P-value meaning
A p-value is about the data under H0, not the probability that H0 is true.
Statistics practice quiz for p-values
P-Value Interpretation Quiz
Practice p-value meaning, statistical significance, alpha, reject and fail-to-reject decisions, confidence interval connections, effect size warnings, software-output wording, and common p-value mistakes.
- 22 original p-value practice questions
- Significance decisions and common interpretation mistakes
- Beginner, intermediate, and advanced filters
- Full visible answer library for review
Reviewed for Statskan: original p-value scenarios, answer explanations, and calculator links. Last reviewed: July 2026.
- Meaning Practice what a p-value does and does not tell you.
- Decision Compare p-values with alpha without changing the rule later.
- Output Read SPSS-style Sig. values and report significance clearly.
- Limits Separate statistical significance from practical importance.
How to Interpret a P-Value
Quick answer: A p-value tells you how unusual the observed result would
be if the null hypothesis were true. Compare the p-value with alpha, then write the
decision in context without saying the p-value is the probability that H0 is true.
P-values appear in t-tests, z-tests, chi-square tests, ANOVA, regression, correlation, SPSS output, Excel output, R summaries, and Stata results. Many students lose points not because they cannot find the p-value, but because they describe it incorrectly.
Practice P-Value Interpretation
Filter by topic or level, answer each question, and review the explanation after choosing.
Meaning
Question 1 of 22
Which statement best describes a p-value?
P-Value Study Guide
Review these rules before interpreting output from SPSS, Excel, R, Stata, or a calculator.
Decision rule
If p is less than or equal to alpha, reject H0. If p is greater than alpha, fail to reject H0.
Significance
Statistical significance does not automatically mean the result is practically important.
Confidence intervals
For many two-tailed tests, a matching confidence interval and p-value lead to the same decision.
Software output
SPSS often labels p-values as Sig. or Sig. (2-tailed). Other software may report Pr, P>|t|, or p.
Reporting
Report the test statistic, p-value, decision, and practical meaning when your assignment asks for interpretation.
Need Help Explaining a P-Value From Your Assignment?
Send the test output, assignment prompt, alpha level, software used, and deadline. Statskan can help explain what the p-value means, what decision to make, and how to write the conclusion.
P-Value Interpretation Question Library
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Question 1
Which statement best describes a p-value?
Answer: The probability of results this extreme or more extreme, assuming the null hypothesis is true
A p-value is calculated under the null hypothesis. It measures how unusual the observed result would be if H0 were true.
Question 2
A student says, "p = 0.04 means there is a 4% chance that H0 is true." What is the problem?
Answer: A p-value is not the probability that H0 is true
The p-value describes the data under H0; it does not directly give the probability that H0 itself is true.
Question 3
If p = 0.021 and alpha = 0.05, what is the correct hypothesis-test decision?
Answer: Reject H0
Because 0.021 is less than 0.05, the result is statistically significant at the 5% level, so H0 is rejected.
Question 4
If p = 0.12 and alpha = 0.05, what is the correct decision?
Answer: Fail to reject H0
Because 0.12 is greater than 0.05, the evidence is not strong enough to reject H0 at the 5% significance level.
Question 5
What role does alpha play when interpreting a p-value?
Answer: Alpha is the cutoff used to decide whether the p-value is small enough to reject H0
Alpha is chosen before the test, often 0.05. The p-value is compared with alpha to make the statistical decision.
Question 6
A result has p = 0.07. It is not significant at alpha = 0.05, but is significant at alpha = 0.10. What should the student avoid doing?
Answer: Changing alpha after seeing the p-value just to make the result significant
Alpha should be set before analyzing the result. Changing the cutoff after seeing the p-value can make the analysis misleading.
Question 7
What does "statistically significant" usually mean in a hypothesis test?
Answer: The p-value is less than or equal to alpha
Statistical significance means the p-value meets the decision cutoff. It does not automatically prove practical importance.
Question 8
A study finds p < 0.001 but the average difference is only 0.2 points on a 100-point scale. What should be considered?
Answer: Practical significance and effect size
A very small p-value can occur with a tiny real-world difference, especially in large samples. Effect size helps judge practical importance.
Question 9
Which conclusion is best when p = 0.18 and alpha = 0.05?
Answer: There is not enough evidence to reject H0
A large p-value means the evidence is not strong enough against H0. It does not prove H0 is true.
Question 10
Which conclusion is best when p = 0.004 and alpha = 0.01?
Answer: Reject H0 and report that the result is statistically significant at the 1% level
Because 0.004 is less than 0.01, the result is significant even at the stricter 1% level.
Question 11
Why can a one-tailed p-value be different from a two-tailed p-value?
Answer: A one-tailed test puts the rejection area in one direction, while a two-tailed test considers both directions
Tail direction changes which extreme results count against H0, so the p-value and interpretation can differ.
Question 12
A result is extreme in the opposite direction from a one-tailed alternative. What should the student be careful about?
Answer: The one-tailed test may not support the claimed direction even if the result is unusual
One-tailed tests must match the planned alternative direction. An effect in the opposite direction does not support that directional claim.
Question 13
In many SPSS output tables, which column often contains the p-value?
Answer: Sig.
SPSS often labels p-values as Sig. or Sig. (2-tailed), depending on the procedure and table.
Question 14
An output table reports "Sig. (2-tailed) = .032." If alpha = .05, what does this usually mean?
Answer: The result is statistically significant for a two-tailed test
.032 is less than .05, so the two-tailed p-value is statistically significant at the 5% level.
Question 15
For a two-tailed test at alpha = 0.05, what does it usually suggest if a 95% confidence interval for a mean difference excludes 0?
Answer: The corresponding test is significant at alpha = 0.05
For many standard two-tailed tests, a 95% interval excluding the null value agrees with rejecting H0 at alpha = 0.05.
Question 16
A 95% confidence interval for a difference includes 0. What does that usually suggest for a matching two-tailed test?
Answer: The p-value is usually greater than 0.05
When the interval includes the null value, the matching two-tailed test is usually not significant at alpha = 0.05.
Question 17
Which statement is a common p-value mistake?
Answer: Saying p = 0.03 means there is a 97% chance the alternative is true
A p-value does not give the probability that the alternative hypothesis is true or false.
Question 18
A p-value is very small. What can the student reasonably say?
Answer: The observed result would be unusual if H0 were true
A small p-value provides evidence against H0, but effect size, bias, assumptions, and study design still matter.
Question 19
Which report style is usually clearer for a significant t-test?
Answer: Report the t statistic, degrees of freedom, p-value, and conclusion in context
Good reporting connects the statistical output to the research question and includes the key values needed to understand the test.
Question 20
When p is extremely small, why do many reports write p < .001 instead of p = 0?
Answer: The p-value is very small but not literally zero in most analyses
Software may display rounded values. Reporting p < .001 is usually more accurate than saying p = 0.
Question 21
A student runs 30 hypothesis tests and reports only the one p-value below 0.05. What is the concern?
Answer: Selective reporting can inflate false-positive risk
Running many tests increases the chance of finding at least one small p-value by chance unless the analysis plan or multiple-testing issue is handled.
Question 22
Why might a professor ask students to mention multiple-comparison adjustments?
Answer: Because many tests can raise the chance of false positives
Multiple-comparison adjustments help control error rates when several tests are performed.
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