Business Statistics - Sampling Factors

Sampling factors refer to the characteristics that affect the sample size and sample design of a research study. These factors can influence the representativeness and accuracy of the sample, and therefore, the validity of the study results. Some of the common sampling factors include:

• Population size: The size of the target population can affect the sample size and design. A larger population may require a larger sample size to ensure representativeness.
• Sampling method: The sampling method used can influence the sample size and design. For instance, a random sampling method may require a larger sample size compared to a non-random method.
• Sampling frame: The sampling frame refers to the list of all the eligible units in the population. A poorly defined or incomplete sampling frame can affect the representativeness of the sample.
• Sampling error: Sampling error refers to the difference between the sample statistic and the population parameter. The sampling error can affect the precision and accuracy of the study results.
• Sampling bias: Sampling bias refers to the systematic error introduced into the sample due to a flawed sampling process. Sampling bias can affect the representativeness and validity of the sample.

Sample Size

The number of samples and the size of the samples can have different implications on the accuracy and reliability of statistical analyses.

A high number of samples generally increases the accuracy and reliability of the results, as it reduces the effect of random variability and increases the representativeness of the sample for the population. However, a high number of samples may also increase the cost and time required to collect and process the data, and may not always be feasible or necessary depending on the research question and available resources.

The size of the samples also has implications for the accuracy and reliability of the results. A larger sample size generally reduces the random variability and sampling error, increases the precision and confidence of the estimates, and allows for more detailed and complex analyses. However, a larger sample size may also increase the complexity and cost of the data collection and analysis, and may not always be necessary or feasible depending on the research question and available resources.

On the other hand, a smaller sample size may lead to more random variability and sampling error, lower precision and confidence of the estimates, and limited statistical power for detecting differences or relationships between variables. However, a smaller sample size may also be more feasible and cost-effective and may be sufficient for exploratory or preliminary analyses or when the population is small or homogeneous.

Hence, the choice of sample size and number of samples should be based on the research question, the characteristics of the population, the available resources, and the desired level of accuracy, precision, and confidence.

Poor Sampling

Poor sampling conditions refer to situations where the sample is not representative of the population, leading to biased or inaccurate results. Some examples of poor sampling conditions include:

• Non-random sampling: When the sampling method is not random, it can introduce bias into the sample. For example, if a company only surveys customers who have complained about a product, the results may not be representative of all customers.
• Small sample size: A small sample size may not provide enough data to draw accurate conclusions. For example, a survey of only 10 customers may not be representative of the entire customer base.
• Self-selection bias: This occurs when individuals self-select into a study or survey, leading to a non-representative sample. For example, if a company surveys only customers who voluntarily sign up to participate, it may not be representative of all customers.
• Response bias: This occurs when participants in a study or survey respond in a way that they think is expected or socially desirable, rather than providing accurate answers. For example, if a company asks customers if they recycle and customers feel that recycling is socially desirable, they may over-report their recycling habits.
• Sampling frame bias: This occurs when the sampling frame (the list of individuals or entities from which the sample is drawn) is not representative of the population. For example, if a company only surveys customers who have provided their email addresses, it may miss customers who do not use email or who have opted out of marketing communications.

Correction Factor

Correction factor is used to adjust the standard deviation of a sample when the sample size is small (less than 30) and the population standard deviation is unknown. It is used to provide a more accurate estimate of the population standard deviation.

The formula for calculating the correction factor is:

Correction factor = sqrt[(N-n)/(N-1)]

where?

N is the population size?

n is the sample size.

Example:??

If a sample of 20 items is taken from a population of 100, the correction factor would be:

Correction factor = sqrt[(100-20)/(100-1)] = 0.8989

The corrected sample standard deviation can be calculated by multiplying the sample standard deviation by the correction factor.

For instance, if the sample standard deviation is 5, then the corrected sample standard deviation would be:

Corrected sample standard deviation = 5 x 0.8989 = 4.49

The correction factor is important in ensuring that the sample standard deviation is not underestimated, which can lead to incorrect statistical inferences.