, so, a different value of the statistic. Although we can always simulate a sampling distribution, the Central Limit Theorem saves us the trouble for means and proportions. The Process Going Into the Sampling Distribution Model What Can Go Wrong? Don’t confuse the sampling distribution with the distribution of the sample. When you take a sample, you look at the distribution of the values, usually with a histogram, and you may calculate summary statistics. The sampling distribution is an imaginary collection of the values that a statistic might have taken for all random samples—the one you got and the ones you didn’t get. Beware of observations that are not independent. The CLT depends crucially on the assumption of independence. You can’t check this with your data—you have to think about how the data were gathered. Watch out for small samples from skewed populations. The more skewed the distribution, the larger the sample size we need for the CLT to work.