Direction of association describes whether two quantitative variables tend to increase together (positive association) or move in opposite directions (negative association); in AP Stats, it's shown by the sign of the correlation coefficient r and is one of the four things you describe in any scatterplot.
Direction of association answers one simple question about a scatterplot. As x goes up, does y tend to go up too, or does it tend to go down? If both variables rise together (like bullfrog length and mass), the association is positive. If one rises while the other falls (like resting heart rate and life expectancy), the association is negative.
In Topic 2.5, direction gets baked into a single number. The correlation coefficient r gives both the direction and the strength of a linear association between two quantitative variables. The sign of r is the direction. A positive r means a positive association, a negative r means a negative association, and r = 0 means no linear association at all. Direction is also unit-free and symmetric, so swapping which variable goes on the x-axis or converting years to months changes nothing about the sign of r.
Direction lives in Unit 2 (Exploring Two-Variable Data), specifically Topic 2.5, and supports learning objectives 2.5.A (determine the correlation for a linear relationship) and 2.5.B (interpret the correlation). The CED is explicit that r 'gives the direction and quantifies the strength' of a linear association, so direction is literally half of what r tells you. Beyond Topic 2.5, direction is the first word out of your mouth whenever you describe a scatterplot on an FRQ. The standard checklist is direction, form, strength, and unusual features, all in context. Get the direction wrong and the rest of your description falls apart, because a negative association means something completely different in the real-world context than a positive one.
Keep studying AP® Statistics Unit 5
Correlation Coefficient (Unit 2)
Direction is the sign of r, and that's the whole relationship. An r of -0.60 and an r of +0.60 describe equally strong linear associations pointing in opposite directions. Reading the sign before the size keeps your interpretation honest.
Strength of Association (Unit 2)
Direction and strength are the two separate pieces of information packed into r. Direction is the sign, strength is the distance from 0. Treat them as independent questions. A scatterplot can be strongly negative, weakly positive, or anything in between.
Z-scores (Unit 1)
The formula for r multiplies the z-score of each x by the z-score of each y. When points sit mostly in the 'both above average' or 'both below average' quadrants, those products are positive and r comes out positive. The direction of association is literally the dominant sign of these z-score products.
Mean (Unit 1)
Direction is really about behavior relative to the means. Positive association means above-average x values tend to pair with above-average y values. Picture lines drawn at x̄ and ȳ splitting the scatterplot into four quadrants, and direction tells you which diagonal the points favor.
Multiple-choice questions love testing what direction does NOT depend on. You'll see stems like a study with r = -0.60 asking what happens if the axes are swapped (nothing, r stays -0.60) or a question converting life expectancy from years to months (r = 0.85 stays 0.85, because correlation is unit-free). The trap answers assume direction or magnitude changes with units or axis choice. On FRQs, direction shows up in scatterplot descriptions. The 2022 FRQ on bullfrog length and mass and the 2023 FRQ on tule elk weight both involved describing a relationship between two quantitative variables, and full credit requires naming the direction (positive or negative) along with form and strength, in context. One more scoring point to remember from 2.5.B: never claim that a positive or negative association proves one variable causes the other. Correlation does not imply causation.
Direction is the sign of r; strength is how close |r| is to 1. r = -0.95 is a strong negative association, while r = +0.20 is a weak positive one. The classic mistake is reading r = -0.95 as 'weaker' than r = +0.20 because it's a smaller number. Compare absolute values for strength, then report the sign separately as direction.
Direction of association is positive when both variables tend to increase together and negative when one increases as the other decreases.
The sign of the correlation coefficient r tells you the direction, while the distance of r from 0 tells you the strength.
Direction doesn't change if you swap which variable is on the x-axis or convert units, because r is unit-free and symmetric.
An r of 0 means there is no linear association, not necessarily no relationship at all (the pattern could be curved).
When describing a scatterplot on an FRQ, state the direction, form, strength, and any unusual features, all in the context of the variables.
A clear positive or negative direction never proves causation; correlation does not imply causation.
It's whether two quantitative variables move together (positive) or in opposite directions (negative). In Topic 2.5, the sign of the correlation coefficient r tells you the direction of a linear association.
No. Correlation is symmetric, so if r = -0.60 with variable A on the x-axis, r is still -0.60 with the axes swapped. Direction belongs to the relationship, not to which variable you put where.
Direction is the sign of r (positive or negative), while strength is how close |r| is to 1. An r of -0.85 has a negative direction but is stronger than an r of +0.40.
Not necessarily. r = 0 only means there's no linear association. A strong curved pattern (like a parabola) can produce an r near 0 even though the variables are clearly related.
No. Because r is unit-free, multiplying every value of a variable by a positive constant (like 12 to convert years to months) leaves r exactly the same, including its sign. This shows up regularly as a multiple-choice trap.
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