Results

Data from Massar et al. (2012). The authors investigated whether age differences in women's tendency to gossip are mediated by their mate value.


Baron and Kenny suggested that mediation is tested through three regression analyses:

  1. A linear model predicting the outcome (gossip) from the predictor variable (age).
  2. A linear model predicting the mediator (mate_value) from the predictor variable (age).
  3. A linear model predicting the outcome (gossip) from both the predictor variable (age) and the mediator (mate_value).


These analyses test the four conditions of mediation: (1) the predictor variable (age) must significantly predict the outcome variable (gossip) in model 1; (2) the predictor variable (age) must significantly predict the mediator (mate_value) in model 2; (3) the mediator (mate_value) must significantly predict the outcome (gossip) variable in model 3; and (4) the predictor variable (age) must predict the outcome variable (gossip) less strongly in model 3 than in model 1.

Baron and Kenny's method: Regression 1

Regression 1: Predicting gossip from age

The analysis indicates that the first condition of mediation was met, in that participant age was a significant predictor of the tendency to gossip, t(80) = −2.59, p = .011.

Model Summary - gossip
Model R R² Adjusted R² RMSE R² Change F Change df1 df2 p
M₀ 0.000 0.000 0.000 0.989 0.000 0 81  
M₁ 0.279 0.078 0.066 0.956 0.078 6.727 1 80 0.011
Note.  M₁ includes age
ANOVA
Model   Sum of Squares df Mean Square F p
M₁ Regression 6.143 1 6.143 6.727 0.011
  Residual 73.060 80 0.913  
  Total 79.203 81  
Note.  M₁ includes age
Note.  The intercept model is omitted, as no meaningful information can be shown.
Coefficients
95% CI
Collinearity Statistics
Model   Unstandardized Standard Error Standardized t p Lower Upper Tolerance VIF
M₀ (Intercept) 2.219 0.109 20.322 < .001 2.002 2.436  
M₁ (Intercept) 2.898 0.282 10.265 < .001 2.336 3.460  
  age -0.022 0.009 -0.279 -2.594 0.011 -0.039 -0.005 1.000 1.000


Baron and Kenny's method: Regression 2

Regression 2: Predicting mate_value from age

The analysis shows that the second condition of mediation was met: participant age was a significant predictor of mate value, t(79) = −3.67, p < .001.

Model Summary - mate_value
Model R R² Adjusted R² RMSE R² Change F Change df1 df2 p
M₀ 0.000 0.000 0.000 0.854 0.000 0 80  
M₁ 0.381 0.146 0.135 0.794 0.146 13.452 1 79 < .001
Note.  M₁ includes age
ANOVA
Model   Sum of Squares df Mean Square F p
M₁ Regression 8.491 1 8.491 13.452 < .001
  Residual 49.863 79 0.631  
  Total 58.354 80  
Note.  M₁ includes age
Note.  The intercept model is omitted, as no meaningful information can be shown.
Coefficients
95% CI
Collinearity Statistics
Model   Unstandardized Standard Error Standardized t p Lower Upper Tolerance VIF
M₀ (Intercept) 2.993 0.095 31.541 < .001 2.804 3.182  
M₁ (Intercept) 3.798 0.237 16.056 < .001 3.327 4.269  
  age -0.027 0.007 -0.381 -3.668 < .001 -0.041 -0.012 1.000 1.000


Baron and Kenny's method: Regression 3

Regression 3: Predicting gossip from age and mate_value

The analysis shows that the third condition of mediation has been met: mate value significantly predicted the tendency to gossip while adjusting for participant age, t(78) = 3.59, p < .001.

The fourth condition of mediation has also been met: the standardized coefficient between participant age and tendency to gossip decreased substantially when adjusting for mate value, in fact it is no longer significant, t(78) = −1.28, p = .206. Therefore, we can conclude that the authors' prediction is supported, and the relationship between participant age and tendency to gossip is mediated by mate value.


