Section 5.1 Designing Samples

Observational vs. Experiment An observational study observes individuals and measures variable of interest but does not attempt to influence the responses. An experiment, on the other hand, deliberately imposes some treatment on individuals in order to observe their responses. AP Statistics, Section 5.1, Part 1

Population and Sample Parameter- # that describes a population 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. Parameter- # that describes a population Statistic- # that describes a sample AP Statistics, Section 5.1, Part 1

Sampling vs. a Census Sampling involves studying a part in order to gain information about the whole. A census attempts to contact every individual in the entire population.

A farmers field of corn is a population A farmers field of corn is a population. He needs to determine the type of insects infesting the field. A census of the field would take too long – he doesn’t have time. By sampling he examines a sample of 10 plants from various parts of the field to inspect for insects.

How to capture a “Sample” Getting a portion of the population is not difficult. Getting a good sample is difficult. Creating a plan to do this is called “sample design”.

How to sample The best way to sample is to use a “simple random sample” 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 and equal chance to be the sample actually selected. AP Statistics, Section 5.1, Part 1

a) by choosing names from a hat In an SRS, every individual has an equal chance of participating and every sample of size n has an equal chance of being chosen. The participants are chosen randomly. This can be done: a) by choosing names from a hat b) by having a computer choose randomly for us c) by assigning a numerical label to every individual in the population and using a table of random digits to select labels at random. AP Statistics, Section 5.1, Part 1

Using a Table of Random Digits Step 1: Label. Assign a numerical label to every individual in the population (sampling frame). All labels must have the same number of digits. Step 2: Table. Use a random number table to select labels at random, or use a computerized random number generator. Example: Consider this class as a population. There are N = 25 students. We wish to select a sample of 3 students. Everyone has a two-digit number from my alphabetized class roll (01 to 25). Start at Line 110 and select a sample of 3 students. AP Statistics, Section 5.1, Part 1

Stratified Random Sampling First divide the population into groups of similar individuals called strata. We then choose a separate SRS in each stratum and combine these SRS's to form the full sample. Groups are often formed around race, gender, residence, or economic status. From this procedure we get a representative sample from the entire population. AP Statistics, Section 5.1, Part 1

Stratified Random Sampling Population Caution: The groups/strata must be selected so members of any particular group/stratum are homogeneous. Stratum A Stratum C Stratum B Divide and conquer – divide the population into strata and take a SRS from each.

Cluster Sampling In this design, the population can be broken into many smaller units called clusters. A list of these clusters is available. A simple random sample, SRS of clusters is selected. From a cluster that would be selected, every unit within a selected cluster would be measured or surveyed.

Cluster Sampling Population has many small clusters Now randomly select (by SRS) several of the clusters and sample each individual in each of the selected clusters.

Cluster Sampling Stratified

Systematic Sampling Start with a list of all members of the population, then select a systematic way of choosing members. A typical example would be to select every 100th person from a list of the population. AP Statistics, Section 5.1, Part 1

Multistage Sampling Design Randomly choose stage 1 strata (for example, states) Randomly choose stage 2 strata (for example, cities within states) and so on until you get down to the sample size. AP Statistics, Section 5.1, Part 1

Probability Sample A probability sample is a sample chosen by chance. We must know what samples are possible and what chance, or probability, each possible sample has. 1. The interviewers and subject themselves are not choosing the subject who is interviewed. 2. There is a definite procedure for selecting participants in the sample and that procedure involves the use of probability. AP Statistics, Section 5.1, Part 1

The design of a study is biased if it systematically favors certain outcomes.

Undercoverage happens when some groups in the population are left out of the process of choosing the sample. Example: Surveys of households will not represent the homeless, inmates, and students in dormitories Bias

Ann Landers Ann Landers asked her readers, if you had to do it all over again, would you have children? More than 70% of those that wrote in, said that kids weren’t worth it. Other, more careful surveys found more than 90% of parents would have children again. Why this huge difference? Voluntary Response Bias

Bias Voluntary response sample (example: Call in opinion polls). The problem with call in opinion polls is that the people who answer the polls tend to have strong opinions, especially strong negative opinions. This sample is biased; this sample is not representative of the population. Bias

Bias Convenience Sampling Example: survey students at the cafeteria at 12:15pm on a Thursday afternoon about some issue. What is likely to be wrong with resulting sample? This is often referred to as ‘street-corner’ sampling. Typical example is standing on a street-corner to sample the population. The subjects available on a street-corner are likely to not represent the population very well. Bias Convenience Sampling

Bias Convenience sample (example: Mall intercept interviews) Convenience sampling may not get you access to all the people in the population. Interviewers often avoid people who may make them feel uncomfortable. This sample is biased; this sample is not representative of the population. Creepy Bias

Nonresponse Bias happens when someone is unavailable for selection or refuses to cooperate. Examples: Some voters refuse to participate in election exit polls. Some people sign up for the no-call list or are not at home when a pollster calls. The surveyors at the mall miss those who do not shop at the mall or who refuse to participate. Bias

Bias happens when someone lies or unintentionally answers falsely. Response Bias happens when someone lies or unintentionally answers falsely. Examples: In an election exit poll, a voter might participate but lie about how he or she voted in hopes that early returns may motivate some voters to get to the polls or to stay home. A participant may think he or she did something recently when it is actually outside the range of time the survey requests Bias

Why Sample? Sampling Variability We want to make inferences about the population as a whole. We can’t afford to talk to everyone. Even though two samples, following the same design most probably will give us different results (Sampling Variability), those results are reasonable estimates of the population as a whole. Sampling Variability