P Value For Z Score -1.09

Finding the p-value for a z-score of -1.09

Picture this: you're staring at a printout of your statistical analysis, and there it is — a z-score of -1.09. Practically speaking, your professor wants the p-value by tomorrow. Plus, or maybe you're running an actual study and need to know whether your result is significant. Either way, you're not here for a lecture on the central limit theorem. You need the number, and you need to know what it actually means.

Here's the short version: for a one-tailed test, the p-value associated with a z-score of -1.Which means both are well above the standard 0. For a two-tailed test, you'd double that to about 0.Worth adding: 2758. 1379. On the flip side, 09 is roughly 0. 05 threshold, which means the result is not statistically significant under the usual conventions.

But the number alone doesn't tell you much. Let's actually break down what's happening and why.

What a p-value and z-score actually are (without the textbook yawn)

A z-score tells you how many standard deviations a data point sits from the mean. Negative means it's below the mean, positive means above. So a z-score of -1.Plus, 09 is sitting just a bit more than one standard deviation below average. That's not extreme. Think about it: that's not even unusual. In a normal distribution, plenty of values fall in that range.

The p-value, on the other hand, is the probability of observing a value at least as extreme as yours, assuming the null hypothesis is true. In practice, that's the part people constantly misread. On top of that, a p-value is not the probability that your hypothesis is wrong. So it's not the probability that the result happened by chance in some vague cosmic sense. It's a very specific conditional probability tied to a very specific assumption (the null).

When you look up -1.On top of that, 09 in a z-table, you're finding the cumulative area to the left of that value. Plus, the area to the left of -1. Here's the thing — 09 is approximately 0. On the flip side, 1379. That area is the one-tailed p-value. If your alternative hypothesis is that the true mean is less than* what the null predicts, then 0.In real terms, 1379 is your p-value. If your alternative is two-sided (just "different," not specifically less or more), you double it because you'd also care about the symmetric tail on the other side.

One-tailed vs. two-tailed: this matters more than people think

The distinction between one-tailed and two-tailed tests isn't pedantic — it changes your conclusion entirely. With a z-score of -1.09:

• One-tailed (left tail): p ≈ 0.1379
• Two-tailed: p ≈ 0.2758

Both are non-significant at α = 0.05. But they imply different things about your research design. Still, choosing one-tailed after peeking at your data is a classic move that inflates Type I error rates. The choice should be made before you run the analysis, based on whether your hypothesis has a directional prediction.

How to find the p-value for -1.09 in practice

There are a few ways to do this, and the best one depends on what tools you have.

Using a z-table (the old-school way)

Standard normal tables list cumulative probabilities from the left. Worth adding: 09) = 1 - 0. If your table only shows positive z-scores, remember the symmetry: P(Z < -1.Practically speaking, 0 in the margin, then move across to the 0. 8621 = 0.In practice, you find -1. On the flip side, that's it. Also, 09) = P(Z > 1. 1379. Consider this: 09 column, and you land on 0. 1379.

Using software

In R, you'd type something like pnorm(-1.In Excel, =NORM.All three should return approximately 0.In Python (with SciPy), it's scipy.Also, 09, TRUE). stats.Think about it: norm. S.Also, cdf(-1. 1379. DIST(-1.09). Because of that, 09). For a two-tailed test, just multiply by 2.

Using an online calculator

There are plenty of free, reputable calculators that do this instantly. The output is the same number. The risk with random online tools is that some use slightly different conventions or rounding, so for anything that matters (a paper, a thesis, a clinical decision), verify with a second source.

Why this result is non-significant (and what that really means)

A p-value of 0.1379 means that if the null hypothesis is true, there's about a 14% chance of seeing a z-score at least this extreme just by random sampling variability. And that's not implausible. It's not even that unusual. By the conventional α = 0.05 cutoff, we fail to reject the null.

Here's where it gets interesting, though. "Fail to reject" is not the same as "accept." It means the evidence isn't strong enough to conclude there's a real effect, given the data you have. The effect could still be real — you might just have a small sample, or a lot of noise, or your measurement might be imprecise. The absence of evidence is not evidence of absence, and statisticians have been saying this for decades.

Also worth noting: statistical significance is not the same as practical significance. A z-score of -1.Consider this: 09 with a sample size of 10,000 might still be statistically significant. Now, a z-score of -2. 5 with a sample size of 8 is significant, but the effect itself is tiny. The p-value tells you about the signal-to-noise ratio, not about whether the effect matters in the real world.

