Statistical Sampling Techniques and Sample Size Calculation

Posted on Oct 16, 2024 in Mathematics

Statistical Sampling

Statistical sampling is a technique for selecting a subset of individuals from a population to infer properties of the entire population. This process saves resources while aiming to obtain similar results as a full population study.

Statistical Sample

A statistical sample is a subset of cases or individuals within a population. Samples are obtained to infer properties of the whole population and should be representative of it. A proper sampling technique is crucial for achieving representativeness.

Sampling Techniques

Probability Sampling

Probability sampling methods allow for calculating the probability of selecting any possible sample. This set of techniques is preferred when feasible.

Random Sampling

Random sampling ensures that each element of a finite population has an equal chance of being included in the sample.

Stratified Sampling

Stratified sampling involves dividing the population into homogeneous groups (strata) based on shared traits. Each stratum is assigned a quota, determining the number of its members included in the sample.

Systematic Sampling

Systematic sampling selects elements from an ordered list at a fixed interval, starting from a randomly chosen point.

Cluster Sampling

Cluster sampling is used when the population is naturally divided into groups (clusters) assumed to represent the population’s variability. Only some of these clusters are selected for the study.

Sample Size

Sample size refers to the number of subjects included in the sample. An appropriate sample size is essential for ensuring that the data obtained are representative of the population.

Objectives of Sample Size Determination

  1. Estimate a parameter with a desired confidence level.
  2. Detect a specific difference between study groups with a minimum guarantee.
  3. Reduce costs or increase the speed of the study.

Calculation of Sample Size

Sample size is determined to obtain an accurate estimate of a population parameter.

Estimation of Parameters

Parameter estimation involves inferring the value of a population parameter using statistical inference from the observed sample values. Key concepts include confidence interval, parameter variability, error, confidence level, critical value, and alpha (α) value.

Estimating a Ratio

The formula for calculating the required sample size (n) for estimating a ratio includes: Zα (Z value for the alpha risk, typically 1.96 for α=0.025), p (presumed population proportion), and i (desired accuracy; 2xi is the confidence interval width).

Estimating a Mean

The formula for calculating the required sample size (n) for estimating a mean includes: Zα (Z value for the alpha risk), s2 (presumed population variance), and i (desired accuracy).

Sample Size Formula

n = (z2 * p * q * M) / ((N-1)2 + z2 * e * p * q)

Where:

  • n: Sample size
  • N: Population size
  • e: Degree of error (typically 5% to 10%)
  • p: Probability of success
  • q: Probability of failure (q = 1 – p)
  • z: Confidence level

Advantages of Sampling

  1. Feasibility for large or infinite populations.
  2. Adaptability to changing population characteristics.
  3. Cost reduction.
  4. Increased speed.
  5. Practicality for complex studies.
  6. Efficiency for homogeneous populations.
  7. Applicability to destructive or consumptive testing.