Designing Samples Section 5.1

70% of Parents Say Kids Not Worth It! “If you had it to do over again, would you have children?” 70% of the nearly 10,000 parents who wrote in said they would not have children if they could make the choice again. Statistically designed poll gave result as 91% of parents would have children again.

Sampling Sampling is studying a part – a sample – in order to gain information about an entire group. A voluntary response sample consists of people who choose themselves by responding to a general appeal. Voluntary response samples overrepresent people with strong opinions.

Experiment Actively imposing some treatment in order to observe the response. Unless experiments are carefully designed, the effects of the explanatory variables can’t be seen because of confounding with lurking variables.

Statistical Inference Provides ways to answer specific questions from data with some guarantee that the answers are good ones. When we do statistical inference, we must think about how to produce data as well as about how to analyze data.

Designing Samples The entire group of individuals that we want information about is called the population. A sample is a part of the population that we actually examine in order to gather information. The design of a sample refers to the method used to choose the sample from the population. Some types of bad sample design include voluntary response sampling and convenience sampling. The design of a study is biased if it systematically favors certain outcomes.

Assignment Problems 5.1 – 5.4 on pages 248-249

Simple Random Samples A sample chosen by chance allows neither favoritism by the sampler nor self-selection by respondents. Choosing a sample by chance attacks bias by giving all individuals an equal chance to be chosen. A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected.

Random Digits The idea of an SRS is to choose a sample by drawing names from a hat. Computer software can choose an SRS almost instantly from a list of the individuals in a population. If you don’t use software, you can randomize by using a table of random digits.

Choosing an SRS Step 1: Label. Assign a numerical label to every individual in the population. Step 2: Table. Use Table B to select labels at random. Don’t try to scramble the labels as you assign them. You can assign labels in any convenient manner. Be certain that all labels have the same number of digits. You can read digits from Table 1 in any order.

Assignment Problems 5.5-5.7 on pages 252-253

Other sampling designs… Probability sample Simple random sample Stratified random sample Multistage sample

Probability Sample A probability sample gives each member of the population a known chance (greater than zero) to be selected. Some probability sampling designs (such as an SRS) give each member of the population on equal chance to be selected. The use of chance to select the sample is the essential principle of statistical sampling.

Stratified Random Sample To select a stratified random sample, first divide the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRSs to form the full sample. Choose the strata based on facts known before the sample is taken.

Multistage Sample Design Another common means of restricting random selection is to choose the sample in stages. A national multistage sample proceeds somewhat as follows: Stage 1. Take a sample from the 3000 counties in the United States. Stage 2. Select a sample of townships within each of the counties chosen. Stage 3. Select a sample of blocks within each chosen township. Stage 4. Take a sample of households within each block.

Assignment Problems 5.8, 5.9 on pages 255 - 256

Cautions about sample surveys Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to cooperate. Response bias can be caused by the behavior of the respondent or of the interviewer. Wording effects: The wording of questions is the most important influence on the answers given to a sample survey.

Assignment Problems 5.10 – 5.12 on pages 258 – 259.

Inference about the population Sample results are only estimates of the truth about the population. Properly designed samples avoid systematic bias, but their results are rarely exactly correct and they vary from sample to sample. The results of random sampling don’t change haphazardly from sample to sample. The results obey the laws of probability that govern chance behavior. Larger samples give more accurate results than smaller samples.

Assignment Problems 5.13 p. 260

Section 5.1 Exercises Problems 5.14 – 5.25 on pages 261 – 265.