Statistical Analysis: Controlling for Confounding Factors and Interactions, Slides of Research Methodology

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Analyzing Data

Multiple Variables

Basic Directions

• Review page 180 for basic directions on which

way to proceed with your analysis

• Provides statistical decision steps based

upon the level of measurement for your

independent and dependent variables

Partialling

• When a control variable is introduced, that is deemed first-order partialling - Should you add a second, 2nd^ order, and so on
• The original bivariate relationship is called the zero-order relationship
• Good for replicating patterns
• Can use minitab stat > tables and put in multiple variables of interest - Don’t use too many – keep it clean

Spurious Relationships

• If you introduce a third variable (a control)

and the relationship that existed in the

bivariate setting is now non-significant or even

less strong… then, the original relationship is

spurious

• Consider the ice cream and murder example

Suppressing Relationships

• If there is no relationship or a very weak one, introduce control variable to see if the ‘weak’ relationship continues - Could be that the variables involved are suppressor variables
• Within this structure you can also identify the

intervening variables: the one that was keeping the original relationship weak

Partial Correlations

• When a correlation exists between two variables, X and Y, the correlation may be explained by a third variable that is correlated with both X and Y.
• A partial correlation is used to control for the effect of a third variable when examining the correlation between X and Y.
• If the correlation between X and Y is reduced, the third variable is responsible for the effect.

Two-Way ANOVA

• The effects
  • Treatment Effect: a difference in population means
  • Main Effect: a difference in population means for a factor collapsed over the levels of all other factors in the design
  • Interaction: occurs when the effect on one factor is not the same at the levels of another
• Select: Stat > ANOVA > Two-Way ANOVA

Multiple R

• Multiple correlation finds the correlation coefficient (r) for every pair of variables
• The multiple correlation coefficient, R, is the correlation coefficient between the observed values of Y and the predicted values of Y. - The value of R will always be positive and will take on a value between zero and one. - The direction of the multivariate relationship between the independent and dependent variables can be observed in the sign, positive or negative, of the regression weights.

Multiple Regression

• Multiple regression finds the linear equation

that best predicts the value of one of the

variables (the dependent variable) from the

others.

Multiple Regression

• Y = a + bX + cZ + e
• The coefficients (a, b, and c) are chosen

so that the sum of squared errors is

minimized.

• The estimation technique is then called least squares or ordinary least squares (OLS).

Multiple Regression

• The standard test of a specified regression

coefficient is to determine if the multiple correlation significantly declines when the predictor variable is removed from the equation and the other predictor variables remain.

• Test is given by the t or F next to the coefficient.