<P> The distribution of the product term αβ is only normal at large sample sizes which means that at smaller sample sizes the p - value that is derived from the formula will not be an accurate estimate of the true p - value . This occurs because both α and β are assumed to be normally distributed, and the distribution of the product of two normally distributed variables is skewed, unless the means are much larger than the standard deviations . If the sample is large enough this will not be a problem, however determining when a sample is sufficiently large is somewhat subjective . </P> <P> In some situations it is possible that (τ--τ') ≠ (αβ). This occurs when the sample size is different in the models used to estimate the mediated effects . Suppose that the independent variable and the mediator are available from 200 cases, while the dependent variable is only available from 150 cases . This means that the α parameter is based on a regression model with 200 cases and the β parameter is based on a regression model with only 150 cases . Both τ and τ' are based on regression models with 150 cases . Different sample sizes and different participants means that (τ--τ') ≠ (αβ). The only time (τ--τ') = (αβ) is when exactly the same participants are used in each of the models testing the regression . </P> <P> One strategy to overcome the non-normality of the product of coefficients distribution is to compare the Sobel test statistic to the distribution of the product instead of to the normal distribution . This approach bases the inference on a mathematical derivation of the product of two normally distributed variables which acknowledges the skew of the distribution instead of imposing normality . </P> <P> Another approach that is becoming more popular in the literature is bootstrapping . Bootstrapping is a non-parametric resampling procedure that can build an empirical approximation of the sampling distribution of αβ by repeatedly sampling the dataset . Bootstrapping does not rely on the assumption of normality . </P>

Procedure and protocol in analyzing interpreting and presenting sobel test