Table 1.

Identical P values with very different interpretations

	Treatment 1 (mean ± SD, n)	Treatment 2 (mean ± SD, n)	Difference between means	P value	95 % CI of the difference between means
Experiment A	1,000 ± 100, n = 50	990.0 ± 100, n = 50	10	0.6	−30 to 50
Experiment B	1,000 ± 100, n = 3	950.0 ± 100, n = 3	50	0.6	−177 to 277
Experiment C	100 ± 5.0, n = 135	102 ± 5.0, n = 135	2	0.001	0.8 to 3.2
Experiment D	100 ± 5.0, n = 3	135 ± 5.0, n = 3	35	0.001	24 to 46

Experiments A and B have identical P values, but the scientific conclusion is very different. The interpretation depends upon the scientific context, but in most fields experiment A would be solid negative data proving that there either is no effect or that the effect is tiny. In contrast, experiment B has such a wide confidence interval as to be consistent with nearly any hypothesis. Those data simply do not help answer your scientific question

Similarly, experiments C and D have identical P values, but should be interpreted differently. In most experimental contexts, experiment C demonstrates convincingly that while the difference is not zero, it is quite small. Experiment D provides convincing evidence that the effect is large