Statistics in Psychology

By the end of this lesson, you will be able to interpret descriptive and inferential statistics, explain what a p-value means in the context of psychological research, and identify appropriate statistical tests.

Descriptive Statistics

Measures of central tendency:

• Mean: arithmetic average; sensitive to outliers
• Median: middle value; resistant to outliers
• Mode: most frequent value; only option for nominal/categorical data

Measures of variability:

• Range: max − min; simple but affected by outliers
• Standard deviation: average distance from the mean; most useful
• Variance: standard deviation squared

Normal distribution: bell-shaped; mean = median = mode; 68% within 1 SD, 95% within 2 SDs, 99.7% within 3 SDs.

The z-Score

$$z = \frac{x - \mu}{\sigma}$$

Tells you how many standard deviations above or below the mean a score is.

Interpretation: "This score is 1.5 standard deviations above the mean."

Used to compare scores across different distributions (e.g., comparing SAT and ACT scores).

Inferential Statistics

The goal: draw conclusions about populations from sample data.

Statistical significance: a result is statistically significant if it is unlikely to have occurred by chance.

p-value: the probability of obtaining results at least as extreme as those observed, IF the null hypothesis is true. A small p-value (p < .05 is conventional) suggests the result is unlikely to be due to chance.

p < .05 does NOT mean:

• The effect is large or important
• The null hypothesis is false (only that we have evidence against it)
• We "proved" our hypothesis

Effect Size

Statistical significance tells you if an effect exists; effect size tells you how big it is.

Cohen's d: standardized measure of the difference between two group means.