TBI Sample Size Calculator — Power Analysis for Research Studies

Select Study Design

One-Sample t-Test

Tests if a population mean equals a hypothesized value. Uses the z-approximation (large n) or t distribution.

Standard deviation (σ)

Minimum detectable diff (Δ)

Significance level (α)

Power (1−β)

Test tails

Cohen's d presets (Δ/σ):

Independent-Samples t-Test

Compares means of two independent groups (equal group sizes assumed). Assumes equal variances (pooled SD).

Pooled standard deviation (σ)

Mean difference to detect (Δ)

Significance level (α)

Power (1−β)

Test tails

Cohen's d presets:

Paired t-Test

Pre-post or matched-pairs design. Provide the SD of the within-pair differences.

SD of differences (σ_d)

Mean difference to detect (Δ)

Significance level (α)

Power (1−β)

Test tails

One-Sample Proportion Test

Tests if a population proportion equals a hypothesized value (e.g. compliance rate, response rate).

Null proportion (p₀)

Alternative proportion (pₐ)

Significance level (α)

Power (1−β)

Test tails

Two-Sample Proportions

RCT or case-control design comparing two event rates or response rates.

Group 1 proportion (p₁)

Group 2 proportion (p₂)

Significance level (α)

Power (1−β)

Test tails

One-Way ANOVA

Compares means across k groups. Uses Cohen's f as the effect size (f = σ_means / σ_error).

Cohen's f (effect size)

Number of groups (k)

Significance level (α)

Power (1−β)

Chi-Square Test

For independence tests or goodness-of-fit. df = (rows−1)×(cols−1) for contingency tables.

Cohen's w (effect size)

Degrees of freedom (df)

Significance level (α)

Power (1−β)

Multiple Regression (F-test)

Total sample size for an OLS model with u predictors. Effect size f² = R²/(1−R²).

Cohen's f² (effect size)

Number of predictors (u)

Significance level (α)

Power (1−β)

Pearson Correlation

Uses Fisher's z transformation to test H₀: ρ = 0.

Correlation (r) to detect

Significance level (α)

Power (1−β)

Test tails

Survival Analysis (Log-Rank)

Schoenfeld formula for log-rank test. Enter survival probabilities at end of follow-up (e.g. 1-year survival).

Survival probability Group 1 (p₁)

Survival probability Group 2 (p₂)

Significance level (α)

Power (1−β)

Survey / Prevalence Study

Estimates required n to achieve a desired margin of error. Optionally apply finite population correction.

Expected prevalence / proportion (p)

Margin of error (MoE ± half-width)

Significance level (α)

Population size (N) — optional

Cronbach's Alpha Reliability

Determine the number of participants needed to establish instrument reliability (Bonett, 2002).

Minimum acceptable α (ρ₀)

Expected α (ρ₁)

Number of scale items (k)

Significance level (α)

Power (1−β)

Key References for This Test

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Erlbaum.
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3. Behavior Research Methods, 39(2), 175–191.

Required Sample Size

Power Curve

● Power curve ● Required N — — 80% threshold

Effect Size Quick Reference

Manuscript Template ↓

Effect	Cohen's d	Cohen's f	Cohen's f²	Cohen's w	Pearson r
Small	0.20	0.10	0.02	0.10	0.10
Medium	0.50	0.25	0.15	0.30	0.30
Large	0.80	0.40	0.35	0.50	0.50

Source: Cohen (1988). d for means; f for ANOVA; f² for regression; w for chi-square; r for correlation.

Common Default Conventions

Parameter	Typical value	Meaning
α	0.05	5% Type I error rate (false positive)
Power (1−β)	0.80	80% chance of detecting a true effect
β	0.20	20% Type II error rate (false negative)
For clinical trials: α = 0.05, power = 0.90 is often required.

Tip: When the expected effect size is unknown, use a medium effect size as a conservative planning assumption. Consider adding 10–20% attrition buffer to your final N for dropout. Pilot studies help refine σ and Δ.

How to Use This Calculator

Choose your study design — Select the test that matches how you plan to collect and compare your data.
Enter your parameters — Plug in your expected standard deviation, effect size, or proportions. Use pilot data or published literature if available; otherwise use Cohen's medium effect size as a conservative default.
Set significance level α — Typically 0.05 (5% false positive risk). Use 0.01 for clinical/high-stakes research.
Set desired power (1−β) — Standard convention is 80%. Some journals require 90% for clinical trials.
Click Calculate — The minimum required N is displayed along with the power curve showing how power scales with sample size.
Apply an attrition buffer — Add 10–20% to your calculated N to account for expected dropout, non-response, or data loss.
Adjusted N = Calculated N ÷ (1 − attrition rate)
Report your power analysis — Copy the result and include it in your Methods section under "Sample Size Justification".

