# Survey Weighting and Effective Sample Size: What Weights Fix and What They Cost

How survey weights work: post-stratification vs raking, the design effect, effective sample size n_eff = (sum w)^2 / sum(w^2) and when weighting hurts.

Published 2026-10-30 · Updated 2026-10-30
Canonical: https://hercules.works/blogs/survey-weighting-effective-sample-size

Weights make a sample's mix match known population shares, but they also cost precision. The effective sample size is n_eff = (sum of weights) squared divided by the sum of squared weights. The design effect from unequal weights is n divided by n_eff. In our worked example, 1,000 interviews weighted to match two benchmarks behave like 831.

## Weights Fix One Problem and Create Another

If your sample has too many metro respondents or too many young ones, weighting counts each person more or less so the totals match known benchmarks. That can reduce bias. But a respondent counted three times carries the information of one person, so precision falls.

This guide explains post-stratification and raking, the formula for effective sample size, a worked example with every number checkable, and the conditions under which weighting helps or hurts. The example data are illustrative. Our [significance testing guide](/blogs/statistical-significance-testing-india/) shows how the design effect enters a test.

## What Does a Survey Weight Do?

A weight tells your analysis how many people a respondent stands for. Underrepresented groups get weights above 1 and overrepresented groups get weights below 1. Weighted totals then match the benchmark shares you chose.

Pew Research Center's comparison of weighting methods found that "choosing the right variables for weighting is more important than choosing the right statistical method" ([Pew, 2018](https://www.pewresearch.org/methods/2018/01/26/for-weighting-online-opt-in-samples-what-matters-most/)). It also found that even the most effective adjustments "were unable to remove most of the bias" in opt-in samples. Weights help, but they do not turn a poor sample into a good one.

## Post-Stratification or Raking: Which Do You Need?

Post-stratification gives every cell of a cross-tabulation (for example metro by age band) its own weight. It needs the population share of every cell. Raking needs less. Pew describes it as iteratively adjusting each case's weight until the sample distribution aligns with the population, and says it "only requires knowing the marginal proportions for each variable used in weighting" ([Pew, how weighting methods work](https://www.pewresearch.org/methods/2018/01/26/how-different-weighting-methods-work/)). Adjusting for one variable can push another out of line, so the cycle repeats.

Raking is also called iterative proportional fitting. The Wikipedia article on the method notes that zeros in the starting table stay zero and that in some cases a solution may not exist, so check convergence and empty cells ([Wikipedia](https://en.wikipedia.org/wiki/Iterative_proportional_fitting)).

Variables you might weight on in India include city, age band, gender and NCCS. Each needs a benchmark you can cite. Do not weight to a figure you cannot source.

## How Do You Calculate Effective Sample Size?

Kish defined the design effect for unequal weights as deff = n × Σw² / (Σw)², where w is each respondent's weight. The effective sample size is the sample size divided by the design effect, which simplifies to n_eff = (Σw)² / Σw² ([Wikipedia, design effect](https://en.wikipedia.org/wiki/Design_effect)).

Two caveats from that article. The formula assumes the weights have no relationship to the outcome. Where they do, other formulas apply. And it treats the weights as known constants, which is only approximately true when they are estimated by raking. Pew's methodology for its 2016 religion survey says of the design effect: "This loss of precision, known as the design effect, is incorporated in all margins of error" ([Pew, 2016](https://www.pewresearch.org/religion/2016/08/23/methodology-10-5/markdown)).

If all weights are equal, deff = 1 and n_eff = n.

## Worked Example: 1,000 Interviews, Two Benchmarks

This sample is illustrative. Interviews by city type and age band:

| | 18 to 34 | 35 and above | Total |
|---|---|---|---|
| Metro | 420 | 280 | 700 |
| Other cities | 180 | 120 | 300 |
| Total | 600 | 400 | 1,000 |

Suppose the targets are 500 and 500 for city type and 550 and 450 for age. Raking converges to weighted totals of 275 and 225 in the metro row and the same in the other row. The weights are:

| Cell | Weight |
|---|---|
| Metro, 18 to 34 | 0.6548 |
| Metro, 35 and above | 0.8036 |
| Other, 18 to 34 | 1.5278 |
| Other, 35 and above | 1.8750 |

The weights sum to 1,000 and the sum of squared weights is 1,202.9. So n_eff = 1,000² ÷ 1,202.9 = 831, and the design effect is 1,000 ÷ 831 = 1.20. The margin of error for a 50% result is 1.96 × √(0.25 ÷ 1,000) = ±3.10 points unweighted, but ±3.40 points once n_eff is used. We checked that deff = 1 + CV², where CV is the coefficient of variation of the weights, gives the same 1.20.

A harsher case shows how the cost grows. If 900 respondents carry weight 0.75 and 100 carry weight 3.25, the weights still sum to 1,000, but n_eff drops to 640. A few heavily weighted respondents can dominate an estimate.

## When Does Weighting Help, and When Does It Hurt?

| Situation | Effect |
|---|---|
| Variables you weight on are related to what you measure | Helps: reduces bias |
| Weights differ little across respondents | Small cost: n_eff stays close to n |
| A few cells need very large weights | Hurts: n_eff falls sharply, estimates become volatile |
| Weighting variables unrelated to the outcome | Adds variance with little bias reduction |
| Benchmark is out of date or unsourced | Moves the sample toward the wrong target |
| Subgroup analysis on thin cells | Margins widen, as Pew notes for subgroups |

Before you weight, check whether the raw and weighted answers differ. If they barely move, report both and keep it simple. If they move a lot, ask why the sample is so uneven and whether better quotas at fieldwork would be cheaper than correcting afterwards.

## A Checklist for Using Weighted Data

1. Write down the weighting variables and the source of each benchmark.
2. Report both n and n_eff.
3. Use n_eff, or standard errors adjusted for weights, in margins of error and significance tests.
4. Look at the largest and smallest weights. Consider whether any respondent counts for a large share.
5. Compare weighted and unweighted results for the main questions.
6. Do not weight away a problem that is really about who answered. See our [sampling methods guide](/blogs/sampling-methods-india/) and [sample size guide](/blogs/sample-size-calculator-india/).

## Running This Study on Hercules

Poseidon, our analytics engine, lists weighting among the formulas it selects by question type. Ask any provider to show the weighting variables, the benchmark sources and n_eff, not only weighted percentages.

Hercules surveys can be targeted by city, age band, gender and NCCS A1 to C1, which can reduce how much correction is needed afterwards. The panel is app-based, so it reaches smartphone users only. The Free plan includes 30 responses.

## Frequently asked questions

### What is effective sample size in a weighted survey?

It is the sample size an unweighted simple random sample would need to give the same precision. With unequal weights, n_eff = (sum of weights) squared divided by the sum of squared weights.

### What is the design effect?

The factor by which weighting inflates variance. For unequal weights, Kish's design effect is n times the sum of squared weights divided by the squared sum of weights. It equals n divided by n_eff.

### What is the difference between post-stratification and raking?

Post-stratification weights each cross-classified cell and needs the population share of every cell. Raking adjusts one variable at a time until all margins match, and only needs the marginal proportions.

### Does weighting always reduce bias?

No. Pew found that even the best procedures it tested did not remove most of the bias in opt-in samples, and that the choice of variables matters more than the method.

### Should I use weights in significance tests?

Yes. Use n_eff or standard errors that account for the weights. Tests that treat weighted data as unweighted can call too many differences significant.

### Can the design effect be less than 1?

Only rarely, according to the design effect article. With weights unrelated to the outcome it is at least 1.