Sample Size: The Formula, a Table and Worked India Examples

For a proportion measured on a simple random sample, the sample size is:

n = z² × p × (1 − p) ÷ e²

Here z is the confidence multiplier, 1.96 for 95 percent confidence. p is the proportion you expect, and 0.5 is the safe choice because it produces the largest sample. e is the margin of error you are willing to accept, written as a decimal: 5 points is 0.05.

With p at 0.5, the top of the formula becomes 0.9604. So n = 0.9604 ÷ e². That is the whole calculation for most studies. Two assumptions matter: the sample is random, and the population is large. A panel with quotas is not random, and a list of 200 customers is not large, so both need the corrections below.

Respondents needed at 95 percent confidence, worst case p = 0.5:

Read the table as precision you are buying. Going from ±5 to ±3 roughly triples the sample. Going from ±3 to ±2 more than doubles it again. Most brand and product studies run at ±5 to ±7 for the total sample, then accept wider intervals inside segments.

If your population is a known list of 200 customers, 384 responses is impossible and unnecessary. Apply the correction:

n adjusted = n ÷ (1 + (n − 1) ÷ N)

With n = 384 and N = 200, the adjusted figure is about 132. In practice, for a population that small, invite everyone and report the response rate. The correction matters most between roughly 300 and 20,000: above that, the difference is small enough to ignore.

A total sample of 1,200 with four equal segments gives 300 per segment, which is a margin near ±5.7 points inside each one, not ±2.8. This is where most studies fail: the headline number looks precise and every cut that matters is not.

Set the target per segment you will report, then add the segments up. If you must report a small cell, such as a Tier 3 male group, either increase the sample for that cell deliberately or report it as directional and say so. The tier 2 and tier 3 guide covers the quota design.

Reading a change between two waves is a different calculation from reading a level. To detect a 2 point difference with 80 percent power at 95 percent confidence, you need roughly 9,800 responses in each wave. That number explains a common confusion: a tracker that reports a 2 point move on 500 responses per wave is reporting noise.

Three ways out: read rolling averages, report only differences that clear the interval, and reserve small movement for open-ended evidence rather than a headline. For the worked arithmetic, see statistical significance.

The formula assumes every eligible person has an equal chance of selection. A panel with quotas does not meet that assumption, for three reasons:

• Incidence. If 6 percent of members qualify for your screener, you field many more invitations than responses. Ask for the incidence before you fix the sample.
• Quota fill. A narrow cell, such as women aged 45 to 55 in one city, may fill slowly or not at all. Feasibility is a sample size question, not an operations one.
• Weighting. If the achieved sample is weighted to population targets, the effective sample is smaller than the raw count. Report the base you actually analysed.

Practical rule: quote the margin for the total, then state the margin for each segment you will report. Do not apply the total's margin to a segment.

National concept test, ±5 points. 384 responses are enough for the total. To report four city tiers, plan 300 per tier, so 1,200 responses. At ₹120 per response on a 400 to 1,000 bundle, 1,200 responses cost ₹1,44,000. At ₹150 on Plus, the same study costs ₹1,80,000.

Small customer list. A list of 250 accounts, all invited, with 150 responses, gives a margin near ±6.6 points at p = 0.5. Report the response rate beside the result.

Two-wave tracker. 9,800 responses per wave is out of reach for most budgets. Run 500 per wave and read a 6 month rolling average instead, with the interval printed on the chart.

These are planning figures. Screened-out respondents do not count towards a response bundle, so a low-incidence study needs a larger field effort than the arithmetic alone suggests.

Set the audience and quotas when you build the survey, then check the feasibility count before you commit the budget. The free plan includes 30 responses for a pilot, and pricing is per response: ₹150 on Plus from 100 responses, ₹120 on Pro in bundles of 400 to 1,000.

Results include the base for every question and significance tests on the comparisons you specify, so a segment that cannot carry a conclusion is visible rather than implied. The panel methodology page states how respondents are verified and what the panel figures mean.