The Attention Dataset

   

Please double check this data table below to make sure I have the same data with you.

   

ID ExecutiveNetworks Depression Anxiety Stress ADHD
SADP01 149.55 18 14 18 35
SADP05 187.46 23 25 26 56
SADP09 125.05 31 28 41 60
SADP11 124.16 22 16 27 62
SADP13 182.02 40 38 47 63
SADP14 218.83 20 28 26 49
SADP15 152.98 14 15 14 48
SADP18 179.28 14 14 20 54
SADP25 116.82 42 18 27 36
SADP27 216.76 48 44 42 53
SADP29 287.74 25 28 31 57
SADP30 170.71 19 16 15 36
SADP36 78.94 15 19 21 40
SADP37 216.64 18 18 22 31
SADP40 78.42 14 14 14 36
SADP42 160.49 34 25 29 38
SADP43 136.10 14 16 16 36
SADP44 363.52 23 46 51 73
SADP45 242.28 33 34 45 68
SADP46 88.30 11 15 18 53
SADP47 146.93 9 7 11 67
SADP49 266.71 18 28 17 58
SADP50 102.96 17 24 22 70

     

PEARSON Correlation Matrix between ALL Variables

 

NOTE: if p value is LESS than 0.05 –> SIGNIFICANT CORRELATION at alpha = 0.05

   

Variable 1 Variable 2 Coefficent r p value
ExecutiveNetworks Depression 0.2322450 0.2862601
ExecutiveNetworks Anxiety 0.6634253 0.0005587
Depression Anxiety 0.6719103 0.0004460
ExecutiveNetworks Stress 0.5188460 0.0111884
Depression Stress 0.7465526 0.0000429
Anxiety Stress 0.8856759 0.0000000
ExecutiveNetworks ADHD 0.3768153 0.0763346
Depression ADHD 0.0924598 0.6747818
Anxiety ADHD 0.4732357 0.0225634
Stress ADHD 0.4984014 0.0154973

Based on the result table, there is a SIGNIFICANT CORRELATION between Executive Networks and (1) Anxiety, and (2) Stress.

(After adding the recent datapoint for participant SADP50, ADHD is NO LONGER SIGNIFICANTLY CORRELATED with Executive)

However, we NOTICE that: Anxiety and Stress are VERY VERY VERY correlated with each other.

Therefore, I would recommend NOT using multiple linear regression because it would result an INSIGNIFICANT MODEL due to COLLINEARITY causing variant inflation.

     

Multiple Linear Regression

## 
## Call:
## lm(formula = ExecutiveNetworks ~ Stress + Anxiety, data = attention)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -84.865 -48.800   0.793  37.945  90.978 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   72.172     29.266   2.466   0.0228 *
## Stress        -1.939      2.148  -0.903   0.3775  
## Anxiety        6.596      2.463   2.678   0.0145 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 54.43 on 20 degrees of freedom
## Multiple R-squared:  0.462,  Adjusted R-squared:  0.4083 
## F-statistic: 8.589 on 2 and 20 DF,  p-value: 0.00203
Estimate Std. Error t value Pr(>|t|)
(Intercept) 72.171705 29.266116 2.466050 0.0228261
Stress -1.938507 2.147616 -0.902632 0.3774643
Anxiety 6.595858 2.463328 2.677621 0.0144686

     

As you can see here, Stress is NOT significant at all in the model result even though our pairwise Pearson results are significant.

       

Mediation model:

SIGNIFICANT mediation model: ADHD (IV) - Anxiety (Mediator) - Executive Networks (DV)

SIGNIFICANT mediation model: Depression (IV) - Anxiety (Mediator) - Executive Networks (DV)

           

Since a mediator is acting as a variable that mediates the relationship between the IV and DV. We expect that the relationship between the Mediator and DV as a significant one. Based on our Pearson result, only Stress/Anxiety is significantly correlated with Executive Networks. We can consider these as mediators.

Whereas Depression/ADHD is not significantly correlated with Executive Networks, we can assume that these variables may have an indirect impact on Excutive Networks, thus considered as IV

     

Mediation Model 1:

IV = ADHD

Mediator = Anxiety

DV = Executive Network

Total effect - Effect of IV on DV
## 
## Call:
## lm(formula = ExecutiveNetworks ~ ADHD, data = attention)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -109.06  -61.41    0.07   36.98  145.35 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)    68.49      58.09   1.179   0.2516  
## ADHD            2.05       1.10   1.864   0.0763 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 67.09 on 21 degrees of freedom
## Multiple R-squared:  0.142,  Adjusted R-squared:  0.1011 
## F-statistic: 3.475 on 1 and 21 DF,  p-value: 0.07633

There is no significant effect of IV (ADHD) on DV (Executive Networks) at alpha = 0.05

