setwd("~/Documents/Dropbox/Research/Don")
r<-read.csv ("JMR_algorithms_new_performance_rigidity.csv", header=T, sep=",")

Testing for Interaction between objectivity and rigidity manipulation

r$recept<-(r$r1 + r$r2 + (8-r$r3R) + (8-r$r4R))/4

r$rigid[r$rigid==1]<-"rigid"
r$rigid[r$notrigid==1]<-"notrigid"

long <- reshape(r, 
                   varying = c("car_1", "joke_1", "cancer_1", "movie_1", "psych_1", "parole_1", "gpa_1", "job_1"), 
                   v.names = "trust",
                   timevar = "task", 
                   times = c("car_1", "joke_1", "cancer_1", "movie_1", "psych_1", "parole_1", "A_gpa_1", "job_1"), 
                   direction = "long")

#taking objectivity ratings from previous study. 
long$obj[long$task=="car_1"]<-69
long$obj[long$task=="joke_1"]<-27
long$obj[long$task=="cancer_1"]<-69
long$obj[long$task=="movie_1"]<-23
long$obj[long$task=="psych_1"]<-77
long$obj[long$task=="parole_1"]<-45
long$obj[long$task=="A_gpa_1"]<-52
long$obj[long$task=="job_1"]<-51


#this is binary measure of objectivity
long$obj2[long$obj>50]<-"obj"
long$obj2[long$obj<50]<-"subj"

summary(aov(trust ~ obj * rigid, long))
##               Df  Sum Sq Mean Sq F value Pr(>F)  
## obj            1    5523    5523   5.328 0.0211 *
## rigid          1       1       1   0.001 0.9735  
## obj:rigid      1    1780    1780   1.717 0.1902  
## Residuals   1732 1795216    1036                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1496 observations deleted due to missingness
summary(aov(trust ~ obj2 * rigid, long))
##               Df  Sum Sq Mean Sq F value   Pr(>F)    
## obj2           1   13122   13122  12.708 0.000374 ***
## rigid          1       1       1   0.001 0.973478    
## obj2:rigid     1     980     980   0.949 0.330010    
## Residuals   1732 1788416    1033                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1496 observations deleted due to missingness

Interaction between rigidness manipulation and performance manipulation? Also just looking at main effects, no interaction term.

r$rigid[r$rigid==1]<-"rigid"
r$rigid[r$notrigid==1]<-"notrigid"

personality <- reshape(r, 
                   varying = c("personality_1","Q56_1"), 
                   v.names = "personality",
                   timevar = "performance", 
                   times = c("yes","no"), 
                   direction = "long")

summary(lm(personality ~ rigid * performance, personality))
## 
## Call:
## lm(formula = personality ~ rigid * performance, data = personality)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -73.64 -20.00   7.36  22.47  40.00 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 73.640      2.924  25.186   <2e-16 ***
## rigidrigid                  -8.180      4.287  -1.908   0.0571 .  
## performanceyes              -8.106      4.105  -1.975   0.0490 *  
## rigidrigid:performanceyes    2.646      5.846   0.453   0.6510    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29.24 on 400 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.02838,    Adjusted R-squared:  0.02109 
## F-statistic: 3.894 on 3 and 400 DF,  p-value: 0.009179
summary(lm(personality ~ rigid + performance, personality))
## 
## Call:
## lm(formula = personality ~ rigid + performance, data = personality)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -72.978 -19.419   8.022  22.022  40.581 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      72.978      2.529  28.852   <2e-16 ***
## rigidrigid       -6.757      2.912  -2.321   0.0208 *  
## performanceyes   -6.801      2.920  -2.329   0.0203 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29.21 on 401 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.02788,    Adjusted R-squared:  0.02303 
## F-statistic: 5.751 on 2 and 401 DF,  p-value: 0.003449
car <- reshape(r, 
                   varying = c("car_1","Q57_1"), 
                   v.names = "car",
                   timevar = "performance", 
                   times = c("yes","no"), 
                   direction = "long")

summary(lm(car ~ rigid * performance, car))
## 
## Call:
## lm(formula = car ~ rigid * performance, data = car)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -73.793 -30.331   8.444  26.375  53.307 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 65.420      3.482  18.787  < 2e-16 ***
## rigidrigid                   8.373      5.105   1.640  0.10177    
## performanceyes             -15.119      4.889  -3.093  0.00212 ** 
## rigidrigid:performanceyes  -11.981      6.962  -1.721  0.08604 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 34.82 on 400 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.08985,    Adjusted R-squared:  0.08303 
## F-statistic: 13.16 on 3 and 400 DF,  p-value: 3.261e-08
summary(lm(car ~ rigid + performance, car))
## 
## Call:
## lm(formula = car ~ rigid + performance, data = car)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -70.35 -30.32   9.63  29.65  52.61 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      68.417      3.023  22.635  < 2e-16 ***
## rigidrigid        1.931      3.480   0.555    0.579    
## performanceyes  -21.026      3.489  -6.026 3.81e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 34.91 on 401 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.08311,    Adjusted R-squared:  0.07854 
## F-statistic: 18.18 on 2 and 401 DF,  p-value: 2.781e-08
joke <- reshape(r, 
                   varying = c("joke_1","Q58_1"), 
                   v.names = "trust",
                   timevar = "performance", 
                   times = c("yes","no"), 
                   direction = "long")

