KEVOS® MAKEOS · Quality
Two-Sample Comparison (t-test)
Is the difference between these two averages statistically significant?
Welch’s two-sample t-test comparing the means of two groups (machines, suppliers, before and after) from their means, standard deviations and sample sizes.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Group 1 | ||
| Mean | Average of group 1. | |
| Standard deviation | Sample standard deviation of group 1. | |
| Sample size | items | Number of independent results in group 1. |
| Group 2 | ||
| Mean | Average of group 2. | |
| Standard deviation | Sample standard deviation of group 2. | |
| Sample size | items | Number of independent results in group 2. |
| Test | ||
| Significance level (two-sided) | choice | Probability of wrongly declaring a difference that is not real (0.05 is common). |
Method and formulas
- SE = √(s₁²/n₁ + s₂²/n₂); t = (m₁ − m₂) ÷ SE.
- Welch–Satterthwaite degrees of freedom: ν = SE⁴ ÷ ((s₁²/n₁)²/(n₁ − 1) + (s₂²/n₂)²/(n₂ − 1)).
- p = 2 × P(T_ν > |t|), from the regularised incomplete beta function.
- Significant when p < α.
- Example: the default groups differ by 2.2 with t = 2.5006, ν = 22.09 and p = 0.020303.
Limitations
- Independent random samples from roughly normal populations; strongly skewed data or small samples need care.
- Statistical significance is not practical importance: judge the size of the difference too.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether a process change really improved the average
- Compare two suppliers or machines
- Support a trial report with statistics
Who it is for
- Quality engineers
- Process engineers
- Test engineers
What you get
- Difference of means and its standard error
- t statistic and degrees of freedom
- Two-sided p-value
- Confidence interval of the difference
Interpreting the result
- A significant result with a tiny difference may not matter; a large but non-significant difference may need more data.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 130–133. Topic reference; no source tables or recommended settings are reproduced.
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