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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 18 of 34 (2) a*b or c or both has large error relative to its effect, enlarging the error of a*b+c to make c’ non significant. But this cannot happen in a complementary mediation, where a*b and c are both significant, meaning each has small error relative to its effect. (3) a*b and c bear opposite signs, so they cancel out each other, reducing the effect of a*b+c to make it non significant. But this cannot happen in a complementary mediation, where a*b and c bear the same sign. As there is no other situation where c’ can be non-significant, it has to be significant. Table 1 displays Panel 1C, the complementary mediation with a non-significant c’, as the only impossible panel in the typology. Some of the complementary mediations, when process is proximal and effect not subtle, would not meet Shrout-Bolger condition for suspending c’ test. But that doesn’t matter as c’ test would always pass with complementary mediations. We conclude therefore that c’ is unnecessary for establishing complementary mediations, therefore should be dropped for this purpose. 4. Fails to help in rejecting direct-only non-mediations. We’ve shown that c’ test can do harm by rejecting some competitive an indirect-only medications, and cannot help in establishing complementary mediation. Let’s see if the test can help in rejecting some non-mediations that a*b test does not reject. Table 1 shows that a*b test rejects all direct-only non-mediations, therefore there is no work left for c’ test. Had there been rejection to be done, c’ test would not have helped, as it passes 10 types of direct-only non-mediations (five 4A and five 4B scenarios). In a direct-only non-mediation c' can be significant when the direct path has large enough effect relative to its error, which makes the combined effect large relative to the combined error. 5. Fails to help in rejecting no-effect non-mediations. Table 1 shows, again, a*b test rejects all the no-effect non-mediations, leaving nothing for c’ test. Again, c’ test passes two types of no-effect non-mediations (5A 1 and 5B 1 ). In a no-effect non-

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 18 of 34 
 
(2) a*b or c or both has large error relative to its effect, enlarging the error of a*b+c to make 
c’ non significant. But this cannot happen in a complementary mediation, where a*b and c are both 
significant, meaning each has small error relative to its effect. 
(3) a*b and c bear opposite signs, so they cancel out each other, reducing the effect of a*b+c 
to make it non significant. But this cannot happen in a complementary mediation, where a*b and c 
bear the same sign. 
As there is no other situation where c’ can be non-significant, it has to be significant.   
Table 1 displays Panel 1C, the complementary mediation with a non-significant c’, as the only 
impossible panel in the typology.   
Some of the complementary mediations, when process is proximal and effect not subtle, 
would not meet Shrout-Bolger condition for suspending c’ test. But that doesn’t matter as c’ test 
would always pass with complementary mediations. 
We conclude therefore that c’ is unnecessary for establishing complementary mediations, 
therefore should be dropped for this purpose. 
4.
 
Fails to help in rejecting direct-only non-mediations. 
 
We’ve shown that c’ test can do harm by rejecting some competitive an indirect-only 
medications, and cannot help in establishing complementary mediation. Let’s see if the test can help 
in rejecting some non-mediations that a*b test does not reject.  Table 1 shows that a*b test rejects 
all direct-only non-mediations, therefore there is no work left for c’ test.  Had there been rejection 
to be done, c’ test would not have helped, as it passes 10 types of direct-only non-mediations (five 
4A and five 4B scenarios). In a direct-only non-mediation c' can be significant when the direct path 
has large enough effect relative to its error, which makes the combined effect large relative to the 
combined error. 
5.
 
Fails to help in rejecting no-effect non-mediations.   
 
Table 1 shows, again, a*b test rejects all the no-effect non-mediations, leaving nothing for c’ 
test.  Again, c’ test passes two types of no-effect non-mediations (5A
1
 and 5B
1
 ). In a no-effect non-


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