Sampling Procedures

• The importance of proper sampling revolves around the degree of confidence with which the analyst is able to answer the questions being asked.
• Simple random sampling:
  • Any particular sample of a specified sample size has the same chance of being selected as any other sample of the same size.
  • Sample size means the number of items in the sample.
• Biased sample:
  • Example: A sample is chosen to answer certain questions regarding political preferences in a certain state.
  • Now, suppose that all or nearly all of the 1000 sampling families chosen live in urban (vs. rural) areas.
  • Biased sample confined the population and thus the inferences need to be confined to the limited population.

• Stratified random sampling:
  • The sampling units are not homogeneous and divide themselves into non-overlapping groups, called strata.
  • Separate random samples are chosen from each stratum with sample sizes proportional to the size of the stratum.
  • The purpose is to be sure that each of the strata is neither over- or under-represented. For example,
    • A sample survey is conducted to gather some political opinions in a city,
    • The city is subdivided into several ethnical group,
    • Separate random samples of families could be chosen from each group.

• In an experiment, we apply treatments to experimental units and proceed to observe the effect.
• Excessive variability among experimental units will wash out any detectable difference among populations.
• A standard approach is to assign the experimental units randomly to different treatments. For example,
  • In a drug study, we use a total of 200 available patients.
  • Age, gender, weight, and other characteristics of the patients may produce variability in the results.
  • In a completely randomized design, 100 patients are assigned randomly to placebo and 100 to the active drug.

• Example 1.3. A corrosion study to determine if coating of an aluminium reduces the amount of corrosion.
• A corrosion measurement can be expressed in thousands of cycles to failure. (more cycles means less corrosion)
• Four treatment combinations:
  • two levels of coating: no coating and chemical coating
  • two relative humidity level: 20% and 80%
• Eight experiment units are used, with two assigned randomly to each of four treatment combinations.
  • The corrosion data are averages of 2 specimens.

Table 2: Data for Example 1.3

Coating	Humidity	Thousands of Cycles to Failure
Uncoated	20%	975
Uncoated	80%	350
Chemical Coated	20%	1750
Chemical Coated	80%	1550

Figure 4: Corrosion results for Example 1.3.

• Consider the variability around the average:
  • The use of the chemical corrosion coating procedures appears to reduce corrosion if two corrosion values at each treatment combination are close together.
  • If each corrosion value is an average of two values that are widely dispersed, then this variability wash away any information we obtain.
• Three concepts are illustrated:
  • Random assignment of treatment combination to experiment units.
  • The use of sample average in summarizing sample information.
  • The need for consideration of measures variability in the analysis of sample sets.