Every SPSS output table has a column labelled “Sig.” — the p-value. It is probably the most looked-at number in statistics, and also one of the most misunderstood. Researchers celebrate when it falls below .05 and worry when it does not, often without being sure what the number actually says.
This tutorial explains what p-values in SPSS really mean, where to find them in your output, the five mistakes almost everyone makes with them, and how to report them correctly in APA style.
What a P-Value Actually Is
A p-value is the probability of getting results at least as extreme as the ones you observed, assuming the null hypothesis is true. In plain language: if there were really no effect and no difference, how surprising would your data be?
Suppose you compare two teaching methods and find a 6-point difference in exam scores, with p = .013. That means: if the two methods were truly identical, you would see a difference of 6 points or more only about 1.3% of the time by chance alone. Because that is unlikely, you reject the null hypothesis and conclude the methods differ.
Just as important is what a p-value is not:
- It is not the probability that the null hypothesis is true. A p-value is calculated by assuming the null hypothesis is true, so it cannot then tell you the probability that the assumption holds.
- It is not the probability that your result happened “by chance” in the everyday sense, and it is not the probability that your finding is wrong.
- It is not the probability that the result will replicate.
- It is not a measure of the size or importance of an effect. A tiny, trivial effect can have a very small p-value if the sample is large enough.
The .05 threshold is a convention, not a law of nature. It became standard largely because of R. A. Fisher’s suggestion in the 1920s, and it means you accept a 5% chance of a false positive (a Type I error) when the null hypothesis is true. Always set your alpha level before you run the analysis, not after seeing the output.
Where P-Values Appear in SPSS Output
In SPSS, p-values almost always appear in a column headed Sig. — short for significance. You will find it in:
- t-tests: the “Sig. (2-tailed)” column of the Independent-Samples T Test output.
- ANOVA: the “Sig.” column of the ANOVA table.
- Correlations: the “Sig. (2-tailed)” row under each correlation coefficient.
- Regression: the “Sig.” column for each predictor in the Coefficients table.
- Chi-square tests: the “Asymptotic Significance (2-sided)” column.
- Nonparametric tests: the “Exact Sig.” or “Asymptotic Sig.” in the Test Statistics table.
Two formatting quirks catch beginners out. First, SPSS prints .000 when the p-value is smaller than .0005. That does not mean the probability is zero — it means the value rounds to zero at three decimals. Always report it as p < .001, never as p = .000. Second, most SPSS procedures report two-tailed p-values by default. A one-tailed p-value is half the two-tailed value, but you should only use a one-tailed test if you predicted the direction of the effect before collecting the data.
How to Read a P-Value in SPSS: A Worked Example
Imagine two groups of 25 students each, taught with different methods. Group A scores a mean of 78.4 (SD = 8.2) and Group B a mean of 72.1 (SD = 9.0). An independent-samples t-test gives t(48) = 2.59, p = .013. Because p is below .05, you reject the null hypothesis: the mean scores differ significantly.
Now suppose the same test returned t(48) = 1.26, p = .214. Because p is above .05, you fail to reject the null hypothesis. Note the wording: you have not proven the methods are equal. You simply do not have enough evidence to say they differ. The difference might be real but too small for this sample to detect — a question of statistical power, not of proof.
The p-value also depends heavily on sample size. With 500 students per group, even a 1-point mean difference could be “statistically significant”. With only 12 students per group, a genuinely large difference might not reach significance. That is why significance alone never tells you whether a finding matters.
This is where effect sizes come in. For the example above, Cohen’s d is 0.73 — the 6.3-point difference divided by the pooled standard deviation of about 8.6 — which is a medium-to-large effect. Report the effect size and the confidence interval next to the p-value, every time.
The 5 Most Common P-Value Mistakes
1. “p = .03 means there is a 97% chance the effect is real”
No. The p-value is computed on the assumption that the null hypothesis is true, so it cannot be turned into a probability that the null is false. A p-value of .03 means results this extreme would occur 3% of the time if there were no effect — nothing more.
2. “p > .05 proves there is no effect”
No. A non-significant result means “not enough evidence”, not “evidence of no effect”. Small samples, noisy measures, and small real effects all produce non-significant p-values. Absence of evidence is not evidence of absence.
3. “A smaller p-value means a bigger effect”
No. The p-value mixes the size of the effect with the size of the sample. A tiny effect in a huge sample and a huge effect in a small sample can produce the same p-value. Compare effect sizes across studies, not p-values.
