psych analysis 13 - t test and ANOVAs

t test

• quantifies the strength and direction of a difference between 2 means

  • use when our IV (or predictor) is categorical and has two levels

• test statistic: t and or d (cohens d)

  • aka point estimate, effect size

• can be positive or negative (the t)

  • 0 = no difference between means

  • farther from 0 = greater differences between means

• interpretation t: p value, then look at means

• interpretation d: 0.2 = small, 0.5 = medium, 0.8 = hard

t test chat

Example: Researchers compare test scores for students who studied with music versus students who studied in silence.

1. Calculate the mean for each group.

2. Use a t-test to compare the means while accounting for variability and sample size.

3. Look at the p-value:

   • p < .05: Significant difference between the groups.

   • p ≥ .05: Not a statistically significant difference.

Remember: A t-test tells you whether the difference between two group means is statistically significant.

what if i have more than 2 IV conditions?

• use ANOVA test

• quantifies the strength of differences between 2+ means

  • use when IV (or predictor) is categorizal and has 2+ levels

• test statistic: f

  • aka point estimate, effect size

• can only be positive

  • 0= no difference between means

  • farther away from 0 = greater difference between means

• interpretation f: p value, then look at means

factorial designs

• IVs (multiple)

  • study with the joint effects of 2+ IVs on a DV

  • within, between, or both (mixed)

  • sometimes term “IV” is used loosly here to mean predictor

• why ?

  • >1IV

  • interactions

    • test limits

    • external validity

  • theory testing and building

factorial notation

number of numbers = number of IVs

• values = # of levels for each IV

continuous vs categorical

Continuous variable: A variable measured on a scale that can take many numerical values (e.g., height, weight, or time). (interval, ratio)

Categorical variable: A variable that places people or things into distinct groups (e.g., gender, eye color, or treatment group). (nominal, ordinal)