Moderator can affect the strength of the relationship between variables, e.g. the relationship between students' learning effects and guidelines are often affected by the student individuality.However, mediator, considering the influence of the independent variable X for the dependent variable Y, if X by influencing variables M to influence the Y, so M is described as intermediary variable(mediator)

The difference can be illustrated with pictures as well. See the following two pictures:

http://www.ats.ucla.edu/stat/stata/faq/model4s.png

http://home.apu.edu/~rareynolds/COMM300/Retired%20Pages/Moderator%20vs_files/Med1.gif

In the first picture, variables "W" and "Z" are the moderators. These two variables influence the relationships between X and M, and M and Z, respectively. For example. Let's say that X = motivation and M = performance, and that higher motivation leads to higher performance. W = job satisfaction. We could then find that motivation leads to better performance, and that this is especially the case when satisfaction is higher.

In the second picture, we see A, B, and C. In this case, there is an assumed direct relationship between A and C. Let's use the the same example: A = motivation, C = performance. In this case, however, the relationship between those two variables is not direct, but indirect. If B = work engagement, then we can find that motivation leads to engagement, which subsequently leads to performance. That is, a mediator does not influence an existing relationship, but is a variable that forms an indirect relationship.

The two comments above are correct descriptions of a moderator and a ´mediator, but did not answer whether direction changes can occur. Yes they can occur.

For moderation. Independent variable is "sight of a well grilled juicy steak" and the dependent variable is "feeling of joy". Now assume that the relation between the two is positive. Now we introduce the moderator variable "vegetarian" and we probably see that the sight of a well grilled steak does not result in an increase joy among the vegetarian rather they will feel less joy, i.e. the relationship between steak and joy becomes negative.

For mediation. Change of direction can happen if the mediator is a supresspr variable. An example: Let us assume that we find that a negative relationship between "how many kilometer someone drives per year" and "the number of accidents caused", if we would now include "driving experience" as mediator, as more kilometers driven result in more experience and consequently less accidents, then the direct relation between kilometers driver and accident rate can become positve, because the more kilometer you drive the more are you at risk of having an accident.

Mediating variables are the variables applied in cases where an intervening affect exists between two variables. For example: If our goal were to establish the relationship between education level and career success. Let us say generally, higher levels of education(independent variable) led to improved career success(dependant variable). An "intervening or mediating" variable might be present, lets say: personal confidence. The mediating variable "personal confidence", for instance, might also influence the variable "career success". High or low confidence could have a positive or negative "intervening affect" on career success.

On the other hand, moderating variables can influence a set of variables during a study. If we, for example, were studying employee "stress levels" and their affect on the success or failure of a "corporate merger". Both the independent variable "stress" and the dependant variable "merger success or failure" could potentially be positively or negatively influenced by the variable "communication strategy". Good communication could lead to a smooth transition period during a merger. Bad communication could scuttle the entire effort.

I hope this clarifies things.

A moderator variable is a variable that has the ability to affect the strenght or the direction of a relation between two existing variables. Using moderator variables in models of analysis is adequate when we are expecting that the model is a contextual one. That is, a relation between two variables exist, but, when a third variable appears, the existing relation changes its direction, strenghtens, or weakens it. It is a context variable.

Example: individuals' motivation leads to commitment, but the magnitude of the relation depends on the gender, or the age of the workers.

As for a mediator variable, it a process variable. It is usually used to analyse a process relation. A relation between A and C existes through B. A leads to B, that leads to C.

Example: Individuals' motivation leads to commitment, and this explains (leads to) productivity.

Consulting Baron & Kenny (1986) research is very relevant as a reference.

More complex models test for moderated-mediation relations, or mediation-moderated ones

Moderated-Mediation: a mediation effect that is affected by a third variable in its strenght or direction: Example: A leads to B, that leads to C, but D affects the strenght or direction of the mediation.

Mediation-Moderated effects: where a moderation effect that triggers a mediational one. A leads to B, that is affected by C (moderator), and this triggers the influence of D (mediator), where a process explanation for the relation appears.

These last two cases are complex to justify and to test them calls for several statistical procedures to assure the effectiveness of the analysis.

Consulting Preacher, Rucker and Hays(2007) is an importante reference for this matter.

I agree with all of the above and would like to add that it is very easy to statistically test if a variable is a moderating variable: in testing if Y= a+bX, put the moderator variable (MOD) as a multiplicative interaction variable as in Y= a+bX + cMOD + d MOD*X and test if d is statistically significant. But how do you formally and statistically test if a variable is truly a mediator variable (MED)? I know of only one formal test by by Baron and Kenny (1986), but that is a very stringent test as at least 4 relationships must hold simultaneously. That is, for ex. if we think MED mediates the positive relationship between X and Y and MED mediates this relationship, then we have to make sure that

a) There is a + relationship between X and Y; and

b) There is a + relationship between X and MED. and

c) There is a + relationship between MED and Y, and finally

d) When we add MED as another variable to the relationship between X and Y, the significance of X should either decrease (partial mediation) or X should loose its significance (full mediation).

I guess my question is, is there a less strict test to statistically conclude that a certain variable mediates the relationship between X and Y??

