Introducing multivariate statistics

PSY 383

• What analyses map onto the following hypotheses?
  • P300 amplitude will be larger in the intervention group than in the control group
  • The effects of our intervention on belonging will be stronger among those with greater sense of purpose
  • Students' ratings of well-being at the end of the semester will be higher than their ratings of well-being at the beginning of the semester
  • Participants who perceive authenticity in hookup culture will report more relationship satisfaction, even after controlling for overall life satisfaction
  • People who rate ChatGPT as easy to use are more likely to rate it as useful

Think about your hypotheses

• Some hypotheses require multivariate statistics. These include hypotheses involving...
  • Multiple dependent variables
  • Multiple relationships among different variables
  • Dimensions underlying the variables in your dataset
  • Clusters of people in your dataset
• Some hypotheses require statistics that aren't multivariate, per se, but you haven't learned about them yet. This includes hypotheses involving...
  • Categorical dependent variables
  • "Nested" observations
    • We'll get into what this means later

Other hypotheses you can test

• Example: We have multiple measures of academic and social functioning among college students - e.g., belonging, academic self-concept, school connectedness. We hypothesize that all of these, in the aggregate, will be higher among those in our intervention group than those in a control group.
• Analysis: MANOVA
  • We typically are not going to use MANOVA, because we will often have hypotheses about how these variables relate to one another. But you will see them sometimes and you should know how to interpret them!

Multiple dependent variables

• Example: We predict that students who perceive authenticity in hookup culture will choose partners whose values are similar to their own and who are high in honesty. This partner choice will lead to high relationship satisfaction.
• Analysis: Structural equation modeling

Relationships among variables

• Example: We administer 10 different items about well-being to a group of college students. We find that their responses reflect 3 broad dimensions: academic confidence, social connectedness, and sense of purpose
• Analysis: Factor analysis (exploratory or confirmatory)

Dimensions underlying your variables

• Example: We administer 10 different items about ChatGPT to our participants. We predict that there will be 3 groups of people in our dataset: people who are generally wary of ChatGPT (40%), people who are generally excited about ChatGPT (40%), and people who feel excited about ChatGPT's usefulness but wary of generative AI's potential misuse (20%)
• Analysis: Mixture modeling

Clusters of people in your dataset

• Example: We are interested in whether ADHD diagnosis is predicted by P300 amplitude, even after controlling for a variety of other physiological variables.
• Analysis: Logistic regression

Categorical dependent variables

• Example: We predict that the relationship between daily ratins of well-being and belonging will strengthen over the course of the semester
• Analysis: Multilevel modeling

Nested dependent variables

• Example: We predict that the relationship between sense of purpose and belonging will be stronger among students in schools with higher overall levels of achievement.
• Analysis: Multilevel modeling

Nested dependent variables