R Notebook

t_small

Error: object 't_small' not found

Descriptive Statistics

table(t$decision_severity)

 3  4  5  6  7 
 4  2 11  5  1 

Correlations with time?

Severity is only correlated with time variables (at p>0.3) are time closing and time overview. Removing all others from further consideration.

Correlations with other variables

I use p<0.3, assuming that these will drop with n increasing:

• Severity has a pos cor with data_viz==1, decision confidence, and time taken.
  • It has a negative cor with ecl.
• Data viz increase decision confidence, decreases ecl, and increases time overview.
  • What exactly is time on overview?
• CL measures are ok.
  • ecl and icl correlated but no others.
• Numeracy works well, with neg cor with ecl, and data viz condition.
  • What exactly is time on closing / overview?
• Skepticism is cor with icl and ecl.

temp  <- t %>% 
  select(-starts_with('time'), -ends_with('time'), time_closing, time_overview) 


p_matrix <- ggcorrplot::cor_pmat(temp)

ggcorrplot::ggcorrplot(cor(temp, use = "pairwise.complete.obs"), 
         lab = TRUE, 
         lab_size = 3, 
         colors = c("red", "white", "blue"), 
         title = "Correlation Matrix (p<.2)",
         sig.level = 0.2,
         p.mat = p_matrix,
         insig = 'blank',
         ggtheme = theme_minimal())

Modeling

Basic model with regression (r.47)

Assuming a pop around 69 (bootstrapping) three times,

• skepticism score slightly decreases severity
• data-viz strongly increases severity
• icl is on the edge of sig, with positive impact
• ecl is on the edge of sig, with negative impact

Going to a pop of around 200, all above reach sig.

temp <- triple(select(t, -starts_with('time'), -ends_with('time')) )


m <- lm(decision_severity ~ ., data = temp)
summary(m)

Call:
lm(formula = decision_severity ~ ., data = temp)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.3521 -0.7413  0.2600  0.5868  1.0686 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)          6.409210   1.161352   5.519 7.39e-07 ***
pre_skepticism      -0.015997   0.008851  -1.807   0.0757 .  
pre_numeracy        -0.118533   0.081129  -1.461   0.1491    
condition_isDataViz  1.411916   0.228886   6.169 6.07e-08 ***
decision_confidence  0.033854   0.087401   0.387   0.6999    
cl_intrinsic         0.199526   0.147256   1.355   0.1804    
cl_germane          -0.043080   0.117471  -0.367   0.7151    
cl_extrinsic        -0.176244   0.155574  -1.133   0.2617    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7915 on 61 degrees of freedom
Multiple R-squared:  0.5212,    Adjusted R-squared:  0.4663 
F-statistic: 9.487 on 7 and 61 DF,  p-value: 6.574e-08

caret::varImp(m)

PCA

print(pca_results)

Standard deviations (1, .., p=6):
[1] 1.4084773 1.1344122 0.9971643 0.9046241 0.8108966 0.5089855

Rotation (n x k) = (6 x 6):
                          PC1        PC2        PC3          PC4         PC5         PC6
pre_skepticism     0.43767103  0.2618586 -0.3788836 -0.002465966 -0.76715101  0.08828701
pre_numeracy      -0.26473757 -0.1022290 -0.8600394 -0.259954670  0.26347298  0.20688417
decision_severity -0.14837812  0.6160380  0.2492391 -0.690686558  0.03252771  0.24136078
cl_intrinsic       0.58535244  0.1950367 -0.1633801 -0.207084206  0.41085128 -0.61720944
cl_germane        -0.03620795  0.6713515 -0.1273448  0.640857218  0.29124292  0.19036568
cl_extrinsic       0.61024055 -0.2296179  0.1083955 -0.042281499  0.29560454  0.68844951

ANOVA

temp <- t %>% 
  mutate(pre_skepticism = ifelse(pre_skepticism < 120, 'low', 
                                   ifelse(pre_skepticism < 130, 'middle', 'high'))) %>% 
  mutate(pre_skepticism = factor(pre_skepticism, levels = c('low', 'middle', 'high')),
         condition_isDataViz = factor(condition_isDataViz, levels = c(0, 1), labels = c('table', 'graph'))
         ) 

table(temp$pre_skepticism)

   low middle   high 
     5     10      8 

m <- aov(decision_severity ~ pre_skepticism + condition_isDataViz, 
          data = triple(temp))
summary(m)

