P-Value Greater Than 0.05: What It Means

A p-value greater than 0.05 means that, if the statistical model you tested (including the null hypothesis) were correct, results at least as extreme as yours would turn up more than 5% of the time. Under the usual rule of rejecting the null hypothesis only when p is at or below a pre-set significance level of 0.05, you fail to reject it. That is a statement about how compatible your data are with the model. It is not a finding that there is no effect, and it is not a probability that the null hypothesis is true.

What does a p-value greater than 0.05 mean?

Start with the definition. Greenland and colleagues describe a p-value as “a statistical summary of the compatibility between the observed data and what we would predict” from the model, and stress that it tests “all the assumptions about how the data were generated (the entire model), not just the targeted hypothesis.” The American Statistical Association (ASA) puts the first of its six principles the same way: “P-values can indicate how incompatible the data are with a specified statistical model.”

A large p-value therefore says the data are not very incompatible with the model. A small one says they are. The cut-off of 0.05 is the conventional significance level (α) that researchers fix before collecting data. It is a convention, not a law of nature, and the ASA’s third principle warns that “scientific conclusions and business or policy decisions should not be based only on whether a p-value passes a specific threshold.”

The decision rule in one line

If p > α (for example p = 0.087 and α = 0.05), do not reject the null hypothesis. If p ≤ α, reject it. For the logic behind that rule, see the null hypothesis explained and test statistic and hypothesis testing guides.

Does p > 0.05 mean there is no effect?

No. Three of the ASA’s principles rule this reading out:

“P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.” So p = 0.30 does not mean there is a 30% chance the null is true.
“A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.” A large p-value is not proof that an effect is small or absent.
“By itself, a p-value does not provide a good measure of evidence regarding a model or hypothesis.”

The careful wording is “we did not find statistically significant evidence of a difference”, not “there is no difference” and not “the null hypothesis is true”. Failing to reject the null is not the same as accepting it.

Worked example: a p-value of 0.087

The numbers below are illustrative and were computed for this page; they are not data from a real study. Two independent groups of 20 each, with a pooled standard deviation of 9.0 (equal variances assumed): group A has mean 52.0 and group B has mean 47.0.

Difference in means: 52.0 − 47.0 = 5.0.
Standard error of the difference: 9.0 × √(1/20 + 1/20) = 9.0 × √0.1 = 9.0 × 0.3162 = 2.846.
Test statistic: t = 5.0 / 2.846 = 1.757, with 20 + 20 − 2 = 38 degrees of freedom.
Two-sided p-value: P(|T₃₈| ≥ 1.757) = 0.087.
Decision at α = 0.05: 0.087 > 0.05, so fail to reject the null hypothesis of equal means.

Now look beyond the p-value, as the ASA recommends when it names methods that “emphasize estimation over testing such as confidence, credibility, or prediction intervals”. The 95% confidence interval for the difference is 5.0 ± 2.024 × 2.846 = 5.0 ± 5.76, which runs from −0.76 to 10.76. The standardised effect (Cohen’s d = 5.0 / 9.0) is 0.56. The interval includes zero, which is why p > 0.05, but it also includes differences as large as about 10.8 points. The data are compatible with no difference and also with a substantial one; the study simply could not tell them apart.

The sample size is the likely reason. A standard power calculation for a two-sided test at α = 0.05, 80% power and a true standardised difference of d = 0.5 needs about 64 participants per group (63.77, rounded up). Twenty per group was too few to detect an effect of that size reliably. For how to plan this before data collection, see power analysis in R and Type I and Type II errors.

How to read a p-value above 0.05

Statement about p > 0.05	Supported?	Why
The data are not very incompatible with the tested model.	Yes	A p-value indicates how incompatible the data are with a specified model (ASA principle 1; Greenland et al. 2016).
The null hypothesis is probably true.	No	P-values do not measure the probability that the studied hypothesis is true (ASA principle 2).
There is no effect.	No	A p-value does not measure effect size or importance (ASA principle 5). Check the confidence interval.
The result is unimportant.	No	Same principle: statistical significance and importance are different things. See statistical vs clinical significance.
The conclusion should rest on p alone.	No	Decisions should not be based only on whether a p-value passes a threshold (ASA principle 3).