Effect of IV on Mediator
## 
## Call:
## lm(formula = Anxiety ~ ADHD, data = attention)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -21.8550  -4.6856   0.2066   3.8066  20.3144 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   4.1158     7.9218   0.520   0.6088  
## ADHD          0.3692     0.1500   2.462   0.0226 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.149 on 21 degrees of freedom
## Multiple R-squared:  0.224,  Adjusted R-squared:  0.187 
## F-statistic:  6.06 on 1 and 21 DF,  p-value: 0.02256

There is significant effect of IV (ADHD) on Mediator (Anxiety) at alpha = 0.05

     

Effect of mediator on DV
## 
## Call:
## lm(formula = ExecutiveNetworks ~ ADHD + Anxiety, data = attention)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -83.062 -48.990   3.249  35.442  90.010 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  50.5484    48.1699   1.049  0.30652   
## ADHD          0.4407     1.0287   0.428  0.67292   
## Anxiety       4.3593     1.3185   3.306  0.00352 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 55.28 on 20 degrees of freedom
## Multiple R-squared:  0.4452, Adjusted R-squared:  0.3897 
## F-statistic: 8.025 on 2 and 20 DF,  p-value: 0.002762

There is significant effect of Mediator (Anxiety) on DV (Executive Networks)

     

Mediation Model Result
## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME              1.610        0.221         3.96   0.016 *
## ADE               0.441       -1.667         2.43   0.783  
## Total Effect      2.050       -0.420         4.53   0.116  
## Prop. Mediated    0.785       -1.981         3.46   0.112  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 23 
## 
## 
## Simulations: 999

Based on the Causal Mediation Analysis, the average causal mediation effects is significant (ACME = 1.610, p = 0.014), meaning that there is an indirect effect of the IV (ADHD) on the DV (Executive Networks) that goes through the mediator (Anxiety). However there is NO significant average direct effects (ADM = 0.441, p = 0.75) of the IV (ADHD) on the DV (Executive Networks) as well as NO significant total effect of IV (ADHD) on DV (Executive Networks) (p = 0.11)

           

Mediation Model 2:

IV = ADHD

Mediator = Stress

DV = Executive Network

Total effect - Effect of IV on DV
## 
## Call:
## lm(formula = ExecutiveNetworks ~ ADHD, data = attention)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -109.06  -61.41    0.07   36.98  145.35 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)    68.49      58.09   1.179   0.2516  
## ADHD            2.05       1.10   1.864   0.0763 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 67.09 on 21 degrees of freedom
## Multiple R-squared:  0.142,  Adjusted R-squared:  0.1011 
## F-statistic: 3.475 on 1 and 21 DF,  p-value: 0.07633

There is NO significant effect of IV (ADHD) on DV (Executive Networks), p = 0.0763

     

Effect of IV on Mediator
## 
## Call:
## lm(formula = Stress ~ ADHD, data = attention)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -22.1073  -6.2943  -0.8339   8.2740  15.6769 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   3.2223     8.9421   0.360   0.7222  
## ADHD          0.4460     0.1693   2.634   0.0155 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.33 on 21 degrees of freedom
## Multiple R-squared:  0.2484, Adjusted R-squared:  0.2126 
## F-statistic: 6.941 on 1 and 21 DF,  p-value: 0.0155

There is significant effect of IV (ADHD) on Mediator (Stress), p = 0.0155

     

Effect of mediator on DV
## 
## Call:
## lm(formula = ExecutiveNetworks ~ ADHD + Stress, data = attention)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -95.96 -53.68   2.58  29.75 111.68 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  59.8612    54.3982   1.100   0.2842  
## ADHD          0.8559     1.1844   0.723   0.4783  
## Stress        2.6779     1.3234   2.023   0.0566 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 62.63 on 20 degrees of freedom
## Multiple R-squared:  0.2878, Adjusted R-squared:  0.2166 
## F-statistic: 4.041 on 2 and 20 DF,  p-value: 0.03358

There is NO significant effect of Mediator (Stress) on DV (Executive Networks), p = 0.0566

     

Mediation Model Result
## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME             1.1945      -0.0914         2.95   0.078 .
## ADE              0.8559      -1.1796         3.50   0.440  
## Total Effect     2.0504      -0.3239         4.41   0.090 .
## Prop. Mediated   0.5826      -1.1124         3.42   0.160  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 23 
## 
## 
## Simulations: 999

Based on the Causal Mediation Analysis, the average causal mediation effects is NOT significant (ACME = 1.194, p = 0.074), meaning that there is NO indirect effect of the IV (ADHD) on the DV (Executive Networks) that goes through the mediator (Stress).

