A Count Went Up, but Did the Rate?

Decorative acrylic columns arranged on grid paper as a visual metaphor for charts, not actual measured data.
Conceptual illustration created with AI; not a research result or laboratory photograph.

A team records 12 defects this week and 10 last week. The count increased. Whether the defect rate increased depends on how many items were inspected and whether the inspections were comparable.

Put the denominator beside the count

In a hypothetical example, last week had 10 defective items among 100 inspected items: 10%. This week had 12 among 200: 6%. The count rose while the fraction of inspected items classified as defective fell.

The example counts defective items, not the total number of defects. An item with several defects would still count once under this definition. Changing that rule would change the meaning of the calculation.

Check comparability

Were the same kinds of items inspected using the same criteria? If the selection or inspection method changed, the rate difference needs further investigation.

A lower observed rate is not automatically evidence that a particular intervention caused improvement. The arithmetic alone cannot establish that causal claim.

Write both pieces of information

A useful summary gives the count, denominator and resulting rate. This allows readers to see the scale of the observations as well as the relative frequency.

Read alongside our guide to causal questions. Keeping counts and rates distinct helps you describe what changed before trying to explain why it changed.