Chapter 12 Statistics

response bias

- (NON SAMPLING ERROR) the behavior of the individual or interviewer may influence the accuracy of the response, may want to lie

nonresponse bias

- (NONSAMPLING ERROR) an individual chosen for the sample cannot be contacted or refuses to respond/cooperate

Census

- Including everyone, "sampling" the entire population. This would be the best possible information about a population. - a sample that consists of the entire population

Population

- It would be preferable to know about the entire population of individuals but that would impractical or impossible. - the entire group of individuals or instances about whom we hope to learn

Sample Size

- The size of the sample is important, not the fraction of the population that you've sampled. - the number of individuals in a sample. It determines how well the sample represents the population, not the fraction of the population sampled.

Sample

- We settles for this instead of a population, a smaller group of individuals selected from the population. - actual people picked - a representative subset of a population, examined in hope of learning about the population.

Statistic or Sample Statistic

- We use summaries of data to estimate the population parameter. Any summery found from data is a statistic. -This tries to get close to the parameter, but it is never exact. - values calculated for sampled data. Correspond to and estimate a population parameter.

Population Parameter

- a parameter used in a model for a population (mu-mean, sigma-standard deviation, rho-correlation, beta-regression coefficient, p-proportion). - The actual truth of the population. - a numerically valued attribute of a model for a population. Rarely expect to know the true value of a population parameter, but hope to estimate it from sampled data.

wording of questions

- confusing or leading questions influence responses; poorly worded questions will not yield accurate responses

convenience sample

- individuals who are easiest to reach are chosen for the sample

Sampling Frame

- is a list of individuals from which the sample is drawn. - The people that have the chance to be selected. - individuals who may be in the population of interest but not in the sampling frame cannot be included in any sample.

Randomizing

- protects us from the influences of all the features of our population by making sure that, on average, the sample looks like the rest of the population. - the best defense against bias is this, in which each individual is given a fair, random chance of selection.

Biased

- sampling methods that by their nature, tend to over- or underemphasize some characteristics of the population are said to be biased. This is the bane of sampling, the one thing above all to avoid. - any systematic failure of a sampling methods to represent its population is bias. (relying on voluntary response, undercoverage of population, nonresponse bias, response bias).

Strata

- when the population is first sliced into homogeneous groups - several subpopulations

Simple Random Sample

- with this method, each combination of people has an equal chance of being selected as well. - everybody has the same chance of being selected, not efficient - simple random sample of sample size n is one in which each set of n elements in the population has an equal chance of selection

undercoverage

-(A SAMPLING ERROR) some groups are left out of the process of choosing the sample, accidentally leaving out a group (ex. leaving out Hawaii or Alaska)

voluntary response sample

-people have the choice to respond or not, people choose themselves to be in the sample by responding to a general appeal

Multistage Samples

-sampling schemes that combine several methods - a combination of any sampling methods -ex.) select several groups; within each group, select a subgroup; within each subgroup select individuals for the sample

Stratified Sampling

-sometimes the population is first sliced into homogenous groups, called strata, before the sample is selected. Then simple random sampling is used within each stratum before the results are combined. The most important benefit is the reduced sampling variability. - split up into groups and then a simple random sample. Benefit: reduces/lowers variation among answers. - sampling design in which the population is divided into several subpopulations or strata and random samples are then drawn from each stratum. If the strata are homogeneous but are different from each other, a stratified sample may yield more consistent results. - divide population into groups of similar individuals, choose a SRS in each group to form the full sample

Cluster Sampling

-splitting the population into representative clusters can make sampling more practical. Then we could simply select one or a few clusters at random and perform a census within each of them. Benefit: efficiency, practicality, and cost. -break into clusters and randomly pick up a cluster and then sample everyone in that sample. It is looking at data in small groups. Benefit: very efficient - each cluster should be heterogenous and representative of population so all the clusters should be similar to each other. - select several groups; within each group, select several subgroups; within each subgroup select ALL individuals for the sample

Systematic Random Sampling

-you might survey every 10th person on an alphabetical list of students. To make it random, you still must start the systematic selection from a randomly selected individual. When the order of the list is not associated in any way with the responses sought, this can give you a representative sample. Benefit: not expensive - randomly pick a number, ask every nth person who walks through door to answer. Benefit: less expensive, efficient. Negatives: may be a bias. - when there is no relationship between the order of the sampling frame and the variables of interest, a systematic sample can be representative.

sample design

The method we use to select the sample. This is very important, if the design is poor, the sample will no accurately represent the population.