# Sampling Errors

Statistical errors that arise when a sample does not represent the whole population

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## What are Sampling Errors?

Sampling errors are statistical errors that arise when a sample does not represent the whole population. They are the difference between the real values of the population and the values derived by using samples from the population.

Sampling errors occur when numerical parameters of an entire population are derived from a sample of the entire population. Since the whole population is not included in the sample, the parameters derived from the sample differ from those of the actual population.

They may create distortions in the results, leading users to draw incorrect conclusions. When analysts do not select samples that represent the entire population, the sampling errors are significant.

### Summary

• Sampling errors occur when numerical parameters of an entire population are derived from samples of the entire population.
• The difference between the values derived from the sample of a population and the true values of the population parameters is considered a sampling error.
• The errors can be eliminated by increasing the sample size or the number of samples.

### Sampling Errors Explained

Sampling errors are deviations in the sampled values from the values of the true population emanating from the fact that a sample is not an actual representative of a population of data.

Since there is a fault in the data collection, the results obtained from sampling become invalid. Furthermore, when a sample is selected randomly, or the selection is based on bias, it fails to denote the whole population, and sampling errors will certainly occur.

They can be prevented if the analysts select subsets or samples of data to represent the whole population effectively. Sampling errors are affected by factors such as the size and design of the sample, population variability, and sampling fraction.

Increasing the size of samples can eliminate sampling errors. However, to reduce them by half, the sample size needs to be increased by four times. If the selected samples are small and do not adequately represent the whole data, the analysts can select a greater number of samples for satisfactory representation.

The population variability causes variations in the estimates derived from different samples, leading to larger errors. The effect of population variability can be reduced by increasing the size of the samples so that these can more effectively represent the population.

Moreover, sampling errors must be considered when publishing survey results so that the accuracy of the estimates and the related interpretations can be established.

### Practical Example

Suppose the producers of Company XYZ want to determine the viewership of a local program that airs twice a week. The producers will need to determine the samples that can represent various types of viewers. They may need to consider factors like age, level of education, and gender.

For example, people between the ages of 14 and 18 usually have fewer commitments, and most of them can spare time to watch the program twice weekly. On the contrary, people between the age of 18 and 35 usually have tighter schedules and will not have time to watch TV.

Hence, it is important to draw a sample proportionately. Otherwise, the results will not represent the real population.

Since the exact population parameter is not known, sampling errors for samples are generally unknown. However, analysts can use analytical methods to measure the amount of variation caused by sampling errors.

### Categories of Sampling Errors

• Population Specification Error – Happens when the analysts do not understand who to survey. For example, for a survey of breakfast cereals, the population can be the mother, children, or the entire family.
• Selection Error – Occurs when the respondents’ survey participation is self-selected, implying only those who are interested respond. Selection errors can be reduced by encouraging participation.
• Sample Frame Error – Occurs when a sample is selected from the wrong population data.
• Non-Response Error – Occurs when a useful response is not obtained from the surveys. It may happen due to the inability to contact potential respondents or their refusal to respond.