# Social Statistics for a Diverse Society

# Chapter Summary

**Chapter 7**

Through the process of sampling, researchers attempt to generalize the characteristics of a large group (the population) from a subset (sample) selected from that group. The term parameter, associated with the population, refers to the information we are interested in finding out.Statistic refers to a corresponding calculated sample statistic.

A probability sample design allows us to estimate the extent to which the findings based on one sample are likely to differ from what we would find by studying the entire population.

A simple random sample is chosen in such a way as to ensure that every member of the population and every combination of *N *members have an equal chance of being chosen.

In systematic sampling, every *K*th member in the total population is chosen for inclusion in the sample after the first member of the sample is selected at random from the first *K *members in the population.

A stratified random sample is obtained by (1) dividing the population into subgroups based on one or more variables central to our analysis and (2) then drawing a simple random sample from each of the subgroups.

The sampling distribution is a theoretical probability distribution of all possible sample values for the statistic in which we are interested. The sampling distribution of the mean is a frequency distribution of all possible sample means of the same size that can be drawn from the population of interest.

According to the central limit theorem, if all possible random samples of size *N *are drawn from a population with a mean μY and a standard deviation σY, then as *N *becomes larger, the sampling distribution of sample means becomes approximately normal, with mean σY and standard deviation σY/√* N*.

The central limit theorem tells us that with sufficient sample size, the sampling distribution of the mean will be normal regardless of the shape of the population distribution. Therefore, even when the population distribution is skewed, we can still assume that the sampling distribution of the mean is normal, given a large enough randomly selected sample size.