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, (2) Stress, (3) ADHD.

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 + ADHD, data = attention)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -97.859 -51.016  -2.035  31.266  89.191 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  48.9393    48.2209   1.015   0.3229  
## Stress       -2.2023     2.2242  -0.990   0.3345  
## Anxiety       6.4744     2.5106   2.579   0.0184 *
## ADHD          0.6421     1.0491   0.612   0.5478  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 55.3 on 19 degrees of freedom
## Multiple R-squared:  0.4724, Adjusted R-squared:  0.3891 
## F-statistic: 5.672 on 3 and 19 DF,  p-value: 0.006
Estimate Std. Error t value Pr(>|t|)
(Intercept) 48.9393206 48.220909 1.0148983 0.3229048
Stress -2.2023018 2.224174 -0.9901663 0.3345360
Anxiety 6.4744225 2.510627 2.5788072 0.0183977
ADHD 0.6420549 1.049121 0.6119934 0.5477966

     

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

       

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        0.222         4.00   0.024 *
## ADE               0.441       -1.875         2.54   0.749  
## Total Effect      2.050       -0.234         4.61   0.100  
## Prop. Mediated    0.785       -2.560         4.02   0.104  
## ---
## 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 = 0.02), 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              1.194       -0.141         2.96   0.088 .
## ADE               0.856       -1.123         3.65   0.412  
## Total Effect      2.050       -0.297         4.54   0.076 .
## Prop. Mediated    0.583       -0.592         2.98   0.156  
## ---
## 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 = 1.610, p = 0.02), meaning that there is NO 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)

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