chapter 12 textbook Flashcards
Determining sample size for probability samples
As a general rule, the larger the sample is, the smaller the sampling error and the margin of error, which is a confidence interval around the sample statistic within which the population parameter is expected to be.
However, larger samples cost more money, and the resources available for a project are always lim- ited.
Budget available
The sample size for a project is often determined, at least indirectly, by the budget avail- able. Thus, it is frequently the last project factor determined
Although this approach may seem highly unscientific and arbitrary, it is a fact of life in a corporate environment.
Rule of thumb
Potential clients may specify in the RFP (request for proposal) that they want a sample of 200, 400, 500, or some other size. Sometimes, this number is based on desired sam- pling error. In other cases, it is based on nothing more than past experience. The justi- fication for the specified sample size may boil down to a “gut feeling” that a particular sample size is necessary or appropriate.
Number of supgrouos analyzed
In any sample size determination problem, consideration must be given to the number and anticipated size of various subgroups of the total sample that must be analyzed and about which statistical inferences must be made
Other things being equal, the larger the number of subgroups to be analyzed, the larger the required total sample size. It has been suggested that a sample should provide, at a minimum, 100 or more respondents in each major subgroup and 20 to 50 respon- dents in each of the less important subgroups.
Traditional statsyicial methods
- an estimate of the population standard deviation
- the acceptable level of sampling error
- the desired level of confidence that the sample result will fall within a certain range (result ± sampling error) of true population values
What you need to estimate a sample size
normal distribution
the normal distribu- tion is useful for a number of theoretical reasons; one of the more important of these relates to the central limit theorem. According to the central limit theorem, for any population, regardless of its distribution, the distribution of sample means or sample proportions approaches a normal distribution as sample size increases. The importance of this tendency will become clear later in the chapter.
the normal distribution is a useful approximation of many other discrete probability distributions.
Central limit theorem: The idea that a distribution of a large number of sample means or sample proportions will approxi- mate a normal distribution, regardless of the distribution of the population from which they were drawn.
standard normal distribution
Normal distribution with a mean of zero and a standard deviation of one.
Population and sample distribution
Pop distribution: A frequency distribution of all the elements of a population.t has a mean, usually represented by the Greek letter μ, and a standard deviation, usually represented by the Greek letter σ.
Sample: A frequency distribution of all the elements of an individual sample. n a sample distribution, the mean is usually represented by X and the standard deviation is usually represented by S
Sampling distribution of the mean
A theoretical frequency distribu- tion of the means of all possible samples of a given size drawn from a particular population; it is normally distributed
Standard error of the mean: The standard deviation of a distri- bution of sample means.
Common sense tells us that, with larger samples, individual sample means will, on the average, be closer to the population mean.
* The distribution has a mean equal to the population mean.
* The distribution has a standard deviation (the standard error of the mean) equal to the population standard deviation divided by the square root of the sample size:
This statistic is referred to as the standard error of the mean (instead of the stan- dard deviation) to indicate that it applies to a distribution of sample means rather than to the standard deviation of a sample or a population —> applies only to a simple random sample
Point and interval estimates
Point estimate: a sepciofic value etsoimate of a population value
Interval estimate: The interval or range of values within which the true population value is estimated to fall
Confidence level: The probability that a particular interval will include the true pop- ulation value; sometimes called confidence coefficient.
Confidence interval: An interval that, at the specified confidence level, includes the true population value.
Sampling distribution of the proportion
A relative frequency distribution of the sample proportions of many random samples of a given size drawn from a particular pop- ulation; it is normally distributed.
Has the following characteristics: * It approximates a normal distribution.
* The mean proportion for all possible samples is equal to the population proportion.
* The standard error of a sampling distribution of the proportion can be computed with the following formula:
In an ideal world, the level of confidence would always be very high and the amount of error very low.
