How Many Participants Do I Need: A Guide to Sample Size

# How Many Participants Do I Need: A Guide to Sample Size

"Is 200 enough?" This might be the single most common question in thesis supervision meetings across the social sciences. And the answer is almost always the same: "It depends." But it depends on specific, quantifiable factors, and this guide will walk you through each of them.

Determining sample size is not a guessing game. It is a calculation, and there are well-established methods for doing it. The problem is that many researchers either skip this step entirely or rely on vague rules of thumb without understanding what those rules actually assume.

Why Sample Size Matters

There are two fundamental problems with getting sample size wrong.

Too few participants: Your study will lack the statistical power to detect a real effect. You might conclude that there is no difference between groups when one actually exists. This is a Type II error, and it turns months of work into a non-finding that tells you nothing.

Too many participants: You waste time and resources collecting data you do not need. In some contexts (clinical research, studies with vulnerable populations), this is also an ethical issue: you are subjecting more people to the study than necessary.

The sweet spot is a sample large enough to detect the effect you care about with adequate confidence, and no larger.

The Core Concepts

Before we get into specific numbers, you need to understand four interconnected terms.

Statistical Power

Power is the probability that your test will detect a real effect when one exists. Convention sets this at 0.80 (80%), meaning you accept a 20% chance of missing a real effect. Some fields (medical research, for instance) aim for 0.90.

Significance Level (Alpha)

This is the threshold for declaring a result "statistically significant." Convention sets it at 0.05, meaning you accept a 5% chance of finding an effect that is not actually there (Type I error).

Effect Size

This is the magnitude of the difference or relationship you are trying to detect. Common effect size metrics include Cohen's d (for differences between means), Pearson's r (for correlations), and Cohen's f (for ANOVA). Larger effect sizes require fewer participants. Smaller ones require more.

Cohen (1988) proposed these benchmarks:

Sample Size

The number of participants you need is a function of the three factors above. Higher power, lower alpha, and smaller expected effect sizes all require larger samples.

Rules of Thumb: Useful Starting Points

Rules of thumb are not substitutes for proper power analysis, but they give you a ballpark when you are in the early planning stages.

For t-tests

• •Minimum: 30 participants per group (so 60 total for an independent samples t-test).
• •Better: 50 per group for medium effects, 100+ per group for small effects.

A study comparing stress levels between psychology and engineering students would need at least 30 students in each group. But if you expect only a small difference, you are looking at 200 or more per group. Knowing when to apply a t-test versus other tests also matters for this decision.

For Correlations

• •Minimum: 50 participants to detect a large correlation (r = 0.50).
• •Medium correlation (r = 0.30): about 85 participants.
• •Small correlation (r = 0.10): about 780 participants.

For Regression

• •Rule of 10: at least 10 participants per predictor variable.
• •Rule of 15: more conservative, recommended by Stevens (2009).
• •Tabachnick & Fidell formula: N >= 50 + 8k, where k is the number of predictors.

So for a regression with 5 predictors: N >= 50 + 40 = 90 participants.

For Factor Analysis

Factor analysis is particularly hungry for data. If you plan to run an exploratory factor analysis on a new scale, you will want to familiarize yourself with the specific requirements outlined in our factor analysis guide.

• •Absolute minimum: 100 participants.
• •Rule of 5: at least 5 participants per item in your questionnaire.
• •Preferred: 10 to 15 participants per item, or 300+, whichever is larger.

For ANOVA

• •One-way ANOVA with 3 groups: about 52 per group (156 total) for a medium effect.
• •One-way ANOVA with 4 groups: about 45 per group (180 total) for a medium effect.
• •Groups do not need to be perfectly equal, but severely unequal group sizes can violate assumptions.

Summary Table

Power Analysis with G*Power: A Step-by-Step Walkthrough

G*Power is a free tool developed at the University of Dusseldorf that calculates the required sample size for most common statistical tests. Here is how to use it for an independent samples t-test.

Step 1: Download G*Power from the official website (psychologie.hhu.de/gpower) and open it.

Step 2: Set the test family to "t tests" and the statistical test to "Means: Difference between two independent means (two groups)."

Step 3: Choose "A priori: Compute required sample size" as the type of power analysis.

Step 4: Enter your parameters:

• •Effect size d: 0.50 (medium). If you have pilot data or previous studies, use their reported effect size instead.
• •Alpha: 0.05
• •Power: 0.80
• •Allocation ratio: 1 (equal group sizes)

Step 5: Click "Calculate." G*Power will tell you that you need 64 participants per group, so 128 total.

Step 6: Write this into your methodology section. State the expected effect size, where it came from (prior literature, pilot study, or convention), and the computed sample size.

What If You Do Not Know the Expected Effect Size?