How to Interpret Your Results

What does the required N mean?

The required N is the minimum number of participants you must recruit to detect the specified effect size with the stated power and significance level. Enrolling fewer participants risks an underpowered study (high Type II error — you miss a true effect). This is the number needed after any exclusions — always recruit more to offset attrition.

Reading the power curve

The power curve plots statistical power (y-axis) against sample size (x-axis). Key points:

● Purple curve — how power increases as you add more participants.
● Yellow dot — your calculated required N and its achieved power.
— — Green dashed line — the 80% power threshold (standard minimum).

A steep curve means adding a few participants gives large power gains. A flat curve means diminishing returns — you may not need a larger N than calculated.

Effect size — what if I don't know it?

If unknown, use the effect size presets (Small / Medium / Large buttons). Cohen (1988) recommended medium effect size as the default planning assumption when no prior data exist. You can also:

• Run a pilot study (n=20–30) to estimate σ and Δ before the main study.
• Use published meta-analyses in your field for typical effect sizes.
• Use the minimum clinically important difference (MCID) from guidelines for clinical outcomes.

Common mistakes in power analysis

1. Over-optimistic effect sizes — Using a large effect size to justify a small sample. Always use realistic estimates from pilot data or literature.

2. Forgetting attrition — The calculated N is the analysed sample. If 20% will drop out, you need N ÷ 0.80 enrolled participants.

3. Post-hoc power ("observed power") — Computing power after a non-significant result is circular and misleading. Plan power before data collection.

4. Multiple comparisons — If testing many outcomes, apply Bonferroni correction: use α / k comparisons in each calculation.

5. Ignoring cluster effects — For cluster-randomised trials (e.g. schools, clinics), multiply N by the design effect = 1 + (cluster size − 1) × ICC.

How to report in a manuscript

Include the following in your Methods / Sample Size section:

"A priori power analysis was conducted using [test name]. Based on an expected [effect size metric] of [value], a significance level of α = [α], and a desired power of 1−β = [power], a minimum sample size of N = [n] was determined [per group / total]. An attrition buffer of [x]% was applied, yielding a target recruitment of N = [adjusted n]. Calculations were performed using the TBI Sample Size Calculator (Tech Bridge Innovations, 2026)."

Replace bracketed values with your actual inputs from the Results panel above.

Test-specific notes

Two-Sample Means: Assumes equal group sizes. Unequal groups increase total N — use allocation ratio adjustment if needed.

Paired t-Test: σ_d is the SD of differences, not of individual scores. This is typically smaller than σ, leading to smaller sample sizes than independent tests.

ANOVA: Cohen's f = σ_means / σ_within. Partial η² ≈ f²/(1+f²). For multiple comparisons across groups, post-hoc tests (Tukey, Scheffé) will reduce effective power.

Chi-Square: df = (rows−1)×(columns−1) for contingency tables; df = (categories−1) for goodness-of-fit.

Regression: f² represents the effect on top of other predictors. For the overall model R², use f² = R²/(1−R²). SPSS uses this parameterisation.

Survival: N here is patients; what truly determines power is the number of events. If event rate is low, you need more patients even if events look adequate.

Survey: p=0.50 gives the most conservative (largest) N. If you have prior prevalence estimates, use those. Finite Population Correction (FPC) reduces N when sampling >5% of the population.

Cronbach's α: k = total number of scale/questionnaire items, not subscales.

How to Cite This Calculator

If you use this calculator in your research, please cite it using one of the formats below.

APA 7th Edition

Tech Bridge Innovations. (2026). TBI Sample Size Calculator [Web application]. https://techbridgeinn.com/samplesize/

MLA 9th Edition

Tech Bridge Innovations. "TBI Sample Size Calculator." TechBridgeInn.com, 2026, techbridgeinn.com/samplesize/. Accessed 22 March 2026.

Chicago 17th Edition

Tech Bridge Innovations. "TBI Sample Size Calculator." Accessed March 22, 2026. https://techbridgeinn.com/samplesize/.

IEEE

Tech Bridge Innovations, "TBI Sample Size Calculator," TechBridgeInn.com. [Online]. Available: https://techbridgeinn.com/samplesize/. [Accessed: 22-Mar-2026].

Vancouver

Tech Bridge Innovations. TBI Sample Size Calculator [Internet]. 2026 [cited 2026 Mar 22]. Available from: https://techbridgeinn.com/samplesize/