Statistical significance is a way of judging whether an observed difference or relationship would be unlikely under a specified chance-based model. The core aim of Science mastery is not to make students worship a p-value threshold. It is to help them understand that statistical significance addresses one narrow question: Could random variation alone plausibly produce a result like this under the null hypothesis?
For students and parents searching for statistical significance, p-value, statistically significant meaning, null hypothesis, significance level or what does p less than 0.05 mean, the most useful principle is this: statistically significant does not automatically mean scientifically important, practically important or causal.
Significance is one piece of evidence, not the whole conclusion.
The 60-Second Statistical Significance Idea
A common significance-testing framework includes:
- null hypothesis — a model with no effect or no difference of the type being tested;
- test statistic — calculated from the data;
- p-value — how compatible the observed result is with the null model;
- significance threshold — a preselected decision rule such as 0.05 in some contexts.
The exact test depends on the data and research design.
Wait, What? p < 0.05 Does Not Mean There Is a 95% Chance the Hypothesis Is True?
Correct.
This is one of the most common misconceptions.
A p-value does not tell you the probability that the research hypothesis is true.
It tells you, under the assumptions of the statistical test and null model, how unusual the observed data or more extreme data would be.
That is a much narrower statement.
The Null Hypothesis
The null hypothesis usually represents:
- no difference;
- no association;
- no treatment effect;
of the type specified by the test.
Statistical testing asks whether the observed data is sufficiently inconsistent with that null model.
What a p-Value Means
Conceptually, a small p-value means:
If the null model were true, data this extreme would be relatively unusual.
That can count as evidence against the null hypothesis.
But the p-value alone does not tell you:
- how large the effect is;
- whether the study is unbiased;
- whether the result is causal;
- whether the result will replicate.
Statistical Significance vs Effect Size
Suppose a huge study detects a 0.1% difference with p < 0.05.
The result may be statistically significant.
But the effect could be too small to matter practically.
Effect size asks how large the difference or relationship is.
Good scientific interpretation considers both.
Sample Size Changes Significance
With a very large sample, even tiny effects can become statistically significant.
With a very small sample, a meaningful effect may fail to reach significance because the estimate is too uncertain.
This is why significance should always be interpreted alongside sample size.
See Sample Size.
A Worked Example: Plant Growth
Two fertiliser groups differ by 0.3 cm in average growth.
A statistical test reports p = 0.03.
This may meet a 0.05 significance threshold.
But the scientist should still ask:
- Is 0.3 cm biologically meaningful?
- Was the sample representative?
- Were groups randomised?
- Were control variables managed?
- How large is the uncertainty?
The p-value is not the conclusion.
A Worked Example: Small Study
A small experiment observes a fairly large difference, but p = 0.12.
That does not prove “there is no effect”.
Possible explanations include:
- the effect is absent;
- the sample is too small;
- variation is too large;
- measurement is noisy.
“Not statistically significant” is not the same as “proven equal”.
Type I Error
A Type I error occurs when a study rejects the null hypothesis even though it is actually true.
This is sometimes called a false positive.
The significance threshold helps control the long-run rate of this kind of error under the test assumptions.
Type II Error
A Type II error occurs when a real effect is not detected.
This is sometimes called a false negative.
Low sample size, high variability and small effect size can increase the risk of missing a real effect.
Multiple Testing
If researchers test many hypotheses, some may appear significant by chance.
This is why advanced research may use:
- multiple-comparison corrections;
- pre-specified outcomes;
- replication.
Students do not need every statistical detail to understand the principle: more tests create more opportunities for chance findings.
Statistical Significance vs Causation
A statistically significant correlation can still be confounded.
Significance says nothing by itself about causal direction.
Statistical Significance vs Replication
One significant result should not settle an important question.
Confidence becomes stronger when:
- methods are sound;
- results replicate;
- effect sizes are consistent;
- multiple lines of evidence converge.
See Repeatability and Reproducibility.
Primary Science Foundations
Primary learners do not need formal significance testing.
They can build the foundation by asking:
- Could this difference be random?
- Did we repeat enough?
- Are the groups really different or just variable?
Secondary Science Statistical Significance
Secondary students can increasingly understand:
- null hypothesis;
- p-value;
- significance threshold;
- effect size;
- sample size;
- false positives and false negatives.
How to Practise Statistical-Significance Reasoning
Given a study result, ask:
- What is the null hypothesis?
- What does the p-value actually say?
- How large is the effect?
- How large is the sample?
- Does the design support causation?
- Has the result replicated?
Common Statistical-Significance Mistakes
- interpreting p < 0.05 as “95% chance the hypothesis is true”;
- equating significance with importance;
- equating non-significance with no effect;
- ignoring sample size;
- claiming causation from a significant association;
- treating one significant study as final proof.
Frequently Asked Questions
What does statistically significant mean?
It means the observed result is sufficiently unusual under a specified null model according to a chosen statistical decision rule.
What does p < 0.05 mean?
Under the null model and test assumptions, data this extreme would occur less than 5% of the time in the long run. It does not mean the hypothesis has a 95% chance of being true.
Does statistical significance mean the effect is important?
No. Effect size and practical importance must be considered separately.
Does non-significant mean no effect?
No. The study may have insufficient power, high variation or an effect too small to detect reliably.
Useful eduKateSG Routes
The Core Aim
Statistical significance asks whether a result is difficult to explain by random variation under a specified null model.
It does not answer everything else.
That is the core aim: use significance as one disciplined clue, then still examine effect size, design, bias, causation and replication.
Properly taught kids shine a bright light into the future.