## Simple Random Sampling

**Definition:**

Simple Random Sampling is a type of probability sampling for selecting a random sample from a population, in which each member of the population has an equal chance of being selected. This means that every member of the population has the same probability of being chosen as any other member, and each possible sample of a given size has an equal probability of being selected.

### Types of Simple Random Sampling

Types of Simple Random Sampling are as follows:

**Simple random sampling with replacement**: In this method, each member of the population has an equal chance of being selected for the sample, and once a member is selected, they are not removed from the population. This means that the same member can be selected more than once.**Simple random sampling without replacement**: In this method, each member of the population also has an equal chance of being selected for the sample, but once a member is selected, they are removed from the population. This means that each member can only be selected once.**Stratified random sampling:**This method involves dividing the population into subgroups or strata based on certain characteristics, such as age or gender, and then selecting a simple random sample from each stratum. This ensures that the sample represents the diversity of the population.

### Simple Random Sampling Formula

The formula for simple random sampling is as follows:

n/N = k

where:

- n is the sample size
- N is the population size
- k is the sampling fraction, which is the ratio of the sample size to the population size

To calculate the sample size, you can rearrange the formula as follows:

n = N x k

For example, if you have a population of 1000 and you want to take a simple random sample with a sampling fraction of 0.10, the formula would be:

n = 1000 x 0.10 = 100

Therefore, you would need to randomly select 100 individuals from the population to create your sample.

### Simple Random Sampling Method

Here are the steps to perform Simple Random Sampling Method:

**Define the population:**The first step is to clearly define the population that you want to study. This population should be well-defined and include all individuals that you are interested in studying.**Determine the sample size:**Next, you need to determine the sample size that you want to use for your study. The sample size should be large enough to provide accurate results, but small enough to be manageable.**Assign a number to each member of the population**: Once you have determined the sample size, you need to assign a number to each member of the population. This can be done using a random number generator or by manually assigning numbers.**Generate random numbers:**If you are using a random number generator, you need to generate a set of random numbers that corresponds to the sample size. These random numbers will be used to select the individuals for your sample.**Select the sample**: Using the random numbers, select the individuals from the population that correspond to the random numbers generated. For example, if the first three random numbers generated were 15, 77, and 94, you would select the 15th, 77th, and 94th individuals from the population.**Analyze the sample:**Once you have selected your sample, you can analyze the data that you collect to draw conclusions about the population as a whole.

### Examples of Simple Random Sampling

Here are some examples of simple random sampling:

**Polling**: Suppose a research organization wants to conduct a poll to determine the approval rating of a political candidate. They can randomly select a sample of registered voters from the population and ask them about their opinion of the candidate. By ensuring that each registered voter has an equal chance of being selected, the researchers can obtain an unbiased estimate of the candidate’s approval rating.**Quality control:**A company may want to test the quality of their products by selecting a random sample from the production line. By randomly selecting items for testing, they can ensure that the sample is representative of the entire production process and obtain accurate information about the quality of their products.**Medical research**: A medical researcher may want to study the prevalence of a particular disease in a population. They can randomly select a sample of individuals from the population and perform medical tests to determine the incidence of the disease. By ensuring that each individual has an equal chance of being selected, the researcher can obtain an unbiased estimate of the prevalence of the disease.**Education research:**A researcher may want to study the effectiveness of a new teaching method on student performance. They can randomly select a sample of students from a school and assign them to either the new teaching method or the traditional teaching method. By randomly selecting students for the study, the researcher can ensure that the sample is representative of the entire student population and obtain accurate information about the effectiveness of the new teaching method.**Social Science Research:**A social science researcher wants to study the attitudes and opinions of the general population towards a particular social issue. They can use simple random sampling to select a representative sample of individuals from the population, and then survey them to collect data on their attitudes and opinions.

**Simple Random Sampling Example Situation**

Simple Random Sampling Example Situation is as follows:

A company wants to conduct a survey to understand the job satisfaction of its employees. The company has a total of 500 employees, and they want to select a sample of 50 employees using simple random sampling.

Formula: The formula for simple random sampling is:

n/N * (N-n)/(N-1)

where:

- n: the sample size
- N: the population size

In this case, n = 50 and N = 500.

So, the formula for calculating the probability of selecting a simple random sample of 50 employees from a population of 500 is:

50/500 * (500-50)/(500-1) = 0.1 * 0.902 = 0.0902, or 9.02%.

Therefore, the probability of selecting a sample of 50 employees using simple random sampling is 9.02%. This means that any set of 50 employees has an equal chance of being selected, and the sample is representative of the population.

