Statistically Significant (alpha = 0.05): Yes — this result is unlikely to be due to chance alone.
Your Recent & Past Results
Restored a past calculation.
Advertisement
Compare Calculations
Side-by-Side Comparison
A comparison of your scenarios' results
Downloads
Includes your inputs and results for this calculation, plus any additional calculations you've compared.
Share & Print
The link includes your inputs and results, so anyone who opens it sees this exact calculation.
How This Calculator Works
A p-value is the probability of seeing a result at least as extreme as the one observed, purely
by chance, if there were actually no real effect. Enter a z-score and choose a test type, and
this calculator converts it into a p-value — the standard figure used to decide whether a result
is statistically significant. If you have raw sample data instead of an already-computed z-score,
find it first with the Z-Score Calculator.
A smaller p-value means the observed result would be less likely to happen by chance alone, which
is stronger evidence against the assumption that nothing real is going on (the “null hypothesis”).
By long-standing convention across most fields, a p-value below 0.05 is generally treated as
statistically significant — but that threshold is a convention, not a law of nature, and what
counts as “significant enough” can vary by field and by how costly a wrong conclusion would be.
The Formula
For a left-tailed test (is the result unusually low?):
p=Φ(z)
For a right-tailed test (is the result unusually high?):
p=1−Φ(z)
For a two-tailed test (is the result unusual in either direction?):
p=2×(1−Φ(∣z∣))
Where z is the z-score and Φ is the standard normal distribution’s cumulative
distribution function — the probability that a randomly drawn value from that distribution falls
at or below a given point, computed here via a well-established polynomial approximation of the
error function.
Worked Example
A z-score of 1.96 is the textbook reference point for a two-tailed test at the conventional
95% confidence level: p=2×(1−Φ(1.96))≈2×(1−0.975)≈0.0500. 2. A p-value of about 0.05 sits right at the conventional significance threshold. 3.
A larger z-score of 2.576 (the two-tailed reference point for 99% confidence) gives a smaller,
more significant p-value of about 0.0100.
Cómo funciona esta calculadora
Un valor p es la probabilidad de observar un resultado al menos tan extremo como el observado,
únicamente por azar, si en realidad no existiera ningún efecto real. Ingresa una puntuación Z y
elige un tipo de prueba, y esta calculadora la convierte en un valor p — la cifra estándar
utilizada para decidir si un resultado es estadísticamente significativo. Si tienes datos de
muestra sin procesar en lugar de una puntuación Z ya calculada, encuéntrala primero con la Z-Score Calculator.
Un valor p más pequeño significa que sería menos probable que el resultado observado ocurriera
solo por azar, lo cual constituye una evidencia más fuerte en contra del supuesto de que no está
pasando nada real (la “hipótesis nula”). Por convención de larga data en la mayoría de los campos,
un valor p por debajo de 0.05 generalmente se considera estadísticamente significativo — pero
ese umbral es una convención, no una ley de la naturaleza, y lo que cuenta como “suficientemente
significativo” puede variar según el campo y según qué tan costosa sería una conclusión
equivocada.
La fórmula
Para una prueba unilateral izquierda (¿el resultado es inusualmente bajo?):
p=Φ(z)
Para una prueba unilateral derecha (¿el resultado es inusualmente alto?):
p=1−Φ(z)
Para una prueba bilateral (¿el resultado es inusual en cualquiera de las dos direcciones?):
p=2×(1−Φ(∣z∣))
Donde z es la puntuación Z y Φ es la función de distribución acumulada de la
distribución normal estándar — la probabilidad de que un valor tomado al azar de esa distribución
caiga en un punto dado o por debajo de él, calculada aquí mediante una aproximación polinómica
bien establecida de la función de error.
Ejemplo resuelto
Una puntuación Z de 1.96 es el punto de referencia clásico para una prueba bilateral al
nivel de confianza convencional del 95%: p=2×(1−Φ(1.96))≈2×(1−0.975)≈0.0500. 2. Un valor p de aproximadamente 0.05 se ubica justo en el umbral de
significancia convencional. 3. Una puntuación Z mayor, de 2.576 (el punto de referencia
bilateral para el 99% de confianza), da un valor p más pequeño y más significativo, de
aproximadamente 0.0100.
What counts as a "statistically significant" p-value?
The most common convention across many fields is a p-value below 0.05 (a 5% chance the result happened by chance alone). This is a widely-used convention, not a strict rule — some fields use stricter thresholds (like 0.01) when a wrong conclusion would be especially costly.
How do I know whether to use a one-tailed or two-tailed test?
Use a two-tailed test when you care whether a result is unusual in EITHER direction (e.g. "is this coin unfair?"). Use a one-tailed test (left- or right-tailed) only when you specifically care about ONE direction ahead of time (e.g. "is this new process FASTER?") — deciding this after seeing the data is considered poor statistical practice.
What's the difference between this and the Z-Score Calculator?
The Z-Score Calculator converts a raw value into a z-score and percentile against a known distribution. This calculator starts from an already-known z-score and answers the specific question a percentile alone does not: how likely is a result this extreme to have happened purely by chance?
We use cookies for analytics and ads to help support this free site. You can accept all, or decline and we'll only use what's needed for the site to work.