summary(lm(trust ~ rigid * performance, joke))
## 
## Call:
## lm(formula = trust ~ rigid * performance, data = joke)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -76.620 -13.675   7.325  19.057  37.757 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 76.620      2.642  29.004  < 2e-16 ***
## rigidrigid                   4.323      3.873   1.116 0.265054    
## performanceyes             -14.377      3.709  -3.877 0.000124 ***
## rigidrigid:performanceyes   -1.890      5.282  -0.358 0.720678    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 26.42 on 400 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.07954,    Adjusted R-squared:  0.07264 
## F-statistic: 11.52 on 3 and 400 DF,  p-value: 2.928e-07
summary(lm(trust ~ rigid + performance, joke))
## 
## Call:
## lm(formula = trust ~ rigid + performance, data = joke)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -77.09 -14.09   6.91  19.60  38.22 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      77.093      2.285  33.738  < 2e-16 ***
## rigidrigid        3.306      2.630   1.257    0.209    
## performanceyes  -15.309      2.638  -5.804 1.32e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 26.39 on 401 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.07925,    Adjusted R-squared:  0.07466 
## F-statistic: 17.26 on 2 and 401 DF,  p-value: 6.462e-08
cancer <- reshape(r, 
                   varying = c("cancer_1","Q59_1"), 
                   v.names = "trust",
                   timevar = "performance", 
                   times = c("yes","no"), 
                   direction = "long")

summary(lm(trust ~ rigid * performance, cancer))
## 
## Call:
## lm(formula = trust ~ rigid * performance, data = cancer)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -68.598 -28.598   0.665  28.589  59.096 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 62.580      3.220  19.435  < 2e-16 ***
## rigidrigid                   6.018      4.721   1.275    0.203    
## performanceyes             -17.813      4.520  -3.941 9.59e-05 ***
## rigidrigid:performanceyes   -9.881      6.438  -1.535    0.126    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 32.2 on 400 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.1152, Adjusted R-squared:  0.1086 
## F-statistic: 17.36 on 3 and 400 DF,  p-value: 1.297e-10
summary(lm(trust ~ rigid + performance, cancer))
## 
## Call:
## lm(formula = trust ~ rigid + performance, data = cancer)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -65.756 -27.367   0.781  28.415  57.633 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     65.0518     2.7929  23.292  < 2e-16 ***
## rigidrigid       0.7047     3.2151   0.219    0.827    
## performanceyes -22.6847     3.2240  -7.036  8.6e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 32.25 on 401 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:   0.11,  Adjusted R-squared:  0.1055 
## F-statistic: 24.77 on 2 and 401 DF,  p-value: 7.163e-11
movie <- reshape(r, 
                   varying = c("movie_1","Q60_1"), 
                   v.names = "trust",
                   timevar = "performance", 
                   times = c("yes","no"), 
                   direction = "long")

summary(lm(trust ~ rigid * performance, movie))
## 
## Call:
## lm(formula = trust ~ rigid * performance, data = movie)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -66.724 -26.724   4.835  25.700  54.835 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 59.300      3.087  19.212   <2e-16 ***
## rigidrigid                   7.424      4.525   1.641   0.1017    
## performanceyes             -14.135      4.333  -3.262   0.0012 ** 
## rigidrigid:performanceyes   -4.826      6.171  -0.782   0.4347    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 30.87 on 400 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.07155,    Adjusted R-squared:  0.06458 
## F-statistic: 10.27 on 3 and 400 DF,  p-value: 1.572e-06
summary(lm(trust ~ rigid + performance, movie))
## 
## Call:
## lm(formula = trust ~ rigid + performance, data = movie)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -65.336 -25.586   5.578  25.749  56.007 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      60.507      2.672  22.649  < 2e-16 ***
## rigidrigid        4.829      3.075   1.570    0.117    
## performanceyes  -16.514      3.084  -5.355 1.44e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 30.85 on 401 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.07013,    Adjusted R-squared:  0.06549 
## F-statistic: 15.12 on 2 and 401 DF,  p-value: 4.664e-07
psych <- reshape(r, 
                   varying = c("psych_1","Q61_1"), 
                   v.names = "trust",
                   timevar = "performance", 
                   times = c("yes","no"), 
                   direction = "long")

