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Sample size: 0
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Run the current sampling method multiple times to see the distribution of sample means.
Probability Sampling
Simple Random Sampling
Every member of the population has an equal and independent chance of being selected. Like drawing names from a hat.
✓ Advantages
- Unbiased and representative
- Easy to understand and explain
- Statistical theory is straightforward
- Sample statistic provides good estimate of population parameter
✗ Disadvantages
- Requires complete population list
- Can be expensive to implement
- May miss small subgroups by chance
Best used when: You have a complete list of the population and want the simplest, most unbiased approach.
Probability Sampling
Stratified Sampling
Population is divided into homogeneous groups (strata) where members within each stratum are similar to each other. Then random samples are taken from each stratum proportionally.
Key Insight: Works best when strata are homogeneous within (similar cases grouped together) but heterogeneous between (strata differ from each other).
✓ Advantages
- Ensures representation of all groups
- More precise estimates than simple random
- Can compare between strata
- Reduces sampling variability
✗ Disadvantages
- Requires knowledge of strata
- More complex to implement
- May need different sampling rates
Best used when: Your population has distinct subgroups (like class year, income level) and you want to ensure each is adequately represented.
Probability Sampling
Cluster Sampling
Population is divided into clusters (often geographic). Then entire clusters are randomly selected and all members of those clusters are surveyed.
Key Insight: Works best when each cluster is heterogeneous within (diverse mix of individuals) and clusters are homogeneous between (similar to each other). Opposite of stratified sampling!
✓ Advantages
- Cost-effective and practical
- No need for complete population list
- Convenient for geographically dispersed populations
- Reduces travel/data collection costs
✗ Disadvantages
- Less precise than other methods
- Clusters may not be representative
- Higher sampling error if clusters differ
Best used when: Your population is naturally grouped (neighborhoods, schools, hospitals) and sampling individuals would be too expensive or impractical.
Probability Sampling
Multistage Sampling
Like cluster sampling, but instead of surveying everyone in selected clusters, we take a random sample within each selected cluster. This is a two-stage process.
Key Insight: More practical than cluster sampling when clusters are large. Combines the cost savings of cluster sampling with better precision from within-cluster sampling.
✓ Advantages
- More economical than simple random sampling
- More precise than pure cluster sampling
- Practical for large, dispersed populations
- Balances cost and accuracy
✗ Disadvantages
- More complex to plan and execute
- Requires sampling at multiple levels
- Analysis is more complicated
Best used when: Clusters are large and you want cost savings without surveying every individual in selected clusters (e.g., select villages, then sample people within each village).
Non-Probability Sampling ⚠️
Convenience Sampling
Samples are selected based on availability and ease of access, without randomization. Not recommended for generalizing to a population.
⚠️ Warning: This method introduces bias and does not allow you to make valid inferences about the population. Results cannot be generalized.
✓ Advantages
- Fast and inexpensive
- Easy to implement
- Useful for pilot studies or exploratory research
✗ Disadvantages
- High risk of bias
- Not representative of population
- Cannot generalize findings
- Sample statistic is likely biased estimate
Best used when: You need quick preliminary data or when other methods are impossible, but you cannot make generalizations about the population.
Non-Probability Sampling ⚠️
Quota Sampling
Non-random sampling where researchers ensure specific numbers (quotas) are met for different groups. Not recommended for valid statistical inference.
⚠️ Warning: While quotas ensure group representation, selection within groups is not random, introducing bias. Cannot generalize to population.
✓ Advantages
- Ensures group representation
- Faster than stratified sampling
- No need for random selection
✗ Disadvantages
- Introduces selection bias
- Not truly representative
- Researcher bias in selection
- Cannot make valid population inferences
Best used when: You need quick representation of subgroups but randomization is not feasible. However, stratified sampling is always preferred if valid inference is needed.
Population Groups
Population Parameter vs Sample Statistic
Measuring: —
The goal of sampling is to use the sample statistic to estimate the unknown population parameter.
Population Parameter (μ)
True value for entire population
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Sample Statistic (x̄)
Estimate from our sample
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Bias: —
With probability sampling methods, the sample statistic provides an unbiased estimate of the population parameter.