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What does a p-value mean in lottery analysis?
A p-value is the probability of a result at least as extreme as the observed one, assuming the null model is true. It is not the probability that the model is true.
Definition
For test statistic T and observed value tobs, one relevant tail is .
Example
If an analysis returns p = 0.03, then, under the null model, a test statistic at least this extreme would occur in about 3% of repeated studies. It does not mean 97% certainty that the draw mechanism is non-random.
The 0.05 threshold
A 0.05 level is a decision convention, not a law of nature. Values 0.049 and 0.051 contain almost the same evidence. Report the exact p-value and deviation size.
Multiple testing
Testing many numbers, windows and measures raises false-alarm risk. With 20 independent tests at 0.05, the probability of at least one false alarm is .
How to report it
State the test, draw range, statistic, degrees of freedom, exact p-value, assumptions and effect size. Limit the conclusion to how the sample compares with the model; do not turn it into a forecast.
Limitations
P-values depend on sample size. A large sample can detect a tiny unimportant deviation, while a small sample may remain inconclusive despite a visible difference.
Frequently asked questions
- Does p = 0.05 mean a five percent chance the hypothesis is true?
- No. It is the probability of data at least as extreme as those observed, calculated under the null hypothesis.
- Does a large p-value prove randomness?
- No. It only means that this sample and test do not provide sufficient evidence to reject the model.
Check it on real draw data
Choose a draw range in Lotto Lab PRO and compare the observed result with the random model.
Related Lotto Lab PRO guides
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