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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.
Table of contents
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 should I report the result?
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.
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