Ed230B/C

Partial and Semipartial Correlation

Experimental Control

  • Controling variances by using equal groups.
  • Randomly assigning subjects to groups.
  • Conditions for all groups identical except for independent variable.

    Statistical Control

  • Control variance by removing unwanted variance from other variables.
  • control by partialing.

    Partial Correlation

  • r12.3 is the correlation between variables 1 and 2 with variable 3 removed from both variables. To illustrate this, run separate regressions using X3 as the independent variable and X1 and X2 as dependent variables. Next, compute residuals for regression...

    Venn Diagram of Partial Correlation

    More Partial Correlation

    Example

  • Let r12 = 0.7;   r13 = 0.6;   r23 = 0.9.

    Using Multiple Correlations

  • Thus, squared partial correlations represent the ratio of incremental variance to the residual variance.

    Example

  • Let R21.23 = .4947 and R21.3 = .62 = .36 (from the above example)

    Higher Order Partial Correlation

    and so on...

    Suppressor Variable

  • A special case when the partial correlation is larger than the zero-order correlation.
  • Zero or close to 0 correlation with the dependent variable.
  • Correlated with one or more independent variables.
  • Serves to suppress or control irrelevant variance.

    Example

  • Let r12 = 0.3;   r13 = 0.0;   r23 = 0.5.

  • Let r212 = 0.09;   r212.3 = 0.12;

  • Note: r212.3 is greater than r212 even though r13 = 0.
  • Standardized regressions Coefficients: β2 = .4 and β3 = -.2
  • Note: suppressor variable receives a negative coefficient.

    Causal Relationships

  • Partial correlation as a control method must be predicated on a sound theoretical framework.
  • Routine presentation of all higher-order partial correlations is a sign that theory explaining the relationship among the variables is missing (Gordon, 1968).
  • With only three variables there are many possible causal models.

    Measurement Error

  • Measurement error leads to biased estimates of zero-order and partial correlations.
  • Measurement error attenuates zero-order correlations.

    Correction for Attenuation

    Example

  • When r12 = .7; r11 = r22 = .8

    Correction for Attenuation in Partial Correlation

  • Partial correlation when correcting for unreliability in X3 only.

    Example

  • When r12 = .7; r13 = .5; r23 = .6; r33 = .8;

    and r12.3 = .58

    Another Example

  • When r12 = .7; r13 = .8; r23 = .7; r33 = .8;

    and r12.3 = .33

    Correction for Attenuation in Partial Correlation

  • Partial correlation when correcting for unreliability in all measures.

    Example

  • When r12 = .7; r13 = .5; r23 = .6; r11 = r22 = r33 = .8;

    and r12.3 = .58

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    UCLA Department of Education

    Phil Ender, 28Jan98