In AP Statistics, independence means the outcome of one event or observation does not affect another; on the exam it shows up as the condition you must verify before any inference procedure (random sampling plus the 10% condition) and as the relationship a chi-square test for independence evaluates.
Independence is the idea that knowing one outcome tells you nothing about another. Two events are independent if one happening doesn't change the probability of the other. Two observations are independent if one person's response doesn't influence another person's response.
In the AP Stats inference units (Units 6-9), independence becomes a condition you have to check before running any confidence interval or significance test. The CED spells it out the same way every time. First, the data should come from a random sample or a randomized experiment. Second, when you sample without replacement, you check the 10% condition (n ≤ 10% of N) because pulling people out of a small population makes the remaining picks slightly dependent on each other. Independence also has a second life in Unit 8, where the chi-square test for independence asks whether two categorical variables are associated in a population. Same word, two jobs, and the exam expects you to handle both.
Independence is the one condition that appears in essentially every inference procedure on the exam. The CED requires you to verify it for a one-proportion z-interval (AP Stats 6.2.B), a two-proportion z-interval (AP Stats 6.8.B), a one-sample t-interval for a mean (AP Stats 7.2.C), a two-sample t-test for means (AP Stats 7.8.C), chi-square tests (AP Stats 8.5.C), and even the t-test for a regression slope (AP Stats 9.4.C). The reason it matters statistically is that the standard error formulas you build intervals and tests from assume observations don't influence each other. If that assumption breaks, your margin of error is wrong and your p-value is meaningless. Then in Topics 8.5 and 8.6, independence flips from a condition to a hypothesis. The null hypothesis of a chi-square test for independence is literally "the two categorical variables are independent" (AP Stats 8.5.A), and rejecting it lets you claim the variables are associated (AP Stats 8.6.D).
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10% Condition (Units 6-9)
The 10% condition is how you rescue independence when sampling without replacement. Technically each draw changes the population a tiny bit, but if your sample is at most 10% of the population, the dependence is so small it's safe to ignore. Every inference procedure in Units 6 through 9 includes this check.
Chi-Square Statistic (Unit 8)
In Unit 8, independence stops being something you assume and becomes something you test. The chi-square statistic compares observed counts in a two-way table to the counts you'd expect if the two categorical variables were truly independent. A big chi-square value means the data look too lopsided for independence to be believable.
Dependent Events (Unit 4)
Dependent events are the probability-unit flip side of this term. Back in Unit 4, you learned that events are independent when P(A|B) = P(A). The inference-unit independence condition is the same core idea applied to data collection, where one observation shouldn't change the probabilities for another.
Confidence Interval (Units 6-7)
Independence is the price of admission for every confidence interval. The formulas like p̂ ± z*√(p̂(1-p̂)/n) only give an honest margin of error when observations are independent. That's why the conditions step comes before the calculation step, not after.
Independence gets tested two ways. First, MCQs and FRQ inference problems expect you to check it as a condition. A typical multiple-choice stem gives you two random samples (say, 200 residents in one region and 250 in another) and asks which conditions are satisfied for a two-proportion interval. You need to name the random sampling and the 10% condition, not just say "it's independent." Second, chi-square FRQs make independence the actual research question. The 2017 FRQ Q5 gave a random sample of 207 men and women being treated for schizophrenia and asked whether the data provide convincing evidence of an association between sex and age at diagnosis, which is a chi-square test for independence. The 2019 FRQ Q3 used a similar two-way table of men, women, and medication habits. On any full inference FRQ, you earn the conditions point by explicitly stating how independence is satisfied (random sample or random assignment, plus the 10% check when sampling without replacement). Skipping it or just writing "conditions are met" loses credit.
These use the same word for two different things. The independence condition is about your data collection, asking whether individual observations affect each other, and you verify it with random sampling and the 10% condition. The chi-square test for independence is about two categorical variables in a population, asking whether knowing someone's category on one variable changes the distribution of the other. Confusingly, a chi-square test for independence still requires you to check the independence condition first. The condition is about how the data were gathered; the test is about what the data say.
Independence means one event or observation does not affect the probability or outcome of another.
For every inference procedure in Units 6-9, you check independence by confirming the data came from a random sample or randomized experiment, plus the 10% condition (n ≤ 10% of N) when sampling without replacement.
Two-sample procedures, like a two-proportion z-interval, require the two samples themselves to be independent of each other, with both samples passing the 10% check (n₁ ≤ 10% N₁ and n₂ ≤ 10% N₂).
The chi-square test for independence has the null hypothesis that two categorical variables are independent (not associated) in the population, and rejecting it supports a claim of association.
Matched pairs data are deliberately not independent between the two measurements, which is exactly why you analyze the differences as a single sample instead of using a two-sample test.
On FRQs, you have to explicitly state how the independence condition is met to earn the conditions point; vague statements like 'conditions are satisfied' don't score.
Independence means one event or observation doesn't affect another. It's both a condition you verify before every confidence interval and significance test (random sampling plus the 10% condition) and the relationship a chi-square test for independence evaluates between two categorical variables.
No, but they're linked. The 10% condition (n ≤ 10% of N) is one part of verifying independence when you sample without replacement. The full independence check also requires that the data came from a random sample or a randomized experiment.
The condition is about data collection, checking that individual observations don't influence each other. The chi-square test asks whether two categorical variables are associated in a population, like the 2017 FRQ that tested whether sex and age at schizophrenia diagnosis were associated. You still check the independence condition before running the chi-square test.
The two measurements within a pair are intentionally dependent, and that's fine. The CED handles this by treating the differences as one sample, so the condition you check is that the pairs themselves are independent of each other, then you run one-sample t procedures on the differences.
No, they're almost opposites. Independent events can both happen, and one occurring doesn't change the other's probability. Mutually exclusive events can't both happen, so knowing one occurred makes the other's probability zero, which is extreme dependence.