### When to Use Simple Random Sampling

Here are some situations where simple random sampling may be appropriate:

**When the population is relatively small:**Simple random sampling is an ideal method to use when the population size is small because it is easy to implement and doesn’t require a lot of resources.**When the population is homogenous:**Simple random sampling is suitable when the population is relatively homogenous, meaning that the characteristics of the individuals or elements are relatively similar.**When the researcher wants to avoid potential bias:**Simple random sampling is an excellent method to use when the researcher wants to avoid any potential bias in the sample selection process.**When the data is not strongly correlated**: Simple random sampling is appropriate when the data is not strongly correlated. Strong correlation between variables can result in an unrepresentative sample.

### Applications of Simple Random Sampling

Simple random sampling has numerous applications in various fields, including:

**Public opinion polls**: Simple random sampling is widely used in public opinion polls to collect data from a representative sample of the population.**Medical research**: In medical research, simple random sampling is used to select participants for clinical trials or to conduct surveys to collect data on health-related issues.**Quality control:**Simple random sampling is used in quality control to select products or items from a production line for inspection to ensure that they meet certain quality standards.**Education research**: Simple random sampling is used in educational research to select students or schools to participate in studies.**Market research:**Simple random sampling is used in market research to collect data on consumer behavior and preferences.**Environmental studies:**Simple random sampling is used in environmental studies to collect data on various environmental factors.**Social science research**: Simple random sampling is widely used in social science research to study various social phenomena.

### Purpose of Simple Random Sampling

The main purpose of simple random sampling is to obtain a representative sample of a population. A representative sample is one that accurately reflects the characteristics of the entire population, such as its demographics, behaviors, opinions, or attitudes.

Simple random sampling ensures that every individual or element in the population has an equal chance of being selected for the sample. By doing so, it eliminates potential biases that could arise from non-random sampling methods, such as convenience sampling or purposive sampling.

A representative sample obtained through simple random sampling can help researchers make generalizations about the population with a high degree of confidence. The results of statistical analyses conducted on the sample can be used to make inferences about the larger population, with a margin of error that can be quantified using probability theory.

### Characteristics of Simple Random Sampling

Characteristics of Simple Random Sampling are as follows:

**Randomness**: Every element or individual in the population has an equal chance of being selected for the sample. This ensures that the sample is representative of the population and reduces the potential for bias.**Independence**: Each element or individual in the population is selected independently of the others. The selection of one element does not influence the selection of another element.**Objectivity**: The selection of elements for the sample is based solely on chance, and there is no subjective judgment or influence involved in the selection process.**Equal probability:**Each element in the population has the same probability of being selected for the sample. This means that every possible sample of a given size has an equal chance of being selected.**Simple to use:**Simple random sampling is easy to understand, implement, and analyze, making it one of the most commonly used sampling methods in statistical research.**Appropriate for any population**: Simple random sampling can be applied to any population, regardless of size or characteristics, as long as a complete list of all elements or individuals in the population is available.

### Advantages of Simple Random Sampling

Simple random sampling has several advantages over other sampling methods, including:

**Representativeness**: Simple random sampling ensures that every individual or element in the population has an equal chance of being selected for the sample, which makes it a highly representative sample of the population.**Unbiased**: Simple random sampling eliminates potential biases that can arise from non-random sampling methods, such as convenience sampling or purposive sampling.**Easy to use**: Simple random sampling is easy to understand, implement, and analyze, making it a popular choice for researchers with limited resources or time.**Probability theory**: Simple random sampling allows for the application of probability theory to estimate the margin of error and the confidence interval of the sample, which provides a measure of the accuracy of the results.**Flexibility**: Simple random sampling can be used in a wide range of research applications and is suitable for any population, as long as a complete list of all elements or individuals in the population is available.

### Disadvantages of Simple Random Sampling

While simple random sampling has several advantages, it also has some disadvantages, including:

**Large sample size**: Simple random sampling requires a large sample size to be representative of the population. A larger sample size can increase the cost and time required to conduct the research.**Inefficiency:**Simple random sampling can be inefficient when the population is large and geographically dispersed, as it requires a complete list of all elements or individuals in the population.**Under-representation:**Simple random sampling can result in under-representation of certain subgroups within the population if they are not properly identified in the sampling process.**Selection bias:**While simple random sampling eliminates selection bias, it does not eliminate other forms of bias, such as measurement bias or response bias.**Not suitable for small populations**: Simple random sampling is not suitable for small populations as it can result in a very small sample size that may not be representative of the population.