How this calculator works
A hypothesis test combines a null value, a sampling model and a preselected rejection rule. The statistic measures departure from the null in standard-error units. A t reference accounts for estimating a mean standard error from a sample; a z reference treats population SD as known. The proportion option uses the null probability in its binomial standard error. A small p-value is evidence against the full null model, including its assumptions, rather than a measure of effect size.
Formula
Statistic = (sample estimate - null value)/SE. Mean SE = SD/√n; proportion null SE = √(p0(1 - p0)/n). Reject when p ≤ α.
Worked example
A mean of 2 with sample SD 2 and n = 4 gives t = 2 and two-sided p ≈ 0.139326, so do not reject at 5%. Treating SD 2 as known instead gives z = 2 and p ≈ 0.0455003.
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Frequently asked questions
Which hypotheses should I enter?
The null fixes the mean or proportion at a stated value. The alternative describes a difference, increase or decrease relative to that value.
Is statistical significance practical importance?
No. Assess the size of the effect, its uncertainty and the consequences of acting on it.
Can I keep testing as observations arrive?
Ordinary fixed-sample p-values do not account for optional stopping. Use a planned sequential procedure when monitoring repeatedly.