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Knowledge Base/t-test: Determining the Difference Between Two Production Lines in 5 Minutes
6 Sigma7 min read

t-test: Determining the Difference Between Two Production Lines in 5 Minutes

Line A averages 97.2% yield, Line B 96.8%, a 0.4% difference. While one might attribute this to random variation, the t-test provides a statistical method to determine if this observed difference is genuinely significant or merely due to chance.

Scenario

You have two production lines, A and B, manufacturing the same part. A colleague mentions that Line B's yield rate is lower. You glance at the numbers—Line A averages 97.2%, Line B 96.8%—a difference of 0.4%. You say, "It's close enough, probably just random variation."

Your colleague asks, "How do you know it's random?"

This is the problem the t-test aims to solve.

Plain Language Explanation

The question addressed by a two-sample t-test is straightforward:

Is the difference in the means of these two groups a genuine difference, or merely due to random chance in sampling?

t-value = Difference between the two group means ÷ Pooled standard error. The larger the difference and the more concentrated the data, the larger the t-value and the smaller the P-value.

Three types of t-tests:

  1. One-sample: One set of data compared against a target value (e.g., is the average part dimension equal to the design specification of 50mm?)
  2. Two-sample (Independent): Two independent sets of data compared against each other (e.g., Line A vs. Line B).
  3. Paired t-test: The same batch of samples compared before and after an improvement (most commonly used for verifying improvements in factories).

Practical Application

The paired t-test is one of the most useful statistical tools in factories.

Measure 20 items before an improvement, then measure the *same* 20 items after. The paired t-test directly tells you "if the improvement worked," without being affected by other confounding factors (e.g., shift changes, material changes).

Assumptions of the t-test:

  • Data follows a normal distribution (check when n < 30).
  • Variances of the two samples are equal (if unequal, use Welch's t-test, which most software handles automatically).

How InsightFab Does It

Upload two columns of data or select grouping fields, and InsightFab automatically determines which t-test to use, outputting a conclusion: "There is a statistically significant difference between lines A and B (P = 0.023), with Line B averaging 0.4% lower. It is recommended to investigate factors specific to Line B that may be interfering."

Key Takeaway

"Intuition in a factory is valuable, but intuition combined with a t-test provides the definitive answer that gains management's approval."

Want to try it yourself?

Every tool mentioned in this article is available on InsightFab — just upload a CSV to analyze.

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