How to Calculate Sample Size for a Longitudinal Study

A longitudinal study follows the same group of people across multiple rounds of data collection. This guide first explains what a longitudinal study is and when it applies, then the general formula behind the calculation, then walks through how to apply it in AnalyZ Solutions.

01What a longitudinal study is, and when it applies

A longitudinal study, sometimes called a panel study, enrols a group of participants and returns to measure the same individuals repeatedly over time, at two or more waves. This is different from a repeated cross-section, which surveys a fresh sample at each round, and different from a single cross-sectional survey, which measures the population only once. Because the same people are tracked, a longitudinal study can describe individual trajectories over time, not just how the population average moved.

A longitudinal design is a strong fit when three conditions hold together.

• The research question is genuinely about tracking individuals over time. Understanding how a specific person's circumstances evolve, or building a full history of exposure, behaviour, or outcomes for the same people, requires following individuals rather than resampling the population at each round.
• Participants can realistically be tracked and re-contacted across waves. This requires a population that is not highly mobile, or a tracking system robust enough to follow people who move, change contact details, or become temporarily unreachable.
• The study can tolerate, and budget for, attrition. Some participant loss between waves is close to unavoidable in any panel that runs for more than a short period. A longitudinal design requires planning for this in advance, both in the sample size and in the field operation.

Why tracking the same people matters

Following the same individuals over time captures information a series of fresh, unrelated samples cannot. It allows a study to describe how individual circumstances change, to identify who improves and who does not, and to examine what individual or household characteristics predict a change in trajectory, none of which is possible from repeated snapshots of different people. This is also what makes the paired designs in Change in Proportion and Change in Mean more statistically efficient than their independent groups equivalents, the same underlying logic of tracking individuals rather than resampling.

Common pitfalls

• Underestimating attrition. Attrition compounds across waves in a way that is easy to underestimate at the planning stage. A rate that seems modest per wave can still produce substantial cumulative loss by the final round of a multi-wave study.
• Attrition that is not random. If the people who drop out differ systematically from those who remain, for example if the most vulnerable or the most mobile households are also the most likely to be lost to follow up, the remaining sample no longer represents the original population, and no amount of baseline oversampling can fix this after the fact.
• Treating tracking as a one-time cost. Locating participants gets harder, not easier, at each successive wave, particularly in populations with seasonal migration, informal housing, or limited stable contact information. Budgeting the same tracking effort for every wave often understates what later waves actually require.
• Confusing a longitudinal design with a test for change. A longitudinal study estimates a value with a stated precision at the final wave. It does not, on its own, test whether that value has changed from baseline with a stated statistical power. See the comparison below for when each tool is the right one.

02Longitudinal versus Change in Proportion or Change in Mean

These tools are frequently confused because they all involve measuring the same people more than once. They answer different questions, and the choice between them depends entirely on what the study is actually trying to establish.

• Use Longitudinal when the goal is to estimate a value, a proportion or a mean, with a stated level of precision at a future wave, accounting for the participants expected to be lost along the way. This tool does not test whether that value is different from an earlier wave, only how precisely it can be estimated once attrition is accounted for.
• Use Change in Proportion or Change in Mean, paired design when the goal is specifically to test whether a value has changed between two time points, with a stated confidence level and statistical power. These tools answer did this proportion or mean actually change, and are built around detecting a specific minimum effect, not simply describing the final wave.

In practice, many studies that track the same people over multiple waves are really trying to answer the change question, in which case the paired designs in Change in Proportion or Change in Mean, not this tool, are the right calculation to size the study around. Longitudinal is the right tool specifically when the study needs a precise final-wave estimate, for example an endline prevalence figure that will stand on its own, rather than a formally tested comparison against baseline.

03The general sample size formula

The starting point is the same precision-based formula used for a single cross-sectional survey, for either a proportion or a mean.

Attrition, participants who drop out between waves, compounds with each additional round. A study with 20% attrition per wave retains only 64% of its original sample by the third wave, since 0.8 × 0.8 = 0.64. To keep the required sample at the final wave, more people must be enrolled at baseline than the precision formula alone suggests.

Each symbol plays a specific role.

