Ψlogical
Testing

Chapter 3…
…Correlation
& Regression

Office keeping 💼

  • Not tested on formulas
    • Concepts are fair game
  • Project:
    • Citi training
    • Share 2-3 empirical articles
      (intragroup)
    • Discuss construct
      (intragroup)

Correlation

  • index of association between 2 variables
  • can be either descriptive or inferential
    • look for p-value
  • reflects both magnitude and valence of association
    • 0 \(\rightarrow\) 1
    • positive (+) or negative (-)

Visualizing association

Scatterplot – visual representation of association
typically 2 variables but can be 3

Scatterplot…

aka Scatter Diagram typically focused on bivariate distribution

  • Histograms & Polygons focus on univariate distribution
    • simply refers to:
      • one thing at a time, or
      • two things simultaneously
  • Sometimes individual histograms also included in visual

Forms of association

Scatterplot and correlation

Let’s construct one!

Regression

Line of best fit through scatterplot

  • Useful for prediction
  • Can have one or more predictor variables
    • 1 = simple regression
    • \(>\) 1 = multiple regression








Warning

Figure 3.4 has an error (p. 68)

Explore Simple Regression

Different datasets:

Try to beat the statistic:

Predicted scores

  • Typically designated \(\hat{Y}\) or \(Y^{\prime}\)
    • Predicted “Criterion” score
    • “Criterion” = DV
  • Select predictor score, then use line of best fit to identify likely \(Y^{\prime}\)

Other indices of association…

…exist as alternatives to the “typical” correlation coefficient (Pearson’s r)

  • Based primarily on
    • level of measurement
      • NOIR
    • end-purpose

Cross-validation

Always a good idea – check to see if association / prediction still good with different sample or scenario

  • Shrinkage – decrease in predictive accuracy when regression estimated in Sample A is later applied to Sample B

Factor analysis

Important data-reduction analytical procedure for measurement specialists

  • Provides us with statistical justification to group item responses into aggregate scale scores
  • Helps confirm:
    • appropriate number of scale scores
    • items to retain or delete from larger measure