AP® Psychology

Statistics you must know

The exam gives you no formula sheet and no calculator. These are the statistics it asks you to work out by hand or read from a study, in our own words: what each means, when to use it, and the trap that costs points.

Three habits that save points

Interpret, do not define. "The mean is the average" earns nothing; "the group that slept 8 hours recalled 5 more words on average" does.
Name the direction. Say which group was higher, or whether r is positive or negative, and what that means for these participants.
Correlation is not causation. Only an experiment with random assignment supports a cause-and-effect claim.

Central tendency

Formula and a worked line	What it is and when to use it	The trap	Learn it in
$\bar{x}$ $= \frac{\text{sum of the scores}}{n}$ Worked: $\frac{4 + 6 + 7 + 7 + 11}{5}$ $= 7$	The mean: the arithmetic average. Describing a typical score when there are no extreme scores.	One extreme score (an outlier) pulls the mean toward it; the median does not move much.	Research skills you need Descriptive StatisticsPractice it: Stats lab
$\text{median}$ $= \text{the middle score in order}$ Worked: $2, 3, \mathbf{5}, 8, 20 = 5$	The median: half the scores are below it, half above. A typical score when the distribution is skewed (incomes, reaction times).	Put the scores in order first; with an even count, average the two middle scores.	Research skills you need Descriptive StatisticsPractice it: Stats lab
$\text{mode}$ $= \text{the most frequent score}$ Worked: $3, 4, 4, 4, 6, 9 = 4$	The mode: the score that occurs most often. Categories (favorite color) or the peak of a distribution.	A distribution can have two modes (bimodal); the mode is a score, not how often it occurs.	Research skills you need Descriptive StatisticsPractice it: Stats lab

Variation

Formula and a worked line	What it is and when to use it	The trap	Learn it in
$\text{range} = \text{highest} - \text{lowest}$ Worked: $20 - 2 = 18$	The range: the distance from the lowest score to the highest. A quick sense of spread.	One outlier makes the range huge; it uses only two scores.	Research skills you need Descriptive StatisticsPractice it: Stats lab
$\text{SD}$ $= \sqrt{\frac{\text{sum of }(x - \bar{x})^2}{n}}$ Worked: $\sqrt{\frac{9 + 1 + 1 + 9}{4}}$ $= 2.24$	The standard deviation: the typical distance of scores from the mean. Comparing how spread out two groups are; reading the normal curve.	A larger SD means more spread, not higher scores. The exam asks you to read and interpret it, not to compute it from a long list.	Research skills you need Descriptive StatisticsPractice it: Stats lab

The normal curve and percentiles

Formula and a worked line	What it is and when to use it	The trap	Learn it in
$z = \frac{x - \bar{x}}{\text{SD}}$ Worked: $\frac{130 - 100}{15} = 2$	A z score: how many standard deviations a score is from the mean. Comparing scores from different tests, or placing a score on the normal curve.	Below the mean, z is negative. Subtract the mean first, then divide by the SD.	Research skills you need The Normal Curve and PercentilesPractice it: Stats lab
$68\% \text{ within } 1\text{ SD},$ $\; 95\% \text{ within } 2,$ $\; 99.7\% \text{ within } 3$ Worked: $34 + 34 + 13.5 + 13.5$ $= 95\,\%$	The 68-95-99.7 rule for a normal distribution. The share of people between two scores, or above or below one.	Half of 68% (34%) lies on each side of the mean; the bands are 34, 13.5, 2.35 and 0.15 percent.	Research skills you need The Normal Curve and PercentilesPractice it: Stats lab
$\text{percentile rank}$ $= \text{percent of scores below}$ Worked: $50 + 34 = 84$	A percentile rank: the percent of a group who scored lower. Interpreting a score: the 84th percentile beats 84% of the group.	A percentile is not a percent correct. One SD above the mean is about the 84th percentile (50 + 34).	Research skills you need The Normal Curve and PercentilesPractice it: Stats lab

Correlation and inference

Formula and a worked line	What it is and when to use it	The trap	Learn it in
$-1 \le r \le +1$ Worked: $r \text{ for } (1,2),(2,4),(3,6)$ $= 1$	The correlation coefficient r: the direction (sign) and strength (closeness to 1 or -1) of a straight-line relationship. Describing a scatterplot or a correlational study.	Correlation is not causation: a third variable may explain both. A negative r is as strong as a positive one of the same size.	Research skills you need Correlation and ScatterplotsPractice it: Stats lab
$p < .05$ Worked: $\text{mean}_1 - \text{mean}_2$ $= 14 - 9$ $= 5\,\text{points}$	Statistical significance: a difference this large would rarely happen by chance alone if the variables were unrelated. Reading an experiment's results: is the difference between groups likely real?	Significant does not mean large or important; effect size says how big the difference is.	Research skills you need Statistical Significance and Effect SizePractice it: Stats lab, Article analysis studio

Ideas to read off a study

Skew. In a positively skewed distribution (a long tail to the right) the mean is pulled above the median; in a negatively skewed one, below it. Descriptive Statistics
Scatterplots. Points rising left to right show a positive correlation; falling, a negative one; a round cloud, little or none. Correlation and Scatterplots
Effect size. How large a difference or relationship is, separate from whether it is statistically significant. A big sample can make a tiny effect significant. Statistical Significance and Effect Size
Read the graph first. On the article analysis question, the statistic part asks what a difference between groups means for these participants. Name the groups, the direction and what it shows. Statistical Significance and Effect Size

On exam day

No calculator. The AP® Psychology exam allows no calculator. Every number it asks for (a mean, a median, a range, a share under the normal curve) can be worked out by hand.
No formula sheet. Nothing on this page is printed in Bluebook: know what each statistic means and how to read it from a table or graph.

Practice with it

Free unit practice tests · Statistics flashcards · Research terms flashcards · Free notes for every topic · Full practice exams