summary(lm(trust ~ rigid * performance, psych))
## 
## Call:
## lm(formula = trust ~ rigid * performance, data = psych)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -77.310 -19.851   5.499  22.690  46.149 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 74.040      2.751  26.910  < 2e-16 ***
## rigidrigid                   3.270      4.034   0.811    0.418    
## performanceyes             -19.079      3.863  -4.939 1.15e-06 ***
## rigidrigid:performanceyes   -4.381      5.501  -0.796    0.426    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 27.51 on 400 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.131,  Adjusted R-squared:  0.1245 
## F-statistic:  20.1 on 3 and 400 DF,  p-value: 3.766e-12
summary(lm(trust ~ rigid + performance, psych))
## 
## Call:
## lm(formula = trust ~ rigid + performance, data = psych)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -76.051 -19.833   5.188  22.378  46.103 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     75.1358     2.3815  31.550   <2e-16 ***
## rigidrigid       0.9149     2.7415   0.334    0.739    
## performanceyes -21.2386     2.7490  -7.726    9e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 27.5 on 401 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.1296, Adjusted R-squared:  0.1253 
## F-statistic: 29.85 on 2 and 401 DF,  p-value: 8.204e-13
parole <- reshape(r, 
                   varying = c("parole_1","Q62_1"), 
                   v.names = "trust",
                   timevar = "performance", 
                   times = c("yes","no"), 
                   direction = "long")

summary(lm(trust ~ rigid * performance, parole))
## 
## Call:
## lm(formula = trust ~ rigid * performance, data = parole)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -76.103 -25.516   3.788  23.897  52.680 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 67.900      3.111  21.827  < 2e-16 ***
## rigidrigid                   8.203      4.561   1.799   0.0728 .  
## performanceyes             -20.580      4.367  -4.712 3.39e-06 ***
## rigidrigid:performanceyes   -7.252      6.220  -1.166   0.2443    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 31.11 on 400 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.1352, Adjusted R-squared:  0.1288 
## F-statistic: 20.85 on 3 and 400 DF,  p-value: 1.43e-12
summary(lm(trust ~ rigid + performance, parole))
## 
## Call:
## lm(formula = trust ~ rigid + performance, data = parole)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -74.018 -24.902   5.363  25.982  54.441 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      69.714      2.695  25.868  < 2e-16 ***
## rigidrigid        4.304      3.102   1.387    0.166    
## performanceyes  -24.155      3.111  -7.765 6.91e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 31.12 on 401 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.1323, Adjusted R-squared:  0.128 
## F-statistic: 30.57 on 2 and 401 DF,  p-value: 4.398e-13
gpa <- reshape(r, 
                   varying = c("gpa_1","Q63_1"), 
                   v.names = "trust",
                   timevar = "performance", 
                   times = c("yes","no"), 
                   direction = "long")

summary(lm(trust ~ rigid * performance, gpa))
## 
## Call:
## lm(formula = trust ~ rigid * performance, data = gpa)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -61.126 -30.515  -2.063  29.388  58.534 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 55.660      3.290  16.916  < 2e-16 ***
## rigidrigid                   5.466      4.824   1.133  0.25782    
## performanceyes             -14.194      4.619  -3.073  0.00227 ** 
## rigidrigid:performanceyes   -4.011      6.579  -0.610  0.54237    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 32.9 on 400 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.05895,    Adjusted R-squared:  0.0519 
## F-statistic: 8.353 on 3 and 400 DF,  p-value: 2.126e-05
summary(lm(trust ~ rigid + performance, gpa))
## 
## Call:
## lm(formula = trust ~ rigid + performance, data = gpa)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -59.973 -29.973  -1.492  30.070  59.508 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      56.663      2.847  19.902  < 2e-16 ***
## rigidrigid        3.310      3.277   1.010    0.313    
## performanceyes  -16.172      3.286  -4.921 1.26e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 32.88 on 401 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.05808,    Adjusted R-squared:  0.05338 
## F-statistic: 12.36 on 2 and 401 DF,  p-value: 6.164e-06
job <- reshape(r, 
                   varying = c("job_1","Q64_1"), 
                   v.names = "trust",
                   timevar = "performance", 
                   times = c("yes","no"), 
                   direction = "long")

