1.2.1. Basic Concepts of Sampling
Definitions
Population refers to the entire group of individuals or items that we want to study or draw conclusions about. Whereas Sample is a subset or part of the population selected for the actual study.
Sampling is a fundamental concept in statistics and research, essential for drawing inferences about a population without examining every individual unit. The basic idea of sampling is to select a subset of individuals or observations from a larger population, analyze the sample, and then generalize the findings to the entire population.
Popoulation and Sample
- Population: The population refers to the entire group of individuals or items that we want to study or draw conclusions about. It includes all the elements we are interested in, and its size can be finite or infinite. For example, if we are studying the average monthly income of adults in a Addis Abeba city, the population would be all adults in that city.
- Sample: A sample is a subset of the population selected for the actual study. The sample should be representative of the population to ensure that the results obtained from the sample can be generalized to the population. For instance, if we select 1,000 adults from the city to survey their monthly income, those 1,000 adults constitute the sample.
The relationship between a population and sample is shown in Figure 1.2.
Figure 1.2. The relationship between sample and popoulation
The relationship between a population and a sample is crucial. If the sample is not representative of the population, the results of the study can be biased and misleading. Therefore, selecting a proper sampling method is essential for accurate and reliable research outcomes.
Sampling and Inference
Sampling and inference are hand-in-hand; without a well-designed sample, the inferences drawn can be biased or inaccurate. The goal of statistical inference is to make valid and reliable conclusions that can be generalized to the population with a known level of confidence.
Without sampling, inference would be restricted to the few instances where the entire population can be studied (Census Study), which is rare. Therefore, sampling is an indispensable tool in statistics world.
- Sampling: is a staitsical process of selecting a respresntative sample from the enitre popoulation of the study. Simply, the process of selecting those 1000 adults from the city adult popoulations is called sampling
- Inference in statistics: refers to the process of drawing conclusions about a population based on information gathered from a sample. Because it is often impractical or impossible to study an entire population, researchers rely on sampling to collect data and then use inferential statistics to make educated guesses or predictions about the broader population.
Look at the following figure 1.3. to learn the relationship between sampling and inferance
Figure 1.2. The relationship between sampling and Inferance
Parameters and Statistics
Both popoulations and samples have there own statistical measurements called parameter and statistcs, respectively.
- Parameter: A parameter is a numerical value that describes a characteristic of the population, such as the population mean (ยต), population variance (ฯ²), or population proportion (P). For instance, the average (ยต) monthly income of adults in the city is 9000 birrs. Parameters are often unknown because it’s usually impractical to measure every member of the population.
- Statistic: A statistic is a numerical value that describes a characteristic of a sample, such as the sample mean (\(\bar{x}\)), sample variance (s²), or sample proportion (p). For instance, the average (\(\bar{x}\)) monthly income of 1000 sample adults is 10,000 birrs. Since the sample is only a part of the population, statistics can vary depending on the sample taken.
A population parameter is a single, fixed or constant value that describes a specific characteristic of the entire population. Since the parameter is derived from the entire population, there is only one true value for any given parameter.
However, sample statistic is a numerical value that describes a characteristic of a sample taken from the population. Since different samples can be drawn from the same population, the value of the statistic can vary from one sample to another. Therefore, there are potentially many different statistics for each characteristic depending on the sample selected. Which meansthe avaerge (\(\bar{x}\)) monthly income of another sample may be differnet from the first sample value of 10,000birrs
Let see some common statistical measures that used throughout for this course. Each measures have population parameter and sample statistic
Table 1 Measurement for Parameter and statistic
| Measurement | Parameter | Statistics |
|---|---|---|
| Mean | \(\mu\) | \(\bar{x}\) |
| Variance | \(\sigma^2\) | \(s^2\) |
| Proportion | \(P\) | \(\hat{p}\) |
| Difference between Means | \(\mu_1 - \mu_2\) | \(\bar{x}_1 - \bar{x}_2\) |
| Difference between Proportions | \(P_1 - P_2\) | \(\hat{p}_1 - \hat{p}_2\) |
Activity 1: Sampling Theory
Case Study: XYZ Corporation is a large multinational company with 10,000 employees across various departments and locations. The company is interested in measuring the overall job satisfaction level of its employees to improve work conditions and boost morale.
To conduct this study, the HR department decided to survey a subset of employees rather than the entire workforce. They randomly selected 500 employees from different departments to participate in the survey.
The survey included questions about job satisfaction, work-life balance, compensation, and management. After analyzing the responses, the HR department found that the average job satisfaction score was 7.8 out of 10.
Required:
- Identify the population in this case.
- Identify the sample in this study.
- Identify the parameter of interest in this case.
- Identify the statistic calculated in this case.
Answers:
- Population: The population is the entire workforce of XYZ Corporation, which consists of 10,000 employees.
- Sample: The sample is the 500 employees who were randomly selected to participate in the survey.
- Parameter: The parameter of interest is the true average job satisfaction score of all 10,000 employees in XYZ Corporation.
- Statistic: The statistic is the average job satisfaction score of 7.8 out of 10, which was calculated from the sample of 500 employees.
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