• Z (confidence level). How sure you want to be that the final estimate falls within the stated margin of error, at 95% confidence this is 1.96.
• p or σ (expected proportion or standard deviation). Your best estimate of the outcome at the final wave. For a proportion, 50% is the most conservative assumption if unknown. For a mean, there is no equivalent conservative default, so this should come from prior data or a pilot wherever possible.
• e (margin of error). How much imprecision in the final estimate is acceptable.
• waves (number of rounds). The total number of data collection points, including the baseline round.
• attrition (dropout rate per wave). The proportion of participants expected to be lost between each consecutive round, not the cumulative loss across the whole study, which the formula calculates automatically.

Choosing your confidence level and margin of error

Because this tool estimates a value at the final wave rather than testing a specific hypothesis, it uses confidence level and margin of error rather than power. There is no beta or effect size to specify here, only how precise the final-wave estimate needs to be.

Confidence level reflects how sure you want to be that the final estimate falls within the stated margin of error. 95% is the standard default. A higher level increases the required sample at every wave, compounding through the attrition adjustment.

Margin of error reflects how much imprecision in the final estimate is acceptable. A narrower margin of error, meaning a more precise final result, requires a larger baseline sample, an effect that is amplified by attrition across multiple waves in a way it is not in a single cross-sectional survey.

Accounting for cluster sampling

If the baseline sample is drawn from clusters, villages, schools, or facilities, rather than a simple random sample, a design effect should be applied before the attrition adjustment. It defaults to 1, meaning no clustering effect, and is always editable. See the dedicated guide on Design Effect and ICC for how to set this correctly.

1. Choose what you are estimating. Select Proportion if your outcome is a percentage or rate, such as prevalence of a condition, or Mean if it is a numeric average, such as household expenditure or a test score. This is the same choice offered in the Cross-sectional tool, and it determines which formula is applied to your final-wave precision target.
2. Set your confidence level and margin of error. Enter both as numbers, not from a fixed list. These describe the precision you want at the final wave specifically, not at every wave along the way. For a proportion, also enter the expected proportion, leaving it at 50% if you have no prior estimate. For a mean, enter the expected standard deviation instead, ideally from a pilot or a prior round of the same instrument.
3. Enter the number of waves your study will run. Count every planned round of data collection, including the baseline round itself. This number, together with your attrition assumption, determines how much the baseline sample needs to be inflated to still meet your precision target by the final round.
4. Enter your expected attrition rate per wave. This is the proportion of participants expected to be lost between each consecutive round, not the total loss across the whole study. The tool compounds this figure across all waves automatically, so a seemingly modest per-wave rate can still produce substantial cumulative loss by the final round.
5. Enter a population size, if relevant. If your population is small enough that a finite population correction should apply, enter it here. Otherwise, leave this field blank. AnalyZ Solutions applies the correction automatically whenever a population size is entered, and skips it otherwise, exactly as in the Cross-sectional tool.
6. Set a design effect, if your baseline sample is drawn by cluster. If you are sampling from villages, schools, or facilities rather than a simple random sample, enter a design effect directly, or calculate one automatically from an intraclass correlation and average cluster size. It defaults to 1, meaning no clustering effect, and is applied before the attrition adjustment, so both effects compound correctly.
7. Calculate. The result shows the number of participants to enrol at baseline, the minimum number needed at the final wave before the attrition adjustment, and your estimated retention rate by the final round, so you can see exactly how much of the baseline sample the attrition assumption is expected to consume.

04Worked example

A nutrition programme tracks the same households across three waves, roughly a year apart. Baseline stunting prevalence is expected around 30%, with a 5% margin of error at 95% confidence, and 20% attrition expected between each wave.

Of these, roughly 323 are needed at the final wave to meet the stated precision. The gap between 323 and 505 is entirely the cost of two rounds of attrition compounding at 20% each.

05Common mistakes to avoid

• Using this tool when the real question is about change. If the study needs to demonstrate that a value moved between waves, with a stated power, use the paired design in Change in Proportion or Change in Mean instead. This tool answers a precision question, not a hypothesis test.
• Applying a flat attrition rate without evidence. Attrition rates vary widely by population, study duration, and tracking effort. A rate borrowed from an unrelated context can understate or overstate the true baseline enrolment needed.
• Underinvesting in tracking relative to sample size. A larger baseline sample compensates mathematically for expected attrition, but does nothing to address attrition that is not random. Tracking effort and sample size inflation are complements, not substitutes.
• Forgetting the design effect for a clustered baseline sample. If the baseline sample is drawn from clusters, skipping the design effect adjustment will understate the true baseline enrolment needed, independent of the attrition adjustment.