Assess representativeness using deviations, weights, and fit metrics. Spot imbalance early with structured share comparisons. Make sampling decisions with confidence, clarity, exports, and visuals.
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| Group | Population Share % | Sample Share % | Comment |
|---|---|---|---|
| Age 18–24 | 22 | 18 | Under-represented in the sample. |
| Age 25–34 | 28 | 31 | Slightly over-represented. |
| Age 35–44 | 26 | 27 | Very close to the target population. |
| Age 45+ | 24 | 24 | Perfectly aligned in this simple example. |
This example shows how the calculator compares population composition with achieved sample composition across meaningful strata.
The calculator combines composition fit, weighting burden, and precision impact. It is designed for practical sample quality review.
Representativeness Index = (1 - 0.5 × Σ|pᵢ - sᵢ|) × 100
pᵢ is the population share for group i, and sᵢ is the sample share. The score reaches 100 when the distributions match exactly.
Mean Absolute Deviation = [Σ|pᵢ - sᵢ| / k] × 100
This shows the average percentage-point mismatch across k entered groups.
RMSE = √[Σ(pᵢ - sᵢ)² / k] × 100
RMSE emphasizes larger mismatches more heavily than simple average deviation.
Chi-Square = Σ[(Oᵢ - Eᵢ)² / Eᵢ], where Oᵢ = n × sᵢ and Eᵢ = n × pᵢ
This compares observed sample counts with expected counts under perfect representativeness.
Weight Ratio = pᵢ / sᵢ
A ratio above 1 suggests under-representation. A ratio below 1 suggests over-representation.
Effective Sample Size = (Σw)² / Σw²
Weights reduce the usable information in a sample. This metric estimates the sample size after weighting burden is considered.
Margin of Error ≈ z × √(0.25 / ESS) × √DEFF × FPC × 100
This is a worst-case proportion margin of error using the effective sample size, design effect, and finite population correction.
It measures how closely the sample distribution matches the population distribution across the groups you entered. Higher values indicate better alignment and usually lower weighting burden.
No. A large sample can still be skewed if important groups are under-covered or over-covered. Composition matters as much as sample size.
Weighting often reduces usable precision. Effective sample size estimates how much information remains after unequal weights are applied to correct imbalance.
Scores above 95 are typically excellent, 90 to 94 are strong, 80 to 89 are fair, and lower scores suggest notable composition issues.
Yes, if you combine categories into mutually exclusive groups, such as region by gender or age by income. Each row should represent one final group.
It can become unreliable when important population groups are missing from the sample or when weighting instability prevents a sensible effective sample size estimate.
Yes, ideally. Minor rounding issues are common, so the auto-normalize option rescales both distributions to 100 before calculating the metrics.
No. It is a strong screening tool for composition quality, but final weighting plans should still consider nonresponse, calibration targets, and design structure.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.