It is real data (Tal-Or et al., 2010) about how likely people are to buy sugar after reading an article about an incoming sugar crisis. This article was either placed on the front page (Condition = 1) or on an inside page (Condition = 0). The outcome variable is Intention, people's intention to buy sugar, and the mediator is MediaInfluence, to what extent people think that other people will buy sugar based on that article. Mediation here is all about taking that association between condition and intention, and then seeing if that association is mediated by perceived media influence. In the Models tab we use the Hayes configuration, model number 4 (mediation #4, moderation #1). There's also the alternative way that is described in the book, where you build your path models more from the bottom up (Input type → Paths). This is also a way to create exactly that mediation analysis.
| AIC | BIC | Log-likelihood | n | df | |
|---|---|---|---|---|---|
| Model 1 | 1030 | 1047 | -509.1 | 123 | 0 |
We can do different model comparisons with this table, but we don't focus on that for now.
| R² | |
|---|---|
| Model 1 | |
| Intention | 0.2059 |
| MediaInfluence | 0.03268 |
Always pay attention to the path plots you get in the output, because that tells you if you put in the right Hayes model number. If you want mediation, then this is the path plot to look out for. The directional arrows imply a causal relationship, but to make that claim you really need experimental manipulation. Only Condition was randomized, so path a is causal but path b may be confounded or reversed.
The second mediation path plot has the different coefficients already filled in (Statistical in the Models tab, and Plots → Parameter estimates). So that's a nice first step to getting an idea of how these different a, b and c pathways look, and you need to be able to read them from the JASP output. These path coefficients are also exactly what is being listed in the path coefficients table. But always also look at the p-values and confidence intervals, because those are your inferential statistics and they give you your uncertainty.
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.
| 95% Confidence Interval | ||||||||
|---|---|---|---|---|---|---|---|---|
| Estimate | Std. Error | z-value | p | Lower | Upper | |||
| Condition1 | → | Intention | 0.2544 | 0.2527 | 1.007 | .314 | -0.2409 | 0.7496 |
| MediaInfluence | → | Intention | 0.5064 | 0.09586 | 5.283 | < .001 | 0.3186 | 0.6943 |
| Condition1 | → | MediaInfluence | 0.4765 | 0.2338 | 2.038 | .042 | 0.01835 | 0.9347 |
| Note. Moderation effect estimates are based on mean-centered variables. | ||||||||
The path coefficients table lists those a, b and c that we also saw on the slides. They are just a single arrow in your path diagram, and each coefficient can also be tested whether it's significantly different from zero. The a pathway (Condition1 → MediaInfluence, 0.4765) is exactly this mediator effect, the extent to which we can predict our mediator based on our predictor (Condition1 is the front page compared to the inside page). For the b pathway (MediaInfluence → Intention, 0.5064) we have a significant association between our media influence and our outcome variable. The c pathway (Condition1 → Intention, 0.2544) comes from the multiple regression, which takes into account also the mediator, and we use exactly that to get an idea of the direct effect. We get a p-value that's not significant, so we cannot conclude that there is a direct effect.
| 95% Confidence Interval | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Condition | Estimate | Std. Error | z-value | p | Lower | Upper | |||||
| Condition | → | Intention | 1 | 0.2544 | 0.2527 | 1.007 | .314 | -0.2409 | 0.7496 | ||
| Condition | → | MediaInfluence | → | Intention | 1 | 0.2413 | 0.1269 | 1.902 | .057 | -0.007379 | 0.4900 |
| Note. Moderation effect estimates are based on mean-centered variables. | |||||||||||
The first row gives the direct effect, so that is immediately going from condition to the outcome intention, and that is still that 0.2544. The second row is the indirect effect, the product of your a and b pathways (0.4765 × 0.5064 = 0.2413). The mediation is an indirect effect, so we test mediation by looking at the p-value for the indirect effect, a × b. The p-value here is answering the question, how likely is it to observe this estimate for the indirect effect, or more extreme, if on the population level there is no mediation effect? We're using the alpha of 0.05, so we have non-significance for both effects. So we fail to reject the null hypothesis, and we cannot conclude that there is a mediation effect going on here. Don't do hypothesis testing with confidence intervals. Confidence intervals are for estimation, and this one shows how precisely a × b is estimated.
| 95% Confidence Interval | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Condition | Estimate | Std. Error | z-value | p | Lower | Upper | ||||
| Total | Condition | → | Intention | 1 | 0.4957 | 0.2753 | 1.801 | .072 | -0.04385 | 1.035 |
| Total indirect | Condition | → | Intention | 1 | 0.2413 | 0.1269 | 1.902 | .057 | -0.007379 | 0.4900 |
| Note. Moderation effect estimates are based on mean-centered variables. | ||||||||||
The last table also shows you the total effect (0.4957), and that's maybe how you can see how the total effect differs from the direct effect, because the direct effect is a part of the total effect, but it's not the full total effect. If we add indirect plus our direct effect, we get back our total effect (0.2544 + 0.2413 = 0.4957), maybe a little bit in the same way as we are partitioning sums of squares. With one mediator, the total indirect effect is simply the indirect effect. Now that we have multiple p-values in our output, always be specific about what p-value you are referring to. Is it the p-value of the total effect, the indirect effect or the direct effect?
Assumptions problematic (normality, heteroscedasticity)? An additional tool in your toolbox, similar to how it is in regression, is the bootstrap (Options → Method → Bootstrap). It is a robust tool to get more robust confidence intervals that do not rely on these assumptions. Only the CI is bootstrapped, not the p-value, and it is based on random number generation, so all of your results will be slightly different.