                    Df Sum Sq Mean Sq F value   Pr(>F)    
pre_skepticism       2   4.23    2.11   3.655   0.0313 *  
condition_isDataViz  1  38.02   38.02  65.778 1.86e-11 ***
Residuals           65  37.57    0.58                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

TukeyHSD(m)

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = decision_severity ~ pre_skepticism + condition_isDataViz, data = triple(temp))

$pre_skepticism
            diff         lwr        upr     p adj
middle-low  -0.6 -1.17668880 -0.0233112 0.0396107
high-low    -0.2 -0.80023673  0.4002367 0.7048456
high-middle  0.4 -0.09942715  0.8994272 0.1409069

$condition_isDataViz
                diff       lwr      upr p adj
graph-table 1.359091 0.9931447 1.725037     0

Lavaan

library(lavaan)
library(lavaanPlot)

temp <- t %>% 
  mutate(condition_isDataViz = factor(condition_isDataViz, levels = c(0, 1), labels = c('table', 'graph'))
         ) %>% 
  rename(condition = condition_isDataViz,
         pre_skepticism = pre_skepticism) %>%   # skepticism_score
  mutate(cognitive_load = cl_extrinsic )  #cl_extrinsic, cl_intrinsic, cl_germane


model <- '
  # Mediation path
  cognitive_load ~ a1*condition + a2*pre_skepticism

  decision_severity ~ b1*cognitive_load + b2*pre_skepticism

  # Indirect effect (mediation)
  indirect := a1 * b1

  # Total effect (direct + indirect)
  total :=  (a1 * b1)
'
fit <- sem(model, data = triple(temp), meanstructure = T)
summary(fit, fit.measures = TRUE, standardized = TRUE)

lavaan 0.6-19 ended normally after 1 iteration

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                         8

  Number of observations                            69

Model Test User Model:
                                                      
  Test statistic                                41.780
  Degrees of freedom                                 1
  P-value (Chi-square)                           0.000

Model Test Baseline Model:

  Test statistic                                59.903
  Degrees of freedom                                 5
  P-value                                        0.000

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.257
  Tucker-Lewis Index (TLI)                      -2.714

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)               -191.715
  Loglikelihood unrestricted model (H1)       -170.825
                                                      
  Akaike (AIC)                                 399.429
  Bayesian (BIC)                               417.302
  Sample-size adjusted Bayesian (SABIC)        392.106

Root Mean Square Error of Approximation:

  RMSEA                                          0.769
  90 Percent confidence interval - lower         0.580
  90 Percent confidence interval - upper         0.976
  P-value H_0: RMSEA <= 0.050                    0.000
  P-value H_0: RMSEA >= 0.080                    1.000

Standardized Root Mean Square Residual:

  SRMR                                           0.161

Parameter Estimates:

  Standard errors                             Standard
  Information                                 Expected
  Information saturated (h1) model          Structured

Regressions:
                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  cognitive_load ~                                                         
    condition (a1)      -0.628    0.223   -2.812    0.005   -0.628   -0.314
    pr_skptcs (a2)       0.028    0.009    3.034    0.002    0.028    0.339
  decision_severity ~                                                      
    cogntv_ld (b1)      -0.297    0.130   -2.285    0.022   -0.297   -0.276
    pr_skptcs (b2)       0.005    0.011    0.432    0.666    0.005    0.052

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .cognitive_load    0.379    1.144    0.331    0.740    0.379    0.380
   .decision_svrty    5.166    1.299    3.977    0.000    5.166    4.803

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .cognitive_load    0.826    0.141    5.874    0.000    0.826    0.828
   .decision_svrty    1.075    0.183    5.874    0.000    1.075    0.929

Defined Parameters:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
    indirect          0.187    0.105    1.773    0.076    0.187    0.087
    total             0.187    0.105    1.773    0.076    0.187    0.087

lavaanPlot(model = fit, 
           node_options = list(shape = 'box', fontname = 'Helvetica'),
           edge_options = list(color = 'grey'),
           coefs = T,
           sig = 0.3,
           stars = 'regress')

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