Assumptions and common mistakes

Because a p-value tests the entire model, a result above 0.05 can reflect a true null, a small sample, noisy measurement, or a violated assumption such as independence or the shape of the distribution. Common mistakes include:

Reading p as the probability the null is true. It is not (ASA principle 2).
Calling a non-significant result “proof of no difference”. Use the confidence interval to see which effect sizes remain plausible. The p-value vs confidence interval comparison shows how the two relate.
Chasing significance. Trying different tests or subsets until p drops below 0.05 is p-hacking. The ASA’s fourth principle is that “proper inference requires full reporting and transparency.”
Treating 0.049 and 0.051 as different in kind. They are almost the same amount of evidence; only the label changes.

How to report a non-significant result (APA)

APA Style’s statistical-symbols guidance covers italicising statistical symbols, how to write the leading zero (or its absence) in p values, reporting exact p values, and writing p < .001 for very small values. Following those topics, report the test statistic, degrees of freedom, exact p, the effect size and the confidence interval. For the example above:

The difference between groups was not statistically significant, t(38) = 1.76, p = .087, d = 0.56, 95% CI of the difference [−0.76, 10.76].

Reporting the interval and effect size, and not only “p > .05”, lets readers judge what the study can and cannot rule out. See how to report confidence intervals and effect size in research.

How to calculate the p-value in Excel, R or Python

Each snippet reproduces the worked example from its summary statistics (t = 1.7568, 38 degrees of freedom).

Excel

=T.DIST.2T(1.7568, 38)    returns 0.0870

With raw data in two ranges, =T.TEST(A2:A21, B2:B21, 2, 2) gives the two-tailed p-value for equal variances.

R

2 * pt(-abs(1.7568), df = 38)    # 0.0870
# with raw vectors x and y:
t.test(x, y, var.equal = TRUE)$p.value

Python

from scipy import stats
r = stats.ttest_ind_from_stats(52.0, 9.0, 20, 47.0, 9.0, 20, equal_var=True)
print(r.statistic, r.pvalue)    # 1.7568  0.0870

FAQ

Is p = 0.06 significant?

At α = 0.05 it is not statistically significant, so you do not reject the null hypothesis. It is still worth reporting as p = .06 with the effect size and confidence interval, because the ASA cautions against basing conclusions only on whether a p-value passes a threshold.

Do we accept the null hypothesis when p > 0.05?

No. You fail to reject it. The data were not incompatible enough with the null model to reject it at the chosen level, which is different from showing the null is true.

Does a high p-value mean the result is unimportant?

No. Importance and statistical significance are separate questions; the ASA states that a p-value does not measure the size of an effect or the importance of a result.

What should I do next after p > 0.05?

Report the exact p-value, the effect size and the confidence interval; check whether the sample was large enough to detect an effect of the size that matters; and avoid re-running analyses until p falls below 0.05. Related reading: two-tailed hypothesis testing and the p-value dictionary entry.

Sources

All sources checked on 2026-10-29.

Wasserstein, R. L. and Lazar, N. A. (2016). The ASA statement on p-values: context, process, and purpose. The American Statistician, 70(2). doi:10.1080/00031305.2016.1154108. ASA press release with the six principles: https://www.amstat.org/asa/files/pdfs/p-valuestatement.pdf
Greenland, S. et al. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. European Journal of Epidemiology. https://pmc.ncbi.nlm.nih.gov/articles/PMC4877414/
APA Style, statistical symbols: https://apastyle.apa.org/style-grammar-guidelines/numbers-statistics/statistical-symbols

P-Value Greater Than 0.05: What It Means and What It Does Not