# Relationship between beta and t-value in Shen (2018)

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:

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.

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

• 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) ... Commented Apr 10, 2023 at 6:38
• "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. Commented Apr 11, 2023 at 9:46
• @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. Commented Apr 12, 2023 at 1:19

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