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As far as I know [source],

$$t_{\widehat{\beta}} = \frac{\widehat{\beta}}{\widehat{SE_{\beta}}}.$$

It means the sign of the t-value should be the same as the sign of beta.

In Table S1 of Shen (2018), the signs are different. Why? Did I miss something?

I have noticed the passage referenced by user @utobi before. But

(1) the first row in Table S1: N17_N15, Beta: 0.054, SE: 0.016, t.value: -3.403, Valence of connection: + clearly did not followed the pattern.

(2)More importantly, a comparison of Figure 1 and Table S1 indicate the beta values in Table S1 means connection strength already, so there is no need to multiply sign one more time. For example,

Table S1: N24_N4 -0.066 (sign of mean value connection is negative)

Figure 1: Figure 1

Note the caption: “Red lines are the connections where strength was positively associated with cognitive performance, and blue lines denote negative associations with cognitive performance”

(3) t-value is used to calculate p-value, and their relationship is symmetry around 0. So changing the sign would mean nothing. enter image description here

Also, if we interpret "Valence of connection" and "95% CI of value of connection" in Table S1-S3 as the sign and CI for the values of connection, they should be the same across the 3 tables. However, they sometimes agree and sometimes not.

Table S1

N45_N15 + 1.233 1.291

Table S2

N45-N15 + 1.233 1.291

Table S1

N17_N15 + 1.215 1.275

Table S2

N17-N15 - -0.825 -0.784

Table S1

N24_N4 - -1.136 -1.075

Table S2

N24-N4 + 0.588 0.651

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  • $\begingroup$ something is missing here. In p.16 of the linked pdf The regression model was applied to test the association between VNR and absolute strength of connections, which was achieved by multiplying values of connections with the sign of their mean value (see Methods) ... $\endgroup$
    – utobi
    Commented Apr 10, 2023 at 6:38
  • $\begingroup$ "t-value is used to calculate p-value, and their relationship is symmetry around 0. So changing the sign would mean nothing" Exactly, from the point of view of the p-value it doesn't do anything, and that is exactly the point. The sign change is to make the t-values easier to interpret, but you don't want that the sign change has an influence on the p-value. $\endgroup$
    – Sextus Empiricus
    Commented Apr 11, 2023 at 9:46
  • $\begingroup$ @SextusEmpiricus The sign of beta is already changed. See my comparison between Figure 1 and Table S1. There is no need to change again. Also, see the note for Table 1: "The values of connections were transformed into strength before conducting the analyses by multiplying the connection values with the signs of their means." The sign was changed before the analysis. $\endgroup$
    – John Smith
    Commented Apr 12, 2023 at 1:19

1 Answer 1

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Mostly an expanded version of my comment, reading the original paper on p. 880

To enable a clearer interpretation of the results, the values of the connections were transformed into connection strength. This was achieved by multiplying the raw connection values with the sign of their values.

Therefore

$$t = \text{(sign of mean value connection)}\times \frac{\beta}{\text{Standard error}}.$$

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  • $\begingroup$ The first row in Table S1: N17_N15, Beta: 0.054, SE: 0.016, t.value: -3.403, Valence of connection: +. So if your interpretation were correct, t should be plus in this case. $\endgroup$
    – John Smith
    Commented Apr 11, 2023 at 1:06
  • $\begingroup$ @JohnSmith I re-checked the paper and actually I agree that in Table S1 the signs disagree. On the other hand, for all the other tables in the paper as well as in supporting materials, except Table S1, the signs agree. I cannot but think that Table S1 reports wrong results. $\endgroup$
    – utobi
    Commented Apr 18, 2023 at 5:14
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    $\begingroup$ You are right. It was confirmed. $\endgroup$
    – John Smith
    Commented Apr 18, 2023 at 8:25

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