Sampling Error: Definition and Formula

“Random variation” or “random error” is inherent in predictive statistical models. It is defined as the difference between the expected value of the variable (according to the statistical model of the problem) and the actual value of the variable. If the sample size is large, these errors are distributed well above and below the mean and then cancel each other out, resulting in the expected value of zero.

This error stands in sharp contrast to another modelling error, the so-called “sampling error.” This is a systematic error that has crept into the system due to biased assumptions or experimental design. Because this error is directly defined by the variable, its expected value is nonzero, creating a serious flaw in the model.

Sampling error is defined as the amount of incorrect information in estimating a particular value, resulting from considering a small portion of the population, called the sample, instead of the entire population. A sample survey focuses on surveying a small portion of the population, this means that there is always a large amount of error in the resulting data since large amount of data is not being considered .This uncertainty can be interpreted as variable error or sampling error.

The size and shape of the sample are used to calculate the sampling error rate. This specific measurement is called the accuracy of the selection process. Selection bias is also an important concept in distinguishing errors. This error is considered a systematic error.

Formula to find the sampling error is given as follows:

Sampling Error (SE) = (1/√ N) 100

where,

• N is Sample Size

To reduce sampling error there are two methods that are:

• Increase Sample Size
• Stratification

Increase Sample Size

Increasing your sample size means getting closer to your population. You can choose any sample of any size from your population. The size depends on your experiment and situation. If you increase your sample size, make sure the portion is appropriate for each demographic and screening question. A larger sample size reduces the chance of sampling error. Therefore, sampling error is inversely proportional to the sample size, which is very important to reduce error.

Stratification

It is very easy to obtain a sample if all the population units are homogeneous or if the populations have the same characteristics. It is very easy to obtain a sample if all the population units are homogeneous or if the populations have the same characteristics. A sample can be considered representative of the entire population. The population is divided into different groups called strata, which contain similar units. A sample can be considered representative of the entire population. However, if the population is not homogeneous (i.e., a population with different characteristics), it is impossible to obtain a complete sample. Therefore, the subsample size for each stratum is proportional to the stratum size.

Other ways to find Sampling Error are,

Split Population into Smaller Groups

Use groups proportional to their existence in your overall target market. For example, if 40% of your target market consists of a certain demographic, ensure that you use 40% of this demographic in your survey study.

Use Random Sampling

In general, you need a more diverse, yet precise approach to recruiting participants for your survey.

For example, you can draw a random sample of participants, but control who can take part in your survey based on demographic and psychographic information. You can also ask questions that participants must answer in a certain way to complete the survey.

Sample Size Too Small: When the sample size is too small, it may lead to errors .

Sampling Bias: It occurs when the members of the sample are unrepresentative of the population.

Sample Coverage Error: This could happen for a variety of reasons, including the sample being too small, the sample being unrepresentative of the population, or the sample being contaminated.

Sample Contamination: There Might be chance where Sample may be diluted .This leads to less accuracy .

Sample Unrepresentativeness: This could happen for a variety of reasons, including the person being too busy to take the survey, the person refusing to take the survey, or the person being unable to take the survey for some reason.

Example 1: A manufacturing company produces light bulbs. It is estimated that 2% of the light bulbs produced are defective. If a box contains 100 light bulbs, what is the probability that exactly 3 light bulbs in the box are defective?

Solution:

To find the probability of getting exactly 3 defective light bulbs out of 100, we can use the binomial probability formula:

P(X = 3) = (¹⁰⁰C₃) × (0.02)³ × (0.98)⁹⁷

≈ 0.1168 or 11.68%

Example 2: In a particular city, 25% of the residents have a certain disease. If 5 residents are selected at random, what is the probability that exactly 2 of them have the disease?

Solution:

Let X be the number of residents with the disease out of 5 selected.

P(X = 2) = (⁵C₂) × (0.25)² × (0.75)³

≈ 0.2734 or 27.34%

Example 3: A fair coin is tossed 10 times. What is the probability of getting exactly 6 heads?

Solution:

Tossing a fair coin 10 times is a binomial experiment with n = 10 and p = 0.5 (probability of getting a head).

P(X = 6) = (¹⁰C₆) × (0.5)⁶ × (0.5)⁴

≈ 0.2051 or 20.51%

What is Sampling Error?

A sampling error is the difference between a statistic based on a sample and the corresponding population parameter. Sampling error is due to chance of error or real differences between a sample and a population.

What is meant by Reducing the Level of Confidence?

If you want to reduce the standard error of the survey, you need to reduce the level of confidence. This means that you need to be less confident in the results.

How Are Sampling Errors Controlled?

By increasing the sample size based on the portion of people, sampling errors can be less common. The likelihood of departures from the real population declines as the sample size grows closer to the population as a whole.