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Does c’ Test Help, Anytime? -- On Communication Fallacy of “Effect to Mediate”
Unformatted Document Text:  Does c’ Test Help, Anytime? -- On Communication Fallacy of “Effect to Mediate” Page 11 of 34 Under Baron and Kenny (1986), a significant c’ is a necessary but not sufficient condition. If a hypothesized mediation passes c’ test, a*b awaits. Passing both tests is a necessary and sufficient condition for establishing mediation. But are both tests necessary? For both tests to be valid, each test must -- i. Do no harm – Do not reject any mediation. In other words, pass all mediations. ii. Do some good -- Reject non-mediations that the other test does not reject. In other words, each test must add something to the other test. If one test passes all mediations and rejects all non-mediations, it is a necessary and sufficient condition, and the other test is not needed. Table 1 shows that a*b test passes all mediations (|a*b| ≠ 0, left half of the table) and rejects all non-mediations (|a*b|≈0, right half of the table). The table also shows that, of the 24 scenarios of mediations, c’ is positive in eight, negative in eight, and near zero in the other eight. Of the 27 scenarios of non-mediations, c’ is positive in six, negative in six, and near zero in 15. A significant c’, therefore, does not necessarily indicate mediation, while a non-significant c’ does not necessarily indicate lack of mediation. These evidences support Hayes (2009) and Zhao, Lynch and Chen’s (2010) assertion that c’ is irrelevant for establishing mediation of any type. The rest of this section will provide more detailed justifications and explanations. We will examine the behavior of c’ test in each type of mediations and non-mediations. When doing so, we will keep an eye on whether c’ test meets the requirements that each must “do no harm” and “do some good.” We knew c’ test fail to pass mediations under the Shrout-Bolger conditions, namely when there is suppression, or when process is distal and effect is subtle. The questions are whether, under non Shrout-Bolger conditions, the test 1) pass all mediations and 2) reject some non-mediations that a*b test does not reject. If the answers are both yes, then we should retain c’ test for non Shrout- Bolger conditions. If one of the answers is no, we should repeal c’ test for all conditions. 1. Fails to pass competitive mediations.

Authors: Zhao, XinShu., Chen, Qimei. and Tong, Bing.
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Does c’ Test Help, Anytime? -- On Communication Fallacy of “Effect to Mediate” 
Page 11 of 34 
 
 
Under Baron and Kenny (1986), a significant c’ is a necessary but not sufficient condition.  
If a hypothesized mediation passes c’ test, a*b awaits. Passing both tests is a necessary and 
sufficient condition for establishing mediation.    
But are both tests necessary?  For both tests to be valid, each test must -- 
i.
 
Do no harm – Do not reject any mediation.  In other words, pass all mediations.    
ii.
 
Do some good -- Reject non-mediations that the other test does not reject.  In other 
words, each test must add something to the other test. 
 
If one test passes all mediations and rejects all non-mediations, it is a necessary and 
sufficient condition, and the other test is not needed. 
Table 1 shows that a*b test passes all mediations (|a*b| ≠ 0, left half of the table) and rejects 
all non-mediations (|a*b|0, right half of the table). The table also shows that, of the 24 scenarios of 
mediations, c’ is positive in eight, negative in eight, and near zero in the other eight.  Of the 27 
scenarios of non-mediations, c’ is positive in six, negative in six, and near zero in 15. A significant 
c’, therefore, does not necessarily indicate mediation, while a non-significant c’ does not necessarily 
indicate lack of mediation.   These evidences support Hayes (2009) and Zhao, Lynch and Chen’s 
(2010) assertion that c’ is irrelevant for establishing mediation of any type. The rest of this section 
will provide more detailed justifications and explanations.  We will examine the behavior of c’ test 
in each type of mediations and non-mediations.  When doing so, we will keep an eye on whether c’ 
test meets the requirements that each must “do no harm” and “do some good.” 
We knew c’ test fail to pass mediations under the Shrout-Bolger conditions, namely when 
there is suppression, or when process is distal and effect is subtle.  The questions are whether, under 
non Shrout-Bolger conditions, the test 1) pass all mediations and 2) reject some non-mediations that 
a*b test does not reject.  If the answers are both yes, then we should retain c’ test for non Shrout-
Bolger conditions.  If one of the answers is no, we should repeal c’ test for all conditions.  
1.
 
Fails to pass competitive mediations.   


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