summary(lm(trust ~ rigid * performance, job))
## 
## Call:
## lm(formula = trust ~ rigid * performance, data = job)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -73.126 -27.718   3.289  26.874  53.845 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 65.740      3.188  20.620  < 2e-16 ***
## rigidrigid                   7.386      4.674   1.580    0.115    
## performanceyes             -19.585      4.476  -4.376 1.55e-05 ***
## rigidrigid:performanceyes   -5.831      6.374  -0.915    0.361    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 31.88 on 400 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.1138, Adjusted R-squared:  0.1071 
## F-statistic: 17.12 on 3 and 400 DF,  p-value: 1.777e-10
summary(lm(trust ~ rigid + performance, job))
## 
## Call:
## lm(formula = trust ~ rigid + performance, data = job)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -71.450 -28.397   2.676  27.261  55.261 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      67.199      2.760  24.346  < 2e-16 ***
## rigidrigid        4.251      3.177   1.338    0.182    
## performanceyes  -22.460      3.186  -7.049 7.92e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 31.87 on 401 degrees of freedom
##   (404 observations deleted due to missingness)
## Multiple R-squared:  0.1119, Adjusted R-squared:  0.1075 
## F-statistic: 25.27 on 2 and 401 DF,  p-value: 4.63e-11
library(metap)
#pooled p values... first for rigidity: 
vcont<-c(.05, .11, .26, .20, .10, .42, .07, .26, .11)
sumlog(vcont)
## chisq =  35.08643  with df =  18  p =  0.009218434
#then for interaction
vcont<-c(.65, .09, .72, .13, .44, .43, .24, .54, .36)
sumlog(vcont)
## chisq =  19.87472  with df =  18  p =  0.3399171

T-tests, for each task compared to scale midpoint (trust both algorithm and human equally)

t.test(r$personality_1, mu=50)
## 
##  One Sample t-test
## 
## data:  r$personality_1
## t = 6.2862, df = 216, p-value = 1.775e-09
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  58.66767 66.58579
## sample estimates:
## mean of x 
##  62.62673
t.test(r$car_1, mu=50)
## 
##  One Sample t-test
## 
## data:  r$car_1
## t = -0.67478, df = 216, p-value = 0.5005
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  43.74811 53.06295
## sample estimates:
## mean of x 
##  48.40553
t.test(r$joke_1, mu=50)
## 
##  One Sample t-test
## 
## data:  r$joke_1
## t = 7.098, df = 216, p-value = 1.796e-11
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  59.76623 67.27525
## sample estimates:
## mean of x 
##  63.52074
t.test(r$cancer_1, mu=50)
## 
##  One Sample t-test
## 
## data:  r$cancer_1
## t = -3.3688, df = 216, p-value = 0.0008938
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  38.48815 46.98650
## sample estimates:
## mean of x 
##  42.73733
t.test(r$movie_1, mu=50)
## 
##  One Sample t-test
## 
## data:  r$movie_1
## t = -1.6988, df = 216, p-value = 0.0908
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  42.50385 50.55606
## sample estimates:
## mean of x 
##  46.52995
t.test(r$psych_1, mu=50)
## 
##  One Sample t-test
## 
## data:  r$psych_1
## t = 2.2392, df = 216, p-value = 0.02616
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  50.52436 58.23140
## sample estimates:
## mean of x 
##  54.37788
t.test(r$parole_1, mu=50)
## 
##  One Sample t-test
## 
## data:  r$parole_1
## t = -0.99897, df = 216, p-value = 0.3189
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  43.51959 52.12096
## sample estimates:
## mean of x 
##  47.82028
t.test(r$gpa_1, mu=50)
## 
##  One Sample t-test
## 
## data:  r$gpa_1
## t = -3.5061, df = 216, p-value = 0.000553
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  37.86258 46.59825
## sample estimates:
## mean of x 
##  42.23041
t.test(r$job_1, mu=50)
## 
##  One Sample t-test
## 
## data:  r$job_1
## t = -1.3064, df = 216, p-value = 0.1928
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  42.40456 51.54014
## sample estimates:
## mean of x 
##  46.97235

We also measured receptivity to algorithms - that doesn’t interact with either manipulation either.

hist(r$recept)

long$rigid[long$rigid==1]<-"rigid"
long$rigid[long$notrigid==1]<-"notrigid"

summary(aov(trust ~ recept * rigid, long))
##                Df  Sum Sq Mean Sq F value Pr(>F)    
## recept          1  133211  133211 138.256 <2e-16 ***
## rigid           1     264     264   0.274  0.601    
## recept:rigid    1     250     250   0.260  0.610    
## Residuals    1732 1668795     964                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1496 observations deleted due to missingness
summary(aov(trust ~ recept * obj, long))
##               Df  Sum Sq Mean Sq F value Pr(>F)    
## recept         1  133211  133211 138.713 <2e-16 ***
## obj            1    5523    5523   5.751 0.0166 *  
## recept:obj     1     491     491   0.512 0.4746    
## Residuals   1732 1663295     960                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1496 observations deleted due to missingness