Statistics

Descriptive Statistics

Describe a set of data

Frequency Polygons

AKA: Bar graphs/histograms

y-axis = frequency

x-axis = what is being graphed

Measures of Central Tendency

Measures to mark the center of a distribution (mean, median, and mode)

Mean

Sum of all scores divided by number of scores

Median

Central score in the distribution when written in ascending or descending order

If odd number of scores, take the average of the two middle scores

Mode

Score that appears most frequently

Bimodal Distribution

A distribution with more than one mode

Skewed Distribution

An asymmetrical distribution

Positively Skewed

Change in mean is caused by low score(s)

Negatively Skewed

More low scores than high scores with mean change caused by aberrant lay high score(s)

Measures of Variability

Describe the diversity of the distribution

Range

Distance between the highest and lowest scores

Variance

The average squared distances from the mean)

Standard Deviation

The square root of the variance (average distance from mean)

Z-Scores

Measure distance of a score from the mean in units of standard deviation

Example: “Scores below the mean have negative z-scores, while scores above the mean have positive z-scores. For instance, if Clarence scored 72 on a test with a mean of 80 and a standard deviation of 8, Clarence’s z-score would be -1. If Maria scored 84 on that same test, her a-score would be +0.5.” (pg. 14 of Barron’s AP Psychology 2025 test)

Normal Curve

Theoretical bell-shaped curve for which the area under the curve lying between any two z-scores has been predetermined

Percentiles

Distance of a score from 0

Correlation

Measures the relationship between two variables

+: one predicts the other

-: one predicts the absence of the other

Correlation Coefficient

Strength of a correlation ranging from -1 to +1

Correlations may be graphed using a ___

Scatterplot

Regression Line

Line of best fit for a scatterplot. Points closer to falling on the straight line = stronger correlation

Descriptive Statistics

Summarize information about the sample studied

Inferential Statistics

Determine whether findings can be applied to the larger population

Sampling Error

Extent to which the sample differs from the population

Tests such as t-tests, chi-square tests, and ANOVAs yield a ___

p-value

p-value

probability that the difference between the groups is due to chance

Can be computed for any correlation coefficient

p-value cutoff for statistically significant results

0.05

Effect Size

Allow psychologists to quantify how large an effect is within a larger population

Statistically vs practically important

The most useful findings have __ p-values and __ effect sizes

Low, high

Replication Crisis

Studies are being replicated and yielding different results

Meta-analysis

Combines the results of many studies on the same topic in order to approximate an average effect

Proposing any academic research requires ___

Proposal to the ethics board or institutional review board (IRB) at the institution

Human participation should be ___ in research

Voluntary

Deception involved in human research must be kept to ___

a minimum 🤷‍♂

Only ___ can consent and minors can give ___

Adults, informed assent

Participants’ privacy must be ___

Protected

Activities that might cause long-term harm require __

Interpretation by the review board to see if risk is warranted

Debriefing

After the study, participants should be told the purpose of the study