Common mistakes people make with z-scores around -1.09

Confusing the direction of the tail

People sometimes report a p-value of 0.8621 for -1.Because of that, 09, which is the area to the right* of the z-score, not the left. Because of that, that's the complement, and it's only relevant if your alternative hypothesis points in the opposite direction. If you want the probability of being at least this far below the mean, you want the left tail: 0.1379.

For more on this topic, read our article on what time is 18 hours from now or check out how do you find an object's mass.

Forgetting to double for a two-tailed test

This one's rampant. Someone runs an analysis, gets z = -1.09, reports p = 0.1379 as the final answer, and moves on. But if the study was designed to detect any difference (not just a decrease), the correct p-value is 0.2758. It's a small change here, but the habit causes bigger problems with other z-scores.

Treating p = 0.06 as "almost significant"

With a z-score of -1.Now, 051, the difference between 0. 06 or 0.05 and 0.The cutoff is arbitrary. On top of that, 1379, which is not "almost" anything under standard conventions. But even if it were 0.09, your p-value is 0.051 is not itself meaningful. Reporting p-values with more precision (like p = 0.0497) doesn't actually make the result more true.

Misinterpreting the z-score as an effect size

A z-score of -1.Worth adding: 09 is not an effect size. It's a standardized distance from the null, which depends on both the effect size and the sample size. To know how big the underlying effect is, you need to look at Cohen's d, r, or whatever effect size metric is appropriate for your design. The z-score just tells you whether to take that effect seriously given the data.

Practical tips for reporting and using this p-value

Report the exact value when you can. 05," and "p = 0.14" if the precision matters. Still, 14" is more informative than "p > 0. 1379" is better than "p = 0.Also, "p = 0. APA style typically allows reporting to two or three decimal places.

Always state whether the test was one-tailed or two-tailed. A reviewer who has to guess will probably guess wrong, and the wrong guess can change the conclusion.

Include a confidence interval alongside the p-value when you can. 09 would span from about -2.A 95% confidence interval for a z-score of -1.13 to +0.Consider this: 95 (using the rough Wald approximation), which tells you that "no effect" is well within the plausible range of true values. That's a useful complement to the p-value, which only tells you about one specific null.

Don't p-hack. Plus, if your z-score is -1. 09 and your pre-registered analysis says two-tailed, report the two-tailed p-value. Don't switch to one-tailed because the two-tailed version is non-significant.

in research and gets flagged in peer review.

Think about the substantive question, not just the number. A p-value of 0.That said, 1379 doesn't tell you whether the effect is real, important, or worth pursuing in future research. It only tells you that, given this sample and assuming the null is true, you'd see a result at least this extreme about 13.8% of the time. That leaves a lot of room for the null to be wrong in either direction.

When z = -1.09 actually matters

There are contexts where a z-score around -1.Now, in equivalence testing, for example, you're trying to demonstrate that an effect is small enough* to be considered negligible. 09 is exactly what you want to see. The "zone of equivalence" is defined by upper and lower bounds, and a z-score inside that zone supports the claim of equivalence rather than failing to reject the null.

In interim analyses during clinical trials or large-scale data collection, a z-score of -1.Now, 09 might be one of many accumulating data points. The Data Safety Monitoring Board might look at trends across multiple outcomes, and a single non-significant z doesn't trigger any action on its own.

For power analysis planning, a z-score of -1.Also, 09 corresponds to a specific observed effect size. If you saw this in a pilot study and the effect was in the direction you hypothesized, you can use it (with appropriate caveats about pilot-study reliability) to estimate the sample size needed for a fully-powered follow-up. A z of -1.09 in one direction suggests the underlying standardized effect might be in the moderate range, though you'd want to compute Cohen's d directly to confirm.

In Bayesian updating, a z-score of -1.09 corresponds to a Bayes factor of roughly 2.7 against the alternative (for a one-tailed test), which is "anecdotal" evidence at best. This is useful for researchers who want to quantify how much the data have shifted their belief in the null versus the alternative, beyond the binary reject/fail-to-reject framework.

The bottom line

A z-score of -1.09 produces a one-tailed p-value of 0.1379 and a two-tailed p-value of 0.The sign indicates the direction of the deviation from the null, and the magnitude tells you the result is about 1.So 2758. Here's the thing — both are well above the conventional 0. Here's the thing — 05 threshold, so the result is not statistically significant under either interpretation. 09 standard errors away from what you'd expect if the null were true, which is not particularly unusual in either direction.

The most common errors people make with this result are confusing the tail, forgetting to double for a two-tailed test, and treating the p-value as a measure of effect size or truth. In practice, avoid those, report the value with appropriate precision, include a confidence interval when possible, and interpret the result in the context of the actual research question rather than as a pass/fail indicator. That's how you use a p-value responsibly, whether it's tiny or comfortably above the threshold.