4. “p = .000 means the probability is zero”
No. SPSS rounds anything below .0005 to .000. The true p-value is small but not zero. Report it as p < .001.
5. “A significant p-value means the finding matters”
No. Statistical significance is not practical importance. A 0.2-point difference on a 100-point scale can be significant with a large enough sample and still be meaningless in practice. Always ask how big the effect is and whether it matters in the real world.
P-Values, Confidence Intervals, and Effect Sizes
A p-value and a confidence interval are two views of the same evidence. A 95% confidence interval gives a range of plausible values for the true effect. If the interval for a mean difference excludes zero, the p-value is below .05; if it includes zero, the p-value is above .05. The interval adds what the p-value lacks: the size of the effect and the precision of the estimate.
Modern guidance, including the American Statistical Association’s 2016 statement on p-values, is consistent on the main points: p-values do not measure the probability that a hypothesis is true, the size of an effect, or the importance of a result, and scientific conclusions should not rest on a p-value alone. The practical rule is simple: report the exact p-value, the effect size, and the confidence interval together, and interpret all three.
Getting P-Values in SPSS: Click-by-Click and Syntax
To get the p-value for a comparison of two group means, run an independent-samples t-test:
- Go to Analyze > Compare Means > Independent-Samples T Test.
- Move your outcome variable (for example, exam score) into the Test Variable(s) box.
- Move your grouping variable (for example, teaching method) into the Grouping Variable box and click Define Groups to enter the two group codes.
- Click OK. Read the p-value in the Sig. (2-tailed) column of the output table.
For a correlation, go to Analyze > Correlate > Bivariate, move your two variables in, and read the “Sig. (2-tailed)” value under each correlation coefficient.
The same t-test in syntax, which you can paste into a syntax window and run:
T-TEST GROUPS=Method(1 2) /MISSING=ANALYSIS /VARIABLES=Score /CRITERIA=CI(.95).
And a correlation with its p-value:
CORRELATIONS /VARIABLES=Hours Score /PRINT=TWOTAIL NOSIG /MISSING=PAIRWISE.
Reporting P-Values in APA Style (7th ed.)
Report the test statistic, degrees of freedom, the exact p-value, and the effect size. Italicize the letter p, and do not put a zero before the decimal point. Examples:
Significant result: “Students taught with Method A scored significantly higher than those taught with Method B, t(48) = 2.59, p = .013, d = 0.73.”
Non-significant result: “The difference between the two methods was not statistically significant, t(48) = 1.26, p = .214.”
Very small p-value: when SPSS prints .000, write p < .001 — for example, “r(48) = .62, p < .001.” Never write p = .000.
Report exact p-values to two or three decimal places (p = .032), and never round a p-value up across the .05 line: p = .052 is not significant at the .05 level, however close it looks.
Key Takeaways
- A p-value is the probability of results at least this extreme if the null hypothesis were true — nothing more.
- p < .05 means reject the null hypothesis at the 5% level; p ≥ .05 means fail to reject it, not “prove there is no effect”.
- SPSS prints .000 when p < .001 — always report it as p < .001, never as p = .000.
- The p-value mixes effect size and sample size, so always report effect sizes and confidence intervals alongside it.
- Do not treat .05 as a cliff: p = .049 and p = .051 are nearly identical evidence.
Frequently Asked Questions
What does p = .05 exactly mean?
It means that if the null hypothesis were true, you would see results at least this extreme about 5% of the time. The .05 cut-off is a convention for deciding when to reject the null hypothesis, not a natural dividing line between true and false.
Why does SPSS show Sig. = .000?
SPSS rounds p-values to three decimal places, so anything below .0005 displays as .000. The true value is small but not zero. Report it as p < .001 in your write-up.
Is a one-tailed p-value half the two-tailed value?
Numerically, yes — SPSS reports two-tailed p-values by default, and halving gives the one-tailed value. But only use a one-tailed test if you predicted the direction of the effect before you saw the data. Choosing one-tailed after seeing the result is not legitimate.
Can I compare p-values across studies?
Not directly. P-values depend on sample size and study design, so a smaller p-value in one study does not mean a larger effect. Compare effect sizes and confidence intervals instead — they are designed for that job.
What should I do if my p-value is .06?
Report the exact p-value, the effect size, and the confidence interval, and interpret them honestly. Do not call the result “marginally significant” as if it had passed the threshold, and do not keep testing until the p-value drops below .05 — that is p-hacking. A p of .06 with a large effect size may simply mean the study lacked power, which is itself a useful finding.
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