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Statistics in psychology help researchers describe data (descriptive stats) and draw conclusions about populations from samples (inferential stats). This topic is high-yield on the AP exam—expect multiple-choice questions on definitions, FRQs asking you to interpret graphs or p-values, and experimental design questions. Real-world example: In the 1950s, psychologist Solomon Asch used statistics to show that 75% of participants conformed to an obviously wrong group answer at least once in his famous line-judgment experiments. Without stats, he couldn’t have proven conformity was a real effect, not just random guessing.
Example: If a class’s test scores are [80, 85, 90, 95, 100], the mean (average) is 90.
Mean (? or x?): The average of a dataset. Formula: Mean = (Sum of all scores) / (Number of scores)
Example: For [3, 5, 7], mean = (3+5+7)/3 = 5.
Median: The middle number when data is ordered. If even # of scores, average the two middle numbers.
Example: For [3, 5, 7], median = 5. For [3, 5, 7, 9], median = (5+7)/2 = 6.
Mode: The most frequent score in a dataset.
Example: In [2, 2, 3, 4], mode = 2.
Range: The difference between the highest and lowest scores.
Example: For [10, 20, 30], range = 30 – 10 = 20.
Standard Deviation (? or s): Measures how spread out scores are from the mean. Low SD = data clustered close to mean; high SD = data spread out.
Formula (for sample): s = ?[?(x – x?)² / (n – 1)]
Normal Distribution (Bell Curve): A symmetric, bell-shaped curve where ~68% of data falls within 1 SD of the mean, ~95% within 2 SDs, ~99.7% within 3 SDs.
Example: IQ scores are normally distributed (mean = 100, SD = 15).
Inferential Statistics: Techniques that let researchers generalize from a sample to a population (e.g., t-tests, p-values).
Example: If a drug trial shows 60% of 100 patients improved, inferential stats help determine if this effect is real or due to chance.
Statistical Significance: A result is unlikely due to chance (usually p < 0.05).
Example: If p = 0.03, there’s a 3% chance the results are random.
p-value: The probability that results occurred by chance. Lower p = stronger evidence against the null hypothesis.
AP Exam Tip: p < 0.05 = statistically significant (reject null hypothesis).
Null Hypothesis (H?): The default assumption that there’s no effect (e.g., "The drug has no impact on memory").
Example: In a study on caffeine and alertness, H? = "Caffeine has no effect on alertness."
Alternative Hypothesis (H?): The researcher’s prediction (e.g., "The drug improves memory").
Example: H? = "Caffeine increases alertness."
Type I Error: False positive—rejecting H? when it’s true (e.g., saying a drug works when it doesn’t).
Example: Convicting an innocent person (H? = "not guilty").
Type II Error: False negative—failing to reject H? when it’s false (e.g., missing a real effect).
Dependent variable (DV): What’s measured (e.g., test scores).
Check descriptive stats:
Check standard deviation to see variability.
Determine if results are significant:
If p > 0.05, fail to reject H? (results may be due to chance).
Interpret the effect size (if given):
Example: A study with p = 0.01 and d = 0.7 means strong, significant results.
Watch for errors:
Correction: Descriptive stats summarize data (e.g., mean, SD); inferential stats make predictions (e.g., p-values, t-tests).
Mistake: Thinking p = 0.05 means a 95% chance the hypothesis is true.
Correction: p = 0.05 means 5% chance the results are due to random variation—not proof of the hypothesis!
Mistake: Ignoring effect size and only looking at p-values.
Correction: A tiny effect (e.g., d = 0.1) can be "significant" (p < 0.05) if the sample is huge—but it may not matter in real life.
Mistake: Assuming correlation = causation because of a low p-value.
Correction: Even if p < 0.01, a study can’t prove causation without experimental control (e.g., random assignment).
Mistake: Misinterpreting standard deviation as "average distance from the mean."
What’s Frequently Tested? - Multiple-choice: Definitions (e.g., "What is standard deviation?"), interpreting p-values, identifying Type I/II errors. - FRQs: Often ask you to interpret a graph (e.g., "Is the difference between Group A and Group B statistically significant?") or design an experiment (e.g., "How would you test if caffeine improves memory?"). - Tricky Distinction: Statistical significance-practical significance. A study can have p < 0.001 but a tiny effect size (e.g., a drug that "works" but only improves scores by 1%).
Common Traps: - Confusing mean, median, and mode (e.g., picking median when mean is asked). - Assuming p < 0.05 means "the hypothesis is proven" (it just means the results aren’t random). - Forgetting that correlation-causation (even with a low p-value).
FRQ Tip: If asked to evaluate a study’s statistical validity, mention:1. Sample size (small = less reliable).2. p-value (is it < 0.05?).3. Effect size (is the effect meaningful?).4. Potential confounds (e.g., placebo effect, experimenter bias).
A researcher finds that students who study with music score 5 points higher on a test than those who study in silence (p = 0.04). What does this p-value mean? A) There is a 4% chance the results are due to the music. B) There is a 4% chance the results are due to random variation. C) The results are 96% likely to be true. D) The effect size is 0.04.
Answer: B Explanation: A p-value of 0.04 means there’s a 4% probability the results occurred by chance (not that the hypothesis is 96% true).*
A psychologist tests whether a new therapy reduces anxiety. After 6 weeks, the therapy group’s mean anxiety score is 45 (SD = 5), and the control group’s mean is 50 (SD = 6). The p-value is 0.02. a) Is the difference statistically significant? Explain. b) What is one potential Type I error in this study?
Answer: a) Yes, the difference is statistically significant because p = 0.02 < 0.05, meaning there’s only a 2% chance the results are due to random variation. b) A Type I error would be concluding the therapy works when it actually has no effect (false positive).
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