Mean difference with confidence interval
Provide data to summarize the mean difference and confidence interval.
TEST OVERVIEW & EQUATIONS
The paired-samples t-test evaluates whether the average difference between two matched observations is credibly non-zero.
\[
\begin{aligned}
d_i &= x_{i, \text{after}} - x_{i, \text{before}} \\
\bar{d} &= \frac{1}{n} \sum_{i=1}^{n} d_i \\
t &= \frac{\bar{d}}{s_d / \sqrt{n}} \quad \text{with} \quad df = n - 1
\end{aligned}
\]
Where:
- \(s_d\) is the sample standard deviation of the pairwise differences.
- The two-tailed p-value comes from the Student's t distribution with \(n-1\) degrees of freedom.
- Confidence intervals use the same critical multiplier: \(\bar{d} \pm t_{\alpha/2} s_d/\sqrt{n}\).
Additional Notes
Focus on the differences: if the pre/post (or control/test) measurements are paired properly, this test cancels out subject-level noise. For skewed or heavy-tailed differences, consider a Wilcoxon signed-rank test.
MARKETING SCENARIOS
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
Drag & Drop raw data file (.csv, .tsv, .txt)
Paired mode: two named numeric columns (before & after). Differences mode: one numeric column named diff. Blank rows are ignored.
We only scan files locally—no uploads leave your browser. Up to 2,000 rows per file.
Upload a file with two columns (before, after). We will parse it immediately and let you know how many rows were accepted.
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Upload a single-column file of difference scores (positive values mean after > before). We will summarize the usable row count.
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Type smaller paired datasets directly. Choose the structure, set how many rows you need (max 50), and enter values inline.
Need more than 50 rows? Head to one of the upload modes.
| Row | Before | After |
|---|
When you only have summary tables, supply the mean and standard deviation of the difference scores plus the sample size.
VISUAL OUTPUT
Distribution of differences
TEST RESULTS
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.
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.