The Language of Sampling Lecture 5 Sections 2.1 – 2.4 Fri, Jan 21, 2005

Why Sample? It is usually impractical or impossible to survey the entire population. We can get excellent results from a sufficiently large sample. A sample can give good results whether it comes from a small population or a large population. The size of the population does not matter.

The Language of Sampling Unit or subject– An individual member of the population or sample. Variable – A characteristic of interest to be measured for each unit in the sample. Population size – The number of members in the population, denoted by N. Sample size – The number of members in the sample, denoted by n.

Parameters and Statistics Parameter – A numerical characteristic of the population. Its value depends on the entire population. Statistic – A numerical characteristic of a sample. Its value depends on the sample.

Parameters and Statistics For numerical data, we will usually use the average of the values in the sample. For example, the average household income. For non-numerical data, we will usually use the proportion of observations in a specific category. For example, the unemployment rate.

Random vs. Representative Random sample – The members of the sample are selected at random from the population. There are various methods of selecting random samples. Representative sample – In all of its characteristics (except size), the sample resembles the population.

Examples Example 2.2, p. 78 – Defective Parts. Example 2.3, p. 78 – Parameter or Statistic? Let’s Do It! 2.1, p. 78 – Parameter or Statistic?

Bias A sampling method is biased if it produces results that systematically differ from the truth about the population.

Example Example 2.5, p. 79 – Biased Too High?

Some Biased Sampling Methods Convenience sampling – Sampling only those units that are easily accessible. Volunteer sampling – Sampling only those units that volunteer to be sampled.

Three Types of Bias Selection bias – The systematic tendency to include or to exclude a certain kind of unit. Nonresponse bias – Bias resulting from some selected units not responding. Response bias – Bias arising from the subject trying to meet the interviewer’s perceived expectations.

Three Types of Bias Selection bias originates in the sampling procedure. Nonresponse bias originates in the subjects who were selected for the sample (but chose not to participate). Response bias originates in the subjects who are in the sample.

Example Example 2.9, p. 81 – Phone Surveys. Example 2.13, p. 82 – Prison Sentences.

Let’s Do It! Let’s Do It! 2.2 – Is It Biased? Let’s Do It! 2.3 – Family Size.