A p-value is a measurement. A decision is a choice — and the choice depends entirely on the significance level you set before you look. Hold the data still, drag α, and watch one unchanged p-value reject the null at one setting and fail to reject it at the next.
If H₀ were true, this is where z would land
rejection region — total area = αp-value tails — total area = p
p against α on one number line
The shaded strip is every p-value small enough to reject at your current α. The blue marker is this sample's p, and it does not move when you drag α.
Set a significance levelthen read the decision
The evidence — 36 resting heart rates
A reference population averages 74 bpm with σ = 9. H₀: μ = 74 · H₁: μ ≠ 74 (two-tailed). Each dot below is one sampled patient.
The truth behind the curtain (you never see this in real life)
Drag your significance level
α = 0.050
p-value
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alpha
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test z
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critical z*
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α is chosen first. Sliding it after you have seen p until the decision comes out the way you wanted is a real practice with a real name — and it destroys the guarantee the whole procedure rests on.
What α actually buys you
300 fresh samples were drawn from the world you selected. Below is how many of them your current α would reject.