All Labs

Sampling & Randomization Lab

Compare five sampling methods on a visual population grid. Draw samples, compute statistics, and build sampling distributions to understand bias, variability, and the Central Limit Theorem.

Guided Experiment: Comparing Sampling Methods

Which sampling method do you think will give the most accurate estimate of the population mean? Will convenience sampling be biased?

Write your hypothesis in the Lab Report panel, then click Next.

Population Grid (20 x 20 = 400 units)

Unselected (shaded by value)

Controls

Population: μ = 170 cm, σ = 10 cm

Sample Size (n)30
Number of samples100

Results

xˉ=∑xin\bar{x} = \frac{\sum x_i}{n}
s=∑(xi−xˉ)2n−1s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}
SE=sn,MOE=1.96×SE\mathrm{SE} = \frac{s}{\sqrt{n}}, \quad \mathrm{MOE} = 1.96 \times \mathrm{SE}

Population Parameters

N
400
μ (true mean)
169.80
σ (true SD)
10.13

Current Sample (Simple Random)

Draw a sample to see statistics

Sampling Distribution of x̄

Data Table

(0 rows)
#Sample #MethodnSample MeanSample SDMargin of Error
0 / 500
0 / 500
0 / 500

Reference Guide

Simple Random Sampling (SRS)

Every member of the population has an equal probability of being selected. This is the gold standard for unbiased estimation.

Each possible sample of size n is equally likely. SRS requires a complete list (sampling frame) of the population.

SRS eliminates selection bias but may not capture every subgroup proportionally, especially in small samples.

Stratified Sampling

The population is divided into non-overlapping strata (subgroups), then a random sample is drawn from each stratum proportionally.

Stratification reduces sampling variability when the strata are internally homogeneous. It guarantees representation from every subgroup.

Common stratification variables include age group, geographic region, income bracket, or grade level.

Cluster Sampling

The population is divided into clusters (groups), then entire clusters are randomly selected and all members within them are surveyed.

Cluster sampling is cost-effective when the population is geographically spread out. It reduces travel and data-collection costs.

The tradeoff is higher sampling variability compared to SRS, especially if clusters differ substantially from each other.

Sampling Distribution & CLT

The sampling distribution of the sample mean shows how the mean varies across many repeated samples from the same population.

SE=σn\mathrm{SE} = \frac{\sigma}{\sqrt{n}}

The Central Limit Theorem states that regardless of the population shape, the distribution of sample means approaches a normal distribution as n increases. The standard error decreases as the square root of n.

MOE95%=1.96×sn\mathrm{MOE}_{95\%} = 1.96 \times \frac{s}{\sqrt{n}}