SAMPLING & INFERENTIAL STATISTICS, Exams of Statistics

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SAMPLING & INFERENTIAL

STATISTICS

Sampling is necessary tomake inferences about apopulation.

SAMPLING

• The group that you observe or collect data from is the sample. - The group that you make generalizations about is thepopulation. - A population consists of members of a well defined segment of people,events, or objects.

STEPS

• Identify the population. • Determine if population is accessible. • Select a sampling method. • Choose a sample that is representative of the population. - Ask the question -- can I generalize to the general population from theaccessible population?

PROBABILITY SAMPLING

• Type of sample in which "every person, object, or event in thepopulation has a nonzero chance ofbeing selected." - When probability sampling is used, inferential statistics allowestimation of the extent to which thefindings based on the sample arelikely to differ from the totalpopulation.

PROBABILITY SAMPLING

TYPES

• Random sample (continued)
  • Random selection for small samples does not guarantee that the sample willbe representative of the population. - The main advantage: the sample guarantees that any differencesbetween the sample and its populationare "only a function of chance" and notdue to bias on your part.

PROBABILITY SAMPLING

TYPES

• Stratified sample
  • Define subgroups, or strata, of interest then select a specified number ofsubjects from each subgroup. - Improves representativeness & allows you to study differences betweensubgroups of the population. - Major advantage is guaranteeing inclusion of the defined populationgroups.

PROBABILITY SAMPLING

TYPES

• Cluster sample (continued)
  • As example, students at ASU are a cluster of occupants of Tempe. If you wanted to study student shoppingpatterns in Tempe you could select acluster sample using ASU. - The data from this example of a cluster sample could not be generalized for thetotal population of Tempe.

PROBABILITY SAMPLING

TYPES

• Systematic sample

• Selection of every kth person, event or object from a list of thepopulation. - First determine number required for sample (n), then determinetotal N in population. - N/n yields the sampling interval to use for the entire list.

NON-PROBABILITY

SAMPLING

• Used when probability methods

for sampling are not possible.

• Main reason is you cannot

enumerate the populationelements.

NON-PROBABILITY

SAMPLING TYPES

• Accidental sample

• Weakest of all sampling procedures. - As example, if I wanted to know about the lighting in this classroomI would turn to the first person Isee in the classroom to interview. - No way to estimate sampling error without repeating the study usingprobability sampling technique.

NON-PROBABILITY

SAMPLING TYPES

• Quota sample
  • Select quota based on known characteristics of the population. - For example, age breakdown of a population Sample would be proportional to the size of each age segment. - You do not know whether the individuals that you select from each characteristicare representative of that characteristic. - Systematic bias can result.

SAMPLE SIZE

• Size needed depends on the precision that you need in yourresearch. - Best idea is to use as large a sample as possible because the larger thesample, the smaller the standarderror. - The standard error of a sample mean is inversely proportionate to thesquare root of the sample size.

SAMPLE SIZE

• Representativeness, not size, is

the more important consideration.

• Can't eliminate bias through

sample size!

SAMPLING ERROR

• Error can occur often with

sampling.

• Sampling error is the difference

between the mean of thepopulation and the mean of thesample.

• Since you don't know the mean

of the population, you mustestimate variability.