Overview:

1. Type 1 error rates are inaccurate and power is low for most tests of mediation
2. A new method to test for mediation effects has more accurate type 1 error rates and power
3. The new method is based on the distribution of Products of Random Variables
4. The statistical background and a computer program to compute cumulative probabilities is described

3 Methods to Test for Significance of the Mediated Effect

1. Causal Step Methods

• Judd & Kenny (1981)
• Baron & Kenny (1986)

• Variance of 
• Variance of the raw minus partial correlation

• Variance of - first order
• Variance of - second order
• Distribution of
• Empirical distribution of

(Craig, 1936, Springer, 1978, Aroian & colleagues, 1947, 1977)

1. Normal distribution is well known
2. Product of two regression coefficients,, is the product of two independent random normal variables
3. Distribution is complicated and not normal
4. When, the distribution has kurtosis of 6. This is why tests for mediated effects have low power and incorrect type 1 error rates.

skewness and kurtosis (mean and variance are similar)
 

		skew	empirical skew	kurtosis	empirical kurtosis
0	0	0	-.16	6	6.97
small	small	1.15	1.15	3.50	3.32

Simulation study of comparison of methods:

Causal step - low Type 1 error

Diff. In Coefficient - low Type 1 error

Product of Coefficient - and Empirical Distribution - good type 1 error and pretty good power at sample size of as low as 50 and 100

Conclusions:

1. The new method directly addresses the distribution of the product which is the mediated effect estimate
2. Accurate type 1 error rates and more statistical power than the other methods
3. Can be used to obtain more accurate asymmetric confidence limits
4. It can be extended for more complicated mediational tests
5. Mathematica program has been developed