The analysis for Study 1

We utlized the ANOVA analysis for the results in our Study 1 for causal priors.

model_word <- lm(Score~QID, data = data_s1)
anova(model_word)
## Analysis of Variance Table
## 
## Response: Score
##             Df Sum Sq Mean Sq F value    Pr(>F)    
## QID         55 3520.4  64.007   53.41 < 2.2e-16 ***
## Residuals 5152 6174.2   1.198                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The analysis for Study 2

This block is the generalized linear model analysis for Study 2 results of causal relationships.

model_causal <- glm(Score~Prior*VA*CT, data = data_s2_causal)
summary(model_causal)
## 
## Call:
## glm(formula = Score ~ Prior * VA * CT, data = data_s2_causal)
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.91705    0.07968  11.509  < 2e-16 ***
## Prior          0.56076    0.02784  20.141  < 2e-16 ***
## VA             1.74008    0.12992  13.393  < 2e-16 ***
## CTT2           0.36997    0.19074   1.940 0.052449 .  
## CTT3           0.61773    0.16361   3.776 0.000160 ***
## Prior:VA      -0.14247    0.04541  -3.138 0.001706 ** 
## Prior:CTT2    -0.07730    0.06548  -1.181 0.237801    
## Prior:CTT3    -0.06534    0.05391  -1.212 0.225532    
## VA:CTT2       -1.07200    0.30958  -3.463 0.000536 ***
## VA:CTT3       -1.03849    0.26535  -3.914 9.14e-05 ***
## Prior:VA:CTT2  0.24292    0.10628   2.286 0.022294 *  
## Prior:VA:CTT3  0.09134    0.08743   1.045 0.296154    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 1.523505)
## 
##     Null deviance: 25703  on 14055  degrees of freedom
## Residual deviance: 21396  on 14044  degrees of freedom
## AIC: 45821
## 
## Number of Fisher Scoring iterations: 2

The last block is the generalized linear model analysis for Study 2 results of confidence.

model_confidence <- glm(Score~Prior*VA*CT, data = data_s2_confidence)
summary(model_confidence)
## 
## Call:
## glm(formula = Score ~ Prior * VA * CT, data = data_s2_confidence)
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    2.62970    0.17943  14.656  < 2e-16 ***
## Prior          0.35639    0.04532   7.865 3.97e-15 ***
## VA             1.11443    0.29096   3.830 0.000129 ***
## CTT2          -0.35988    0.44437  -0.810 0.418035    
## CTT3          -1.05642    0.43477  -2.430 0.015117 *  
## Prior:VA      -0.26932    0.07352  -3.663 0.000250 ***
## Prior:CTT2     0.12189    0.11607   1.050 0.293701    
## Prior:CTT3     0.22971    0.11266   2.039 0.041467 *  
## VA:CTT2       -0.71385    0.72445  -0.985 0.324462    
## VA:CTT3       -0.10112    0.70396  -0.144 0.885780    
## Prior:VA:CTT2  0.12775    0.18921   0.675 0.499572    
## Prior:VA:CTT3  0.05554    0.18241   0.304 0.760755    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 1.087497)
## 
##     Null deviance: 15566  on 14055  degrees of freedom
## Residual deviance: 15273  on 14044  degrees of freedom
## AIC: 41082
## 
## Number of Fisher Scoring iterations: 2