In AP Statistics, a result is statistically significant when it is so extreme that it is unlikely to have occurred by random chance alone, assuming the null hypothesis is true. You decide this by comparing the p-value to a significance level α, usually 0.05, and rejecting the null when p < α.
"Statistically significant" is the conclusion you reach when your data would be really weird if the null hypothesis were true. Formally, you run a significance test, get a p-value (the proportion of values in the null distribution as extreme or more extreme than your observed test statistic), and compare it to your significance level α. If the p-value is smaller than α, the result is statistically significant and you reject the null hypothesis. The data give you convincing evidence of a real effect, not just sampling variability doing its thing.
The term actually shows up before you ever compute a p-value. In Unit 3, the CED says that random assignment of treatments lets researchers conclude that some observed differences between groups are "so large as to be unlikely to have occurred by chance," and those differences are called statistically significant (VAR-3.E.2). That's the intuition version. Unit 6 gives you the machinery, the z-statistic z = (p̂ - p₀) / √(p₀(1-p₀)/n) and the p-value that turns "that seems unlikely" into an actual number.
This term is the bridge between two units. In Unit 3 (Topic 3.7), learning objective AP Stats 3.7.A asks you to interpret the results of a well-designed experiment, and statistically significant differences between randomly assigned treatment groups are the evidence that the treatment caused the effect. In Unit 6 (Topic 6.5), learning objectives AP Stats 6.5.A and AP Stats 6.5.B ask you to calculate a test statistic and p-value for a population proportion and then interpret that p-value. "Statistically significant" is the verdict that interpretation leads to. It's also the gatekeeper for causal claims on the exam. Significance plus random assignment lets you say "caused." Significance without random assignment does not.
Keep studying AP Statistics Unit 6
p-Value (Unit 6)
The p-value is the number; statistical significance is the verdict. A small p-value (below α) means your result lands in the unlikely tail of the null distribution, which is exactly what "statistically significant" means.
Random Assignment (Unit 3)
Significance alone tells you the difference probably isn't chance. Random assignment is what lets you upgrade that to "the treatment caused it," because it balances out lurking variables between groups.
Null Hypothesis (Unit 6)
Statistical significance is always relative to a null hypothesis. You're asking how surprising your data would be in a world where the null is true, so "significant" really means "surprising under H₀."
Sampling Variability (Units 3 and 5)
Sampling variability is the chance noise that significance testing exists to rule out. A significant result is one too big for ordinary sample-to-sample variation to explain.
This term gets tested in two ways. MCQs love interpretation traps. They'll hand you a significant result (like p = 0.02 or p = 0.03) and ask which conclusion is appropriate, with wrong answers that claim the null is proven false, that the result is practically important, or that causation holds without random assignment. One classic stem describes a confounding variable sneaking in (a diet group that also exercised more) and asks what that does to your causal conclusion. On FRQs, statistical significance shows up constantly in experiment and inference questions, including the 2018 (ACL surgery), 2021 (walking and cholesterol), 2022 (allergy clinics), and 2023 (fiber concrete) FRQs. You'll be asked to interpret a p-value in context, state whether the result is significant at a given α, and say what conclusion the design justifies. Always write your interpretation in context, link p to α explicitly, and check whether treatments were randomly assigned before claiming cause and effect.
Statistically significant means "unlikely to be chance," not "big" or "important." With a huge sample size, a tiny, useless effect (a drug lowering blood pressure by 0.5 points) can still produce p < 0.05. Practical significance asks whether the effect is large enough to matter in real life, and the exam loves answer choices that quietly swap one for the other.
A result is statistically significant when its p-value is less than the significance level α, meaning the data would be unlikely if the null hypothesis were true.
Statistically significant differences between randomly assigned treatment groups are evidence that the treatment caused the effect (VAR-3.E.3).
Without random assignment, a statistically significant difference shows association, not causation, because confounding variables could explain it.
Statistically significant does not mean the effect is large or practically important; it only means the result is hard to explain by chance.
Significance never proves the null hypothesis is false. There's always a chance (equal to α) of rejecting a true null, which is a Type I error.
Always interpret significance in context on FRQs by stating the p-value, the comparison to α, and the conclusion about the parameter or treatment.
It means a result is so extreme that it's unlikely to have happened by random chance alone, assuming the null hypothesis is true. In practice, you call a result statistically significant when its p-value is less than the significance level α, often 0.05.
No. Significance only means the result is unlikely to be chance, not that the effect is big or useful. A massive sample can make a trivially small effect statistically significant, which is why the exam distinguishes statistical significance from practical importance.
No. A significant result gives convincing evidence against the null, but you could still be wrong. If α = 0.05, there's a 5% chance of rejecting a null hypothesis that's actually true (a Type I error).
The p-value is the probability of getting a result as extreme or more extreme than yours if the null is true. Statistical significance is the yes/no call you make by comparing that p-value to α. A p-value of 0.02 is significant at α = 0.05 but not at α = 0.01.
Only if treatments were randomly assigned. In a well-designed experiment, significance plus random assignment supports a causal conclusion (VAR-3.E.3). In an observational study, a significant result only shows an association, because lurking variables weren't controlled.