In statistical analysis, p-value indicates the probability that the observed results happened by chance. A p-value of 0.05 is a commonly used as a threshold for measuring a significance level in statistical testing, meaning there’s a 5% probability that the observed results occurred by chance. If the p-value is below 0.05, results are typically considered statistically significant, suggesting a real effect or difference beyond random variation.

Let’s say you have two roast batches of the same coffee, Batch A and Batch B, and you suspect that Batch A is more soluble because it consistently achieves a higher extraction percentage.

Here’s how we’d test this with the help of a p-value:

1. Collect Data: You pull multiple espresso shots using both batches and measure the extraction percentage for each shot. You find that Batch A has an average extraction of 20%, while Batch B has an average of 18.5%.
2. Run a Statistical Test: After running a test comparing the extraction percentages, you get a p-value of 0.03.
3. Interpret the p-value:
   • A p-value of 0.03 means there’s only a 3% chance that the observed difference (20% vs. 18.5%) is due to random variability alone.
   • Since 0.03 is below the common threshold of 0.05, the p-value is low enough to indicate a statistically significant difference in extraction between the two batches.

This low p-value suggests it’s unlikely that the difference is due to chance. You can confidently say that Batch A is indeed more soluble than Batch B, possibly due to differences in roast profile or chemical changes affecting solubility.

If the p-value were high (say, 0.4):

A high p-value, like 0.4, would imply a 40% chance that the difference is just due to random variation in your measurements. In this case, you wouldn’t have strong evidence that Batch A is more soluble than Batch B, and the difference in extraction might not be reliable.