Page 8 - FINAL CFA II SLIDES JUNE 2019 DAY 2

LOS 7.b: Describe limitations to correlation analysis. MODULE 7.1: COVARIANCE & CORRELATION

1. Outliers: A few extreme values for sample observations can suggest a significant relationship exists when, in fact, there is
none, or that there is no relationship when, in fact, there is a relationship.
2. Spurious Correlation (Correlation ≠ causation (not necessarily)! Pure chance factors!
3. Nonlinear Relationships: Correlation measures linearity in the form , say, Y = 6 – 3X. However, 2 variables could have a
nonlinear yet a zero correlation; thus correlation analysis fails to capture strong nonlinear relationships!

LOS 7.c: Formulate a test of the hypothesis that the population correlation coefficient, r, equals zero and determine
whether the hypothesis is rejected at a given level of significance.

With the exception r extremes close to ±1.0, we cannot assess r strength without a statistical test of significance.

Assuming both populations are normally distributed, the test This is a 2TT
statistic is computed using the sample correlation, r, with n – 2 df: (Why?)

To be provided! e.g. @ 95%

Decision rule:
Reject H if
0
+t critical < t; OR t < –t critical