SOUTHERN NEW HAMPSHIRE UNIVERSITY • SNHU • MAT-240

What does a p-value actually tell you?

A p-value tells you how often a result at least as incompatible with the null model as the observed result would occur in repeated data under that model and the test assumptions. It does not tell you the probability that the null hypothesis is true, the chance the result was caused by randomness, the size or importance of an effect, or whether a result will replicate. Interpret it with the estimate, confidence interval, design, assumptions, and decision context. A threshold can guide a rule, but it does not turn uncertain evidence into certainty.

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Decision resource

P-Value Misconception Table

A correction table that separates null-model compatibility from hypothesis truth, effect size, importance, and replication.

Step 1

misconception: Probability the null is true
correction: Compatibility of data with a null model under assumptions
better question: What model and statistic produced this value?

Step 2

misconception: Size of the effect
correction: Evidence strength is distinct from magnitude
better question: What is the estimate and interval in meaningful units?

Step 3

misconception: Importance of the result
correction: Importance depends on consequences and context
better question: Would plausible effects change a decision?

Step 4

misconception: Chance of replication
correction: Replication depends on design, effect, variability, and new sampling
better question: What uncertainty and study limitations remain?

The meaning is conditional on the null model

A p-value begins by assuming a null model and the conditions of the selected test. It then evaluates the observed statistic relative to the distribution expected under that setup. Smaller values indicate greater incompatibility between the data and that model, not a direct probability assigned to the hypothesis. The result also depends on the test statistic, one- or two-sided alternative, sample information, and assumptions. Before interpreting the number, state the null, alternative, parameter, and procedure so a reader knows exactly which conditional question was calculated.

What the p-value does not tell you

It does not give the probability the null is true or false. It does not measure the probability that chance caused the result. It does not report effect size, practical importance, data quality, bias, or the chance of successful replication. A small p-value can accompany a trivial effect, and a large p-value can accompany an imprecise estimate that leaves important effects plausible. Design flaws can make a precise calculation answer the wrong question. These limits are why p-values belong with estimates, intervals, graphs, assumptions, and subject context.

Fictional example: packaging fill weights

A fictional manufacturer examines whether the population mean fill weight differs from a target. Its test returns a small p-value and a very narrow interval around a difference of only a fraction of a gram. The evidence is inconsistent with exact equality under the model, but the operational importance depends on tolerance, cost, compliance, and measurement precision. A different sample might produce a larger p-value even with a similar estimate if uncertainty were higher. The manager should not translate the number into a probability that the process is wrong; the decision requires magnitude and consequences.

Use the P-Value Misconception Table

Check the sentence you are about to write against four questions. Did you describe compatibility with a null model rather than hypothesis truth? Did you separate statistical evidence from effect magnitude? Did you retain assumptions and design limits? Did you avoid turning a threshold into certainty? If any answer is no, revise. Replace statements such as the p-value proves an effect with precise language about evidence under the model. Add the estimate and interval so the reader can evaluate direction, size, and precision.

How should a threshold be used?

A prespecified significance threshold can make a decision rule consistent, but it should not create two different scientific realities on either side of the cutoff. Values just below and just above a threshold can represent similar evidence. Report the actual p-value when permitted, the estimate, interval, and context. Explain the consequence of false-positive and false-negative decisions when relevant. If many analyses were explored or the decision rule changed after seeing data, the interpretation needs added caution. Thresholds organize decisions; they do not erase uncertainty.

How to write a responsible MAT-240 interpretation

Name the null model and parameter, report the observed estimate and its units, state the p-value as conditional evidence, and include uncertainty and practical meaning. Describe any design or assumption limitation. Use the exact instructions in your current classroom and your own output. Domyclass can help you understand the logic or review a sentence you wrote, but it will not interpret a current graded result on your behalf. we explain; you submit your own work keeps the analysis and authorship with the learner.

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