This is common, especially for novel research questions. You have several options:

1. Look at previous studies on similar topics. If three studies on attitudes toward AI in education reported effect sizes of d = 0.45, 0.52, and 0.38, use the average (0.45) or the smallest (0.38, for a conservative estimate).
2. Run a pilot study with 20 to 30 participants and compute the observed effect size.
3. Use "medium" as a default (d = 0.50). This is not ideal but is common practice when no prior data exist. Acknowledge this limitation.
4. Think about the minimum effect that would be practically meaningful. If a difference smaller than d = 0.30 would not matter for your purposes, then plan for d = 0.30.

Margin of Error and Survey Research

For descriptive survey research (where you are estimating a percentage or proportion, not testing a hypothesis), the relevant concept is margin of error rather than statistical power.

The formula is straightforward:

n = (Z2 p (1-p)) / E2

Where:

• •Z = 1.96 for 95% confidence
• •p = expected proportion (use 0.50 for maximum variability)
• •E = desired margin of error

For a finite population, you can adjust with a correction factor, but for populations above 10,000, the difference is negligible.

Practical Example: Planning a Study on Social Media and Self-Esteem

Suppose you are a psychology master's student investigating whether the frequency of social media use is related to self-esteem among university students.

Research design: Correlational study, measuring social media use (hours per day) and self-esteem (Rosenberg Self-Esteem Scale).

Step 1: Find prior effect sizes. You search the literature and find four relevant studies with correlations of r = -0.19, -0.23, -0.28, and -0.15. The average is about r = -0.21, which is in the small-to-medium range.

Step 2: Run a power analysis. In G*Power, select "Correlation: Bivariate normal model." Set r = 0.21, alpha = 0.05, power = 0.80. The result: you need 175 participants.

Step 3: Account for attrition. Online surveys typically have 10-20% incomplete responses. So inflate your target: 175 / 0.80 = 219 participants. Round up to 220 or 230 for safety.

Step 4: Report it. In your methodology section, write: "Based on a power analysis conducted in G*Power 3.1 for a bivariate correlation with an expected effect size of r = 0.21 (based on the average of four prior studies), alpha = 0.05, and power = 0.80, the minimum required sample size was 175. Accounting for approximately 20% anticipated attrition, the target sample size was set at 220."

Common Mistake: "I Have 500 Participants, So It Must Be Fine"

This is one of the most widespread misconceptions in quantitative research. A large sample does not automatically mean your study is well-powered, and a large sample can actually create problems.

The issue with "bigger is always better":

1. Post-hoc rationalization. If you collected 500 participants without doing a power analysis, you cannot know whether 500 is enough for the effect sizes and analyses you are running. For a multiple regression with 15 predictors and small effects, 500 might still be underpowered.

1. Trivial significance. With very large samples, almost any difference becomes statistically significant, even if it is practically meaningless. With N = 5,000, a correlation of r = 0.03 will be statistically significant at p < 0.05. But a correlation of 0.03 explains less than 0.1% of the variance. That is not a finding worth reporting.

1. Effect size neglect. Researchers who rely on "I have lots of data" tend to focus on p-values and ignore effect sizes. The p-value tells you whether an effect is likely to be non-zero. The effect size tells you whether it is large enough to matter. Always report both.

What to do instead:

• •Do the power analysis before data collection.
• •Report the expected effect size and its source.
• •After analysis, report effect sizes alongside p-values (Cohen's d, eta-squared, R-squared).
• •If your sample is very large, pay extra attention to effect sizes and practical significance.

Online Surveys: Special Considerations

When collecting data online, sample size planning must account for several additional factors.

Response rate. If you are distributing a survey via email, expect a response rate of 10-30%. To get 200 completed responses, you may need to send 800 to 1,000 invitations.

Completion rate. Not everyone who starts a survey finishes it. For surveys longer than 10 minutes, expect 20-40% abandonment. Build this into your target.

Data quality. Some responses will be unusable: straight-lining (selecting the same answer for every item), random responding, or completing the survey in impossibly short time. Plan to exclude 5-10% of responses during data cleaning.

Adjusted formula: Target N = Required N / (response rate completion rate quality rate). For a required sample of 150 with 25% response rate, 80% completion, and 90% quality: 150 / (0.25 0.80 0.90) = 833 invitations.

When Is a Small Sample Acceptable?

Not all research requires hundreds of participants. Qualitative research, case studies, and some advanced statistical methods work with smaller samples. In quantitative research, a small but well-justified sample is better than a large, unexplained one. The key is to match your sample size to your research design and report your reasoning transparently.

Wrapping Up

Sample size determination is not a formality you put in your methodology section to satisfy your committee. It is a fundamental design decision that affects whether your study can answer the question it sets out to answer. Do the power analysis, report it clearly, and plan for the realities of data collection.

If you want to keep track of progress during data collection, the Istrazimo platform displays a real-time progress bar toward your target sample size, along with completion rate tracking and response quality indicators. It takes some of the uncertainty out of the process so you can focus on the research itself.