Paired t-Test Studio

Updated Feb 2026 Paired means

Compare two related measurements with rich narratives, diagnostics, and visuals ready for stakeholder decks.

QUICK START: Choose Your Path

MARKETING SCENARIOS

Load a marketing use case:

Select a preset to auto-fill inputs for common measurement tasks (matched market uplift, pre/post surveys, creative benchmarks). Each preset references the raw CSV so you can inspect the required formatting.

INPUTS & SETTINGS

Data Entry

ℹ️ Significance level (α)

Drag & Drop raw data file (.csv, .tsv, .txt)

Upload a file with two named numeric columns (before & after). Blank rows are ignored.

Upload a file with two columns (before, after). We will parse it immediately and let you know how many rows were accepted.

No file uploaded yet.

Tip: For datasets with more than ~20 pairs, uploading a CSV is usually faster and less error-prone.

Type your Before & After values directly. Set how many rows you need (max 50) and enter values inline.

Row count (max 50)

Row	Before	After

When you only have summary tables, supply the mean and standard deviation of the difference scores plus the sample size.

Mean difference SD of differences Sample size (pairs)

DECISION

⏳ Awaiting Data

Enter paired data or summary statistics to see if the mean difference is significantly different from zero.

p-value

—

α (threshold)

0.05

Mean Diff

—

VISUAL OUTPUT

Mean Difference • Fan Chart (50/80/95%)

Provide data to summarize the mean difference and confidence interval.

Distribution of Differences

TEST RESULTS

💡 How to Interpret These Results

Reading the t-statistic and p-value:

t-statistic: Measures how many standard errors the mean difference is from zero. Larger |t| = stronger evidence of a real difference.
p < 0.05: Strong evidence that the mean difference is not zero. Reject H₀ (no change between conditions).
p ≥ 0.05: Insufficient evidence. Cannot conclude the before/after conditions differ significantly.
Very small p (< 0.001): Very strong evidence. The observed difference is highly unlikely due to chance.

Understanding the confidence interval:

The CI shows the plausible range for the true population mean difference
If the CI excludes zero, the result is statistically significant at that confidence level
Wider intervals = more uncertainty (often from smaller samples or higher variance)
The interval width matters for practical decisions—a significant but tiny effect may not be actionable

Effect size (Cohen's d_z):

d_z < 0.2: Small effect—difference may be statistically detectable but practically minor
d_z ≈ 0.5: Medium effect—noticeable difference that stakeholders can act on
d_z > 0.8: Large effect—substantial difference with clear business implications

Effect size helps contextualize significance: a large sample can detect tiny, meaningless differences as "significant."

Analysis Status

Enter data to see the paired t-test.

Paired t-Test

t(--)=--

p = --

95% CI: [--, --]

Effect sizes

Cohen's dz = --

Hedges' g = --

Mean difference = --

Overview

n = -- pairs

Mode: Paired columns

APA-Style Statistical Reporting

Summary will appear after analysis.

Managerial Interpretation

Business-facing copy will appear after analysis.

LEARNING RESOURCES

📚 When to use the Paired t-Test

Use the paired t-test when:

You have two related measurements for each subject/unit
You want to test if the mean difference is zero
Examples: before/after studies, matched market tests, crossover trials
Each pair is independent of other pairs
The differences are approximately normally distributed

Why paired instead of independent?

By focusing on within-subject changes, the paired t-test removes between-subject noise, increasing statistical power to detect real effects.

⚠️ Common mistakes to avoid

Using independent t-test on paired data: Ignores the pairing structure and loses power
Ignoring non-normality of differences: With small n and skewed differences, consider Wilcoxon signed-rank test
Confusing significance with importance: Small p-values can emerge from trivial effects with large samples
Pairing incorrectly: Ensure each "before" value is matched to the correct "after" value for the same unit
Ignoring outliers in differences: One extreme difference can dominate a small sample

📊 Interpreting Cohen's dz (Effect Size)

Cohen's dz measures how many standard deviations the mean difference is from zero:

|dz| < 0.20: Small effect
|dz| = 0.20–0.50: Small-to-medium effect
|dz| = 0.50–0.80: Medium effect
|dz| ≥ 0.80: Large effect

In practice: A significant p-value with dz = 0.15 means the effect exists but is tiny. For marketing ROI, consider whether such a small effect justifies investment.

🔬 The Paired t-Test Equations

The test transforms paired data into differences and tests whether the mean difference is zero:

d_i = After_i - Before_i

t = d̄ / (s_d / √n)

Where:

d̄ = mean of differences
s_d = standard deviation of differences
n = number of pairs
df = n - 1

The confidence interval: d̄ ± t_α/2 × (s_d/√n)

DIAGNOSTICS & ASSUMPTIONS

Assumption checks

The paired t-test assumes the differences follow an approximately normal distribution, pairs are matched correctly, and each pair is independent of the others. We will summarize diagnostics here after you provide data.