The Independence Condition is the inference requirement that one observation doesn't influence another, verified by random sampling or random assignment, plus the 10% condition (n ≤ 10% of N) when sampling without replacement. It appears in every AP Stats inference procedure, from proportions to slopes.
The Independence Condition says that observations in your data can't influence each other. If knowing one person's response tells you something about the next person's response, your standard error formulas break, and every confidence interval and p-value built on them becomes unreliable.
On the AP exam, you verify independence the same way every time, and the CED spells it out across [AP Stats 6.8.B], [AP Stats 7.4.C], and [AP Stats 9.4.C]. First, the data should come from a random sample or a randomized experiment. Second, if you're sampling without replacement (which is almost always), check the 10% condition, meaning the sample size is at most 10% of the population (n ≤ 10% N, and for two samples, n₁ ≤ 10% N₁ and n₂ ≤ 10% N₂). The 10% check matters because pulling people out of a small population without putting them back changes the odds for everyone left, which technically makes draws dependent. As long as you only take a small bite of the population, that dependence is negligible.
Independence is one of the few ideas that shows up in literally every inference unit. It's a required condition check in Unit 6 for two-sample z-intervals comparing proportions ([AP Stats 6.8.B]), in Unit 7 for one-sample t-tests for means and matched pairs ([AP Stats 7.4.C]), and in Unit 9 for the t-test for a regression slope ([AP Stats 9.4.C]). The wording barely changes across all three. That's good news for you, because mastering it once means you've got a guaranteed piece of every inference FRQ.
The deeper reason it matters is that the standard error formulas on the formula sheet assume independent observations. Violate independence and your stated confidence level or p-value is fiction, even if the math is perfect.
Keep studying AP Statistics Unit 6
10% Condition (Units 6-9)
The 10% condition isn't a separate requirement. It's the tool you use to verify independence whenever you sample without replacement. Think of it as the math backup for the independence claim.
Random Sampling (Units 3, 6-9)
Random sampling or random assignment is the first half of every independence check. The data collection design from Unit 3 is what earns you the right to do inference later, which is why FRQs love asking about it.
Dependent Samples (Unit 7)
Matched pairs data looks like a violation of independence, but it isn't if you handle it right. You take the difference within each pair first, and then those differences form one sample where independence applies between pairs, not within them.
Confounding Variables (Unit 3)
Both are design problems you can't fix with a bigger sample. Confounding wrecks your ability to claim causation, while dependence wrecks your standard errors. Spotting either one in a scenario is a classic MCQ skill.
Independence shows up in two main ways. In multiple choice, you'll get a scenario and have to spot whether independence holds or is violated. A favorite trap is time-series data, like a researcher recording temperature and ice cream sales for 30 consecutive days. Consecutive days aren't independent (today's sales relate to yesterday's), so the independence condition for the slope test is the one most likely violated. In free response, condition-checking is a standard scored component of inference questions. Released FRQs like 2021 Q4, 2023 Q4, and 2024 Q1 all required setting up inference procedures where you verify conditions before computing anything. To earn credit, name the condition, state how the data were collected (random sample or randomized experiment), and explicitly check the 10% condition with numbers when sampling without replacement. Writing "conditions are met" without showing the check earns nothing.
These aren't the same thing, even though they travel together. The Independence Condition is the actual requirement (observations don't affect each other). The 10% condition is just one check within it, used only when you sample without replacement. A complete independence check on an FRQ has two parts. First, confirm random sampling or random assignment. Second, verify n ≤ 10% N if sampling without replacement. Citing the 10% condition alone, without mentioning randomness, is an incomplete answer.
The Independence Condition requires that one observation does not influence or relate to another, and it must be checked before any inference procedure on the AP exam.
You verify independence in two steps, first confirming the data came from a random sample or randomized experiment, then checking the 10% condition (n ≤ 10% N) when sampling without replacement.
For two-sample procedures like comparing proportions, you need two independent random samples and the 10% condition checked separately for each group (n₁ ≤ 10% N₁ and n₂ ≤ 10% N₂).
Matched pairs data doesn't violate independence as long as you analyze the differences within pairs as a single sample.
Data collected over consecutive time periods, like daily sales for 30 days in a row, is a classic independence violation because each observation is linked to the one before it.
On FRQs, you must explicitly state and verify the independence check with the scenario's actual numbers; just writing "conditions are met" earns no credit.
It's the requirement that observations in your sample don't influence each other, which every confidence interval and significance test depends on. You check it by confirming random sampling or random assignment, plus the 10% condition when sampling without replacement.
No. The 10% condition is just one part of checking independence, used only when sampling without replacement. A full independence check also requires that the data came from a random sample or randomized experiment.
No. The two values within a pair are related on purpose, but you analyze the differences, and those differences form one sample where each pair is independent of the other pairs. That's exactly how the CED frames matched pairs in Topic 7.4.
The t-test for a slope in Unit 9 assumes the data points are independent, just like tests for means and proportions. Time-ordered data is the usual violation, like measuring temperature and ice cream sales over 30 consecutive days, where one day's value is tied to the next.
State both parts explicitly with the problem's numbers. For example, write that the sample was randomly selected, then show n ≤ 10% N (like 300 adults ≤ 10% of all adults in the city). Vague claims that conditions hold don't earn the point.