           

Mediation Model 3:

IV = Depression

Mediator = Anxiety

DV = Executive Network

Total effect - Effect of IV on DV
## 
## Call:
## lm(formula = ExecutiveNetworks ~ Depression, data = attention)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -86.978 -54.941  -7.008  34.373 189.450 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  138.082     35.623   3.876 0.000873 ***
## Depression     1.565      1.430   1.094 0.286260    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 70.44 on 21 degrees of freedom
## Multiple R-squared:  0.05394,    Adjusted R-squared:  0.008887 
## F-statistic: 1.197 on 1 and 21 DF,  p-value: 0.2863

There is NO significant effect of IV (Depression) on DV (Executive Networks), p = 0.286260

     

Effect of IV on Mediator
## 
## Call:
## lm(formula = Anxiety ~ Depression, data = attention)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -17.5741  -4.0218  -0.4517   3.9960  22.7590 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   8.3115     3.8896   2.137 0.044538 *  
## Depression    0.6491     0.1561   4.157 0.000446 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.692 on 21 degrees of freedom
## Multiple R-squared:  0.4515, Adjusted R-squared:  0.4253 
## F-statistic: 17.28 on 1 and 21 DF,  p-value: 0.000446

There is significant effect of IV (Depression) on Mediator (Anxiety), p = 0.000446

Effect of mediator on DV
## 
## Call:
## lm(formula = ExecutiveNetworks ~ Depression + Anxiety, data = attention)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -91.740 -34.163   6.195  36.884  88.217 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   84.469     28.592   2.954 0.007841 ** 
## Depression    -2.622      1.404  -1.867 0.076597 .  
## Anxiety        6.451      1.454   4.437 0.000253 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 51.24 on 20 degrees of freedom
## Multiple R-squared:  0.5232, Adjusted R-squared:  0.4756 
## F-statistic: 10.98 on 2 and 20 DF,  p-value: 0.0006067

There is significant effect of Mediator (Anxiety) on DV (Executive Networks), p = 0.000253

     

Mediation Model Result
## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME              4.187        0.947         7.84   0.018 *
## ADE              -2.622       -5.204         1.06   0.094 .
## Total Effect      1.565       -0.614         5.17   0.136  
## Prop. Mediated    2.676       -7.925        13.75   0.150  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 23 
## 
## 
## Simulations: 999

Based on the Causal Mediation Analysis, the average causal mediation effects is significant (ACME = 4.187, p = 0.008), meaning that there is an indirect effect of the IV (Depression) on the DV (Executive Networks) that goes through the mediator (Anxiety). However there is NO significant average direct effects (ADE = -2.622, p = 0.096) of the IV (Depression) on the DV (Executive Networks) as well as NO significant total effect of IV (Depression) on DV (Executive Networks) (p = 0.098)

           

Mediation Model 4:

IV = Depression

Mediator = Stress

DV = Executive Network

     

Total effect - Effect of IV on DV
## 
## Call:
## lm(formula = ExecutiveNetworks ~ Depression, data = attention)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -86.978 -54.941  -7.008  34.373 189.450 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  138.082     35.623   3.876 0.000873 ***
## Depression     1.565      1.430   1.094 0.286260    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 70.44 on 21 degrees of freedom
## Multiple R-squared:  0.05394,    Adjusted R-squared:  0.008887 
## F-statistic: 1.197 on 1 and 21 DF,  p-value: 0.2863

There is NO significant effect of IV (Depression) on DV (Executive Networks), p = 0.286260

     

Effect of IV on Mediator
## 
## Call:
## lm(formula = Stress ~ Depression, data = attention)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -15.0563  -4.8935  -0.2025   1.8656  24.6613 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   7.3122     4.0078   1.824   0.0823 .  
## Depression    0.8272     0.1609   5.142 4.29e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.925 on 21 degrees of freedom
## Multiple R-squared:  0.5573, Adjusted R-squared:  0.5363 
## F-statistic: 26.44 on 1 and 21 DF,  p-value: 4.289e-05

There is significant effect of IV (Depression) on Mediator (Stress), p = 0.0000429

     

Effect of mediator on DV
## 
## Call:
## lm(formula = ExecutiveNetworks ~ Depression + Stress, data = attention)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -99.702 -52.683   3.269  33.339 125.149 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  103.386     33.223   3.112  0.00549 **
## Depression    -2.361      1.862  -1.268  0.21951   
## Stress         4.745      1.681   2.823  0.01050 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 61.04 on 20 degrees of freedom
## Multiple R-squared:  0.3235, Adjusted R-squared:  0.2559 
## F-statistic: 4.783 on 2 and 20 DF,  p-value: 0.02006

There is significant effect of Mediator (Stress) on DV (Executive Networks), p = 0.01050

     

Mediation Model Result
## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME              3.925       -1.926         7.58    0.16
## ADE              -2.361       -4.855         4.01    0.40
## Total Effect      1.565       -0.382         4.51    0.12
## Prop. Mediated    2.509      -13.107        12.01    0.27
## 
## Sample Size Used: 23 
## 
## 
## Simulations: 999

Based on the Causal Mediation Analysis, the average causal mediation effects is NOT significant (ACME = 3.925, p = 0.20), meaning that there is NO indirect effect of the IV (Depression) on the DV (Executive Networks) that goes through the mediator (Stress).

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