2.3 Sampling units and sampling errors

Sampling units and errors are crucial in survey design. They determine how accurately we can measure a population. Understanding these concepts helps researchers select the right sample and interpret results.

Sampling errors can skew findings, but proper techniques minimize their impact. By grasping these ideas, we can create more reliable surveys and draw better conclusions from the data we collect.

Sampling Basics

Population and Sample Concepts

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• Population encompasses all individuals or objects of interest in a study
• Sample represents a subset of the population selected for investigation
• Sampling frame consists of a comprehensive list of all units in the population
• Sampling unit refers to the individual entity selected from the sampling frame
• Element denotes the specific characteristic or attribute being measured within each sampling unit

Selection and Representation

• Proper sample selection ensures representativeness of the population
• Random sampling techniques promote unbiased selection of units
• Sample size affects the precision and reliability of estimates
• Stratification divides the population into homogeneous subgroups before sampling
• Cluster sampling involves selecting groups of units rather than individual units

Sampling Errors

Types of Sampling Errors

• Sampling error arises from using a sample to estimate population parameters
• Non-sampling error occurs due to factors unrelated to the sampling process
• Bias introduces systematic deviation from the true population value
• Precision measures the consistency of results across repeated samples
• Accuracy reflects how close the sample estimate is to the true population value

Sources and Mitigation of Errors

• Selection bias results from improper sampling methods or incomplete sampling frames
• Response bias occurs when respondents provide inaccurate or misleading information
• Measurement error stems from inaccurate data collection instruments or procedures
• Coverage error happens when the sampling frame does not fully represent the population
• Strategies to reduce errors include increasing sample size and improving sampling techniques

Sampling Statistics

Measures of Variability

• Standard error quantifies the variability of sample estimates
• Margin of error represents the range within which the true population parameter likely falls
• Confidence interval provides a range of plausible values for the population parameter
• Sampling distribution describes the probability distribution of sample statistics

Calculation and Interpretation

• Standard error calculation: $SE = \frac{s}{\sqrt{n}}$ where s is the sample standard deviation and n is the sample size
• Margin of error computation: $MOE = z * SE$ where z is the critical value from the standard normal distribution
• Confidence interval construction: $CI = \hat{\theta} \pm MOE$ where $\hat{\theta}$ is the sample estimate
• Sampling distribution shape approaches normal distribution as sample size increases (Central Limit Theorem)