Diagram of the mediation model, taken from Massar et al. (2011):

Model Summary - gossip
Model R R² Adjusted R² RMSE R² Change F Change df1 df2 p
M₀ 0.000 0.000 0.000 0.995 0.000 0 80  
M₁ 0.461 0.213 0.193 0.894 0.213 10.547 2 78 < .001
Note.  M₁ includes age, mate_value
ANOVA
Model   Sum of Squares df Mean Square F p
M₁ Regression 16.849 2 8.425 10.547 < .001
  Residual 62.306 78 0.799  
  Total 79.155 80  
Note.  M₁ includes age, mate_value
Note.  The intercept model is omitted, as no meaningful information can be shown.
Coefficients
95% CI
Collinearity Statistics
Model   Unstandardized Standard Error Standardized t p Lower Upper Tolerance VIF
M₀ (Intercept) 2.216 0.111 20.054 < .001 1.996 2.436  
M₁ (Intercept) 1.196 0.549 2.177 0.032 0.102 2.290  
  age -0.011 0.009 -0.139 -1.275 0.206 -0.029 0.006 0.854 1.170
  mate_value 0.455 0.127 0.390 3.592 < .001 0.203 0.707 0.854 1.170


Classical Process Model

The first output of interest is the table with the R2 value that tells us that the model explains 21.3% of the variance in tendency to gossip and 14.6% in mate value (the model summary table is not so interesting when we are only estimating a single model and don't do model comparison). Next is a visualization of the model, including the path coefficients.

Model summary
  AIC BIC Log-likelihood n df
Model 1 1045.633 1060.000 -516.816 81 0
R-squared
R²
  Model 1
gossip 0.213
mate_value 0.146

Path plots

Model 1

Statistical path plot

Parameter estimates

The first table with parameter estimates shows the path coefficients that are also presented in the graphical model above, and includes some additional statistics for hypothesis testing and parameter estimation. The output shows that age significantly predicts mate value, b = −0.027, z = −3.714, p < .001. The fact that the b is negative tells us that the relationship is negative: as age increases, mate value declines (and vice versa).


The output also shows the results of the model predicting tendency to gossip from both age and mate value. We can see that while age does not significantly predict tendency to gossip with mate value in the model, b = −0.011, z = −1.3, p = .194, mate value does significantly predict tendency to gossip, b = 0.455, z = 3.66, p < .001. The negative b for age tells us that as age increases, tendency to gossip declines (and vice versa), but the positive b for mate value indicates that as mate value increases, tendency to gossip increases also. These relationships are in the predicted direction.

Important : Parameter estimates can only be interpreted as causal effects if all confounding effects are accounted for and if the causal effect directions are correctly specified.

Model 1

Path coefficients
95% Confidence Interval
      Estimate Std. Error z-value p Lower Upper
age → gossip -0.011 0.009 -1.300 0.194 -0.028 0.006
mate_value → gossip 0.455 0.124 3.661 < .001 0.211 0.698
age → mate_value -0.027 0.007 -3.714 < .001 -0.041 -0.013
Direct and indirect effects
95% Confidence Interval
          Estimate Std. Error z-value p Lower Upper
age → gossip -0.011 0.009 -1.300 0.194 -0.028 0.006
age → mate_value → gossip -0.012 0.005 -2.607 0.009 -0.021 -0.003

The second table in the output below displays the results for the indirect effect of age on gossip (i.e., the effect via mate value), as well as the effect of age on gossip when mate value is included as a predictor (the direct effect). We’re given an estimate of this indirect effect (b = −0.012) as well as a standard error and confidence interval. Remember that the indirect effect is the product of the pathway from age to mate_value and the pathway from mate_value to gossip: 


As we have seen many times before, 95% confidence intervals contain the true value of a parameter in 95% of samples. Therefore, we tend to assume that our sample isn’t one of the 5% that does not contain the true value and use them to infer the population value of an effect. In this case, assuming our sample is one of the 95% that ‘hits’ the true value, we know that the true b-value for the indirect effect falls between −0.028 and −0.006. This range does not include zero (although both values are not much smaller than zero), and remember that b = 0 would mean ‘no effect whatsoever’; therefore, the fact that the confidence interval does not contain zero means that there is likely to be a genuine indirect effect. Put another way, mate value is a mediator of the relationship between age and tendency to gossip.

Total effects
95% Confidence Interval
        Estimate Std. Error z-value p Lower Upper
Total age → gossip -0.023 0.009 -2.702 0.007 -0.040 -0.006
Total indirect age → gossip -0.012 0.005 -2.607 0.009 -0.021 -0.003

The third table in the output below shows the total effect of age on tendency to gossip (outcome). The total effect is the effect of the predictor on the outcome when the mediator is not present in the model. When mate value is not in the model, age significantly predicts tendency to gossip, b = −0.02, t = −2.7, p = .007. Therefore, when mate value is not included in the model, age has a significant negative relationship with gossip (as shown by the negative b value).