Example: cushioning force
64 independent specimens: 32 of each cushioning material.
Download the example data (CSV)This is the same example used in Help. Import the CSV to follow the steps, or use Open example in a practice copy in Help to prefill the inputs.
1. Create the workspace
In the sidebar, open Basic Statistics and choose Means: Two-Sample (t). Create an analysis, name it, select New blank worksheet, then choose Create analysis.
2. Import the example data
Download the CSV above and import it into the worksheet. Choose Comma as the delimiter, Dot as the decimal separator and First row contains column names.
3. Assign the input columns
On Inputs, Choose Two sample (independent) for Test type. Assign sample_1 to Sample 1 and sample_2 to Sample 2. These columns contain Foam A and Foam B respectively. The specimens are independent; sharing a worksheet row does not make a pair. Blank cells outside each 32-specimen sample are intentional, not missing paired readings.
4. Set the test and plots
Enter 0.05 in Significance level (α) and choose Two-sided (≠) for Alternative hypothesis. Leave Assume equal variances unchecked. Choose Integer — validation dataset convention for Degrees of freedom to reproduce this Welch result. This rounds 56.3241 down to 56. Open Additional comparisons and leave Include Mann–Whitney U test unchecked.
Open Plot options. Set Histogram binning to Automatic and Histogram scale to Frequency. Leave Show normal curve unchecked and check Show confidence interval for mean difference.
5. Run analysis
Choose Run analysis, then open Results.
6. Interpret results
Identify the independent samples
Each material has 32 different specimens. Sample 1 is Foam A and Sample 2 is Foam B. The comparison is their population mean compression force, using Welch’s test.
Read the difference and interval
Foam A minus Foam B averages 5.625 N. The 95% interval is −0.901–12.151 N and crosses zero; p = 0.08975. At the 5% level, the study does not establish a difference. It also does not establish equivalence. This example uses 56 integer degrees of freedom.
Difference confidence interval View full-size chart (opens in a new tab) Compare the sample shapes
The boxes show each sample’s middle half, with the median inside. Whiskers and fence flags describe the observations, not acceptance limits. Foam B has a larger sample SD: about 14.96 N versus 10.77 N for Foam A.
Sample boxplots View full-size chart (opens in a new tab) Read the histogram
Bar heights count measurements in value intervals. Compare shape and spread, without treating the bars as confidence limits. Independence comes from using different specimens, not from this chart.
Sample histogram View full-size chart (opens in a new tab) Decide what the result supports
Compare the full difference interval with the improvement needed for the cushioning decision. More data may be useful if that interval is too wide; p above 0.05 does not prove equal performance.
More details: read each result section
Complete result tables use six significant digits, as in Help.
Two-sample t-test
Mean difference is Sample 1 minus Sample 2; Standard error measures its uncertainty. t statistic is difference divided by Standard error. Degrees of freedom, Alpha, Alternative, Method and Confidence level document the inference. CI lower and CI upper bound the population mean difference. DF convention records integer Welch degrees of freedom. Unrounded Welch DF is 56.3241; DF used is 56. This setting affects p-values and interval width.
| Statistic | Value |
|---|---|
| t statistic | 1.72662 |
| Degrees of freedom | 56 |
| DF convention | Integer — validation dataset convention |
| Unrounded Welch DF | 56.3241 |
| DF used | 56 |
| p-value | 0.0897498 |
| Mean difference | 5.625 |
| Standard error | 3.25782 |
| Alpha | 0.05 |
| Alternative | two-sided |
| Method | Welch t-test |
| Confidence level (%) | 95 |
| CI lower | -0.90119 |
| CI upper | 12.1512 |
- Fail to reject H₀ (μ₁ − μ₂ = 0) at α=0.05 (p=0.0897)
- H₀: μ₁ − μ₂ = 0
- H₁: μ₁ − μ₂ ≠ 0
Sample summaries
n counts readings; Mean, Median, Min, Max and Range describe each sample. SD is sample spread, SE is uncertainty in its mean, and IQR is the middle-half spread. Each material has 32 independent specimens.
| Sample | n | Mean | SD | SE | Median | Min | Max | Range | IQR |
|---|---|---|---|---|---|---|---|---|---|
| Sample 1 | 32 | 184.925 | 10.766 | 1.90318 | 185.15 | 168.4 | 209.2 | 40.8 | 16.9 |
| Sample 2 | 32 | 179.3 | 14.9573 | 2.6441 | 178.2 | 145.7 | 211.7 | 66 | 20.9 |
Boxplot coordinates
Q1 and Q3 bound the middle half, with Median between them. IQR is Q3 minus Q1. Lower and Upper fences use 1.5 × IQR; whiskers end at the extreme observations inside the fences. These coordinates are not acceptance limits.
| Sample | Q1 | Median | Q3 | IQR | Lower fence | Upper fence | Lower whisker | Upper whisker |
|---|---|---|---|---|---|---|---|---|
| Sample 1 | 175.85 | 185.15 | 192.75 | 16.9 | 150.5 | 218.1 | 168.4 | 209.2 |
| Sample 2 | 170.275 | 178.2 | 191.175 | 20.9 | 138.925 | 222.525 | 145.7 | 211.7 |
Boxplot flags
Each row would identify a Sample, Worksheet row and Value beyond a fence. This empty table means neither sample has fence flags. A flag would call for investigation, not automatic deletion.
| Sample | Worksheet row | Value |
|---|
No rows were returned for this section.
7. Create a report
Keep the complete Two-sample t-test, Sample summaries, boxplot coordinates and flags, difference interval, boxplots and histogram. State Sample 1 minus Sample 2 and the integer Welch degrees-of-freedom convention.
Choose Add to report from the completed run. Open Choose individual items and advanced options to select tables and charts, then choose Add to draft. Hidden items stay in the saved analysis.
Name the report and add the purpose of the study and your interpretation. Choose Save, review Preview, then use Export → Download HTML. The example below contains the full selected content, including results beyond one screen.