© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Sampling CHAPTER 7 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Q. 1. Define Sample.

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Sample  A subgroup of the elements of the population selected for participation in the study.

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q. 2. What are the benefits of Sampling?

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Sampling: An Introduction  benefits of sampling, relative to a complete census:  lower cost  less time investment  can be more accurate  allows control of interactive testing effect

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q. 3. What are some basic sampling concepts?

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Sampling: An Introduction  some basic sampling concepts  element – the unit about which we seek information  population – aggregate of all the elements, defined prior to sample selection  sampling unit – elements available for selection  sampling frame – list of all sampling units available for selection, from which the actual sample will be drawn  study population – group we wish to make inferences about

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q. 4. What are the five steps in the sampling process?

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. The Sampling Process: An Overview  Step 1. Define the population  elements  sampling units  extent  time frame  Step 2. Identify the sampling frame  Step 3. Decide sample size  too large: resources wasted  too small: inference impossible  Step 4. Select procedure for selection  Step 5. Physically select the sample

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q. 5. What are the two types of sampling procedures?

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Sampling Procedures  probability sampling – each element has a known chance of selection  nonprobability sampling – selection is based in some part on human judgment FIGURE 7.1 Sampling procedures

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Probability Sampling Procedures (continued)

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Estimating the Population Mean: Area Within One Standard Error of the Sample Mean for a Normal Distribution Drawing Inferences from Sample Statistics for Continuous Variables FIGURE 7.2

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. The Normal Curve

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Mean Distribution

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. The central limit theorem determines likelihood that the true population mean lies within a calculated confidence interval (around the sample mean):  sample mean ± 1 standard error = 68% confidence interval  sample mean ± 2 standard errors = 95% confidence interval  sample mean ± 3 standard errors = 99.7% confidence interval Note: this measure of sampling error is only possible with the use of probability- based sample selection procedures. Drawing Inferences from Sample Statistics for Continuous Variables (continued)

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q. 6. What are the types of probability sampling?

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Probability Sampling Procedures simple random sampling – simplest probability-based method Statistical terms:

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q. 7. Define simple random sampling.

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Simple Random Sampling A process by which each element has an equal chance of being selected, and any combination sample elements has an equal chance of being selected as another of the same size.

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stratified Sampling If strata within the population are more homogenous than the overall population, stratified sampling can decrease the standard error (i.e., increase efficiency) of an estimator. 1. Divide the defined population into mutually exclusive and collectively exhaustive subgroups or strata. 2. Select independent simple random sample from each strata.  mutually exclusive – membership in one stratum precludes membership in any other stratum  collectively exhaustive – all possible categories of a variable are used to define the strata

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Variance and standard deviation within each stratum are much lower than the variance and standard deviation of the total sample. Overall sample mean for the stratified sample ( ) is a weighted average of the within-strata means, with the weight given to each stratum W j = N st.j /N. standard error of the mean:  proportionate stratified sampling – simple random sample of each stratum with sample sizes proportional to number of elements in that strata Stratified Sampling (continued)

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  disproportionate stratified sampling – overall standard error can be reduced by sampling more heavily in strata with higher variability  overall mean and standard error calculated with the same formulas as in proportionate stratified sampling: W j = N st.j /N  formulas for proportionate stratified sampling: Stratified Sampling (continued)

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Cluster Sampling  population divided into mutually exclusive and collectively exhaustive groups, followed by selection of a random sample from among these groups  clusters defined as close as possible to the population in heterogeneity on the variables of interest – each cluster should look like a simple random sample  if the groups are less heterogeneous than the population, the standard error will be smaller  can be far less costly than other procedures  2 types:  systematic sampling  area sampling

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Systematic Sampling  every k th element in the frame is selected  advantages:  ease of sample selection  lower cost  no need for a complete sampling frame  mean from any one sample is an unbiased estimator of the population mean – results are often nearly identical to simple random sampling  disadvantages:  possible periodicity –cyclical pattern coinciding with sampling interval  potential for larger standard errors than random sample of same size  sampling interval, k, is the reciprocal of the desired sampling fraction:

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Area Sampling From a population of NB geographic areas, a simple random sample of nB areas is selected.  multistage area samples – multiple stages of selection, from largest geographic area down to actual residents  less statistically efficient than simple random sampling 1. equal-chance (or equal-proportion) selection of clusters – each element has an equal chance of being selected  each cluster given equal chance of selection  same proportion of elements selected from each cluster  disadvantage: elements selected to represent larger clusters may not be very representative

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 2. probability proportionate to size (PPS) – probability of cluster selection proportional to size of cluster, with equal probability of element selection  probability of selecting element in block B = block probability × within-block element probability  net result of selection stages is equal probability of selection  relatively statistically efficient  all but guarantees that large clusters are represented in the sample Area Sampling (continued)

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q. 8. Define Parameter and Statistic.

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Parameter and Statistic Parameter is the true value of quantity of interest in a specific population. Statistic is any quantity deriving from a sample, used to estimate a population parameter.

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q. 9. Define Cluster Sampling.

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Cluster Sampling A process of selecting a cluster or group of elements randomly.

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q. 10. What are the four types of non- probability sampling?

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Nonprobability Sampling Procedures convenience sampling – convenience-based selection  advantages:  helpful for generating hypotheses in exploratory research  can occasionally be used for conclusive studies when inaccuracies are considered acceptable  disadvantages:  difference in size and direction between the population and sample value can never be known  cannot measure sampling error  cannot make any conclusive statements about the results  inappropriate for conclusive research

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Nonprobability Sampling Procedures (continued) judgment sampling – selection based on judgment by expert  advantages:  good for deciding which cities to test market  can improve sample with selection for informed opinion  if the expert’s judgment is valid, the sample will be better than a convenience sample  limitations:  degree and direction of error are unknown  conclusive statements cannot be viewed as meaningful

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. quota sampling – selection engineered to match the population on specified “control characteristics”  number of categories of control characteristics multiplied to determine the number of cells of combinations  cell sample size = [total sample size] x [proportion desired]  limitations:  respondents must be assigned to cells in accurate proportions  all characteristics related to the measures of interest must be included in the control characteristics  can difficult to find a sufficient number of desired respondents for each cell  selection of respondents may be biased Nonprobability Sampling Procedures (continued)