As Daniel Gomes stated above, the Preacher and Hayes method is a very good alternative. Actually, quite some scholars would argue that the classis Baron & Kenny approach is not completey justified because mediation can also exist when the relationship between A and B is not significant in the first place. I have used the Preacher and Hayes logic myself in combination with structural equation modeling, which I feel is a better and stronger test of mediation than the Baron & Kenny method with the sobel tests.

Yes all those answers have their points. But in my opinion, moderator affects the relationship in either strengthening or weaken the relationship. Moderator could be a modifier that could enhance the relationship but without moderator does not affect the model, moderator provides the contingent affect. On the other hand, mediator supposed to surface between the variable, without mediator the model considered incomplete and could be void. Thus mediating effect does not need to show the strength, as long as there is statistical signficance for both direct and indirect relationship (beta should be lower in indirect relationship) it proves as full mediator but if only direct relationship showed significant result, the indirect showed non significant then partial mediation justified. Please refer both Baron and Kenny as well as Preacher and Hayes. Sobel test is usually used to reexamine the relationship that will show an index, it is a post hoc application.

Mediating variable: Synonym for intervening variable. Example: Parents transmit their social status to their children directly, but they also do so indirectly, through education:viz.

Moderating variable: A variable that influences, or moderates, the relation between two other variables and thus produces an interaction effect.

Let me try to pass through an example differentiating moderation and mediation. Topic: “The Influence of Psychological Counselling on Employee Adjustment”. Let me put a socio-demographic variable “Gender” here. We may assume 'gender' variation in its influence on psychological counselling among male and female employees. Whether ‘male’ are more receptive to psychological counseling or ‘female’, and this question needs to be answered first. Here we need to establish a relationship between gender and psychological counseling and further to its interaction effect on employee adjustment. In this case gender act as a moderator on psychological counselling. While if you consider ‘family support’ as variable in between Psychological Counselling on Employee Adjustment. the "level of support" changes the "level of employee adjustment". The former has more influence on the independent variable and the later has more into dependent variable. 

Yes. The moderating effects can change the sign of the relationship. 

Yes it can effect both sign and strength of relationship

• It both affect the strength of the relationship as well as changes the direction. It can crystallize effect of the introduced variable and also shows which direction whether it makes the DV decreases or increases.

Hello Mahfuz Judeh,

It's the basic/foundation questions, like this one that gets people interested on this site:

Here is a simple way of looking at:

moderator => strengthen or weak a relationship between variables

mediator => connects or disconnects the path between variables.

Perhaps too simple, it does get more complex which I think you are aware.

Cheers,

Daryn

In short and precise words,

Mediator: specif ywhy or how a particular effect or relationship occures.

Moderator: change the strength of an effect between variable

What is the difference in the role of moderator, and/or mediator.

According to known definitions:

Mediator - a person who attempts to make people involved in a conflict come to an agreement; a go-between.   

Moderator. 1 : one who arbitrates : mediator. 2 : one who presides over an assembly, meeting, or discussion: such as a : the presiding officer of a Presbyterian governing body; b : the nonpartisan presiding officer of a town meeting; c : the chairman of a discussion group.

A moderator is rather keeping under control of tolerance, mutual respect, and a professional comments the direction and flow of a a general conversation, or discussion at a big gathering, meeting, or conference. Whereas a mediator works with two particular parties on order to prevent a conflict and to reach an agreement

Can a moderator or a mediator affect the strength of the relationship or change the direction of the relationship between variables.

I think, a professional moderator can do it, whereas a mediators’ key objective is to prevent an ‘explosion’ at the meeting.

Yes, a mediator can change the direction of relationship between IV to DV (i.e. causality), in such case, this mediator is known as the suppressor.

Ref: http://davidakenny.net/cm/mediate.htm

Baron & Kenny (1986) highlighted the importance of not using the terms moderator and mediator interchangeably.

Baron & Kenny (1986) wrote:

“The moderator function of third variables, which partitions a focal independent variable into subgroups that establish its domains of maximal effectiveness in regard to a given dependent variable. The mediator function of a third variable, which represents the generative mechanism through which the focal independent variable is able to influence the dependent variable of interest.”

Moderating Variable- moderator is a variable which will cancel the relationship with two variables. Moderator is a variable which will refuse the degree of relationship between two variables. Moderator can be totally canceled the relationship between two variables.

Moderating - changing

Eg: You feel sleep in the class after having a heavy lunch. So there is a relationship. But assume you don’t feel sleep in the class after having a huge lunch. The answer is the moderator, may be the interesting nature of the lecturer or exam fear.

Intervening variable alternatively called mediating variable

Intervening variable – Assume training and job performance, the relationship is positive. Greater the job training better the job performance. How does the training increase the job performance? If you have an answer, then the answer is the intervening variable. Learning is the acquisition of new knowledge and attitude. So training will result in learning which will result in job performance.

For more details please refer the articles given below.

References

Frazier, P.A., Tix, A.P. and Barron, K.E., 2004. Testing moderator and mediator effects in counseling psychology research. Journal of counseling psychology, 51(1), p.115.

Baron, R.M. and Kenny, D.A., 1986. The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of personality and social psychology, 51(6), p.1173.

The moderator "Z" is used to assess the strength between the two variables "X" and "Y" (independent and dependent respectively). While the mediator variable is used to explain the relationship between the two variables X and Y

moderator always tend to strengthen the relationship between independent and dependent variables while mediator explain the relationship between independent and dependent variables , check Baron & Kenny (1986)