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Descriptives

summary(LandBpracdata2023Nomissing)

       ID           Gender         Age            InstructionCond
 Min.   :  1.0   Male  :159   Min.   :13.00   Naturalistic:169   
 1st Qu.: 79.5   Female:151   1st Qu.:21.00   Analytic    :142   
 Median :164.0   NA's  :  1   Median :24.00                      
 Mean   :163.4                Mean   :32.75                      
 3rd Qu.:245.5                3rd Qu.:49.00                      
 Max.   :325.0                Max.   :76.00                      
    Presses           Taskrating     Controlrating   
 Min.   :   1.556   Min.   :  0.00   Min.   :  0.00  
 1st Qu.:  93.500   1st Qu.:  0.00   1st Qu.:  0.00  
 Median : 265.000   Median : 20.00   Median : 15.00  
 Mean   : 427.700   Mean   : 26.79   Mean   : 24.66  
 3rd Qu.: 541.500   3rd Qu.: 50.00   3rd Qu.: 50.00  
 Max.   :2864.000   Max.   :100.00   Max.   :100.00  
          Strategy       Drake       EverydayIllusions
 Yes, strategy:171   Min.   :11.00   Min.   :17.00    
 No strategy  :139   1st Qu.:21.00   1st Qu.:32.00    
 NA's         :  1   Median :31.00   Median :36.00    
                     Mean   :30.93   Mean   :35.61    
                     3rd Qu.:39.00   3rd Qu.:40.00    
                     Max.   :55.00   Max.   :56.00    

describeBy(LandBpracdata2023Nomissing, group = LandBpracdata2023Nomissing$InstructionCond)

 Descriptive statistics by group 
group: Naturalistic

------------------------------------------------------ 
group: Analytic

Hypothesis 1a & 1b:Subjective rating of task: 1: Participants in the naturalistic condition should rate the task as more controllable and that they personally exerted more control compared to the ones in the analytical condition.

t.test(Taskrating ~ InstructionCond, data=LandBpracdata2023Nomissing)

    Welch Two Sample t-test

data:  Taskrating by InstructionCond
t = 2.0639, df = 303.06, p-value = 0.03988
alternative hypothesis: true difference in means between group Naturalistic and group Analytic is not equal to 0
95 percent confidence interval:
  0.304916 12.792425
sample estimates:
mean in group Naturalistic     mean in group Analytic 
                  29.78107                   23.23239 

hist(LandBpracdata2023Nomissing$Taskrating)

cohensD(Taskrating ~ InstructionCond, LandBpracdata2023Nomissing)

[1] 0.2342429

t.test(Controlrating ~ InstructionCond, data=LandBpracdata2023Nomissing)

    Welch Two Sample t-test

data:  Controlrating by InstructionCond
t = 2.8669, df = 307.18, p-value = 0.004431
alternative hypothesis: true difference in means between group Naturalistic and group Analytic is not equal to 0
95 percent confidence interval:
  2.715474 14.599802
sample estimates:
mean in group Naturalistic     mean in group Analytic 
                  28.61538                   19.95775 

hist(LandBpracdata2023Nomissing$Controlrating)

cohensD(Controlrating ~ InstructionCond, LandBpracdata2023Nomissing)

[1] 0.3236142

Behavioural effects: Hypothesis 2 Participants who receive the naturalistic instructions should press the buttons more than those who receive the analytical instructions.

hist(LandBpracdata2023Nomissing$Presses)

t.test(Presses ~ InstructionCond, data=LandBpracdata2023Nomissing)

    Welch Two Sample t-test

data:  Presses by InstructionCond
t = -0.2854, df = 279.04, p-value = 0.7755
alternative hypothesis: true difference in means between group Naturalistic and group Analytic is not equal to 0
95 percent confidence interval:
 -125.95195   94.05454
sample estimates:
mean in group Naturalistic     mean in group Analytic 
                  420.4175                   436.3662 

cohensD(Presses ~ InstructionCond, LandBpracdata2023Nomissing)

[1] 0.03293285

Hypotheses 3: Perception of Strategy: People who are allocated to the naturalistic condition will be more likely to report a strategy than those in the analytical condition.

Confusion_Matrix <- table(LandBpracdata2023Nomissing$InstructionCond, LandBpracdata2023Nomissing$Strategy)
prop.table(Confusion_Matrix, margin=2) 

              
               Yes, strategy No strategy
  Naturalistic     0.6081871   0.4604317
  Analytic         0.3918129   0.5395683

chisq.test(Confusion_Matrix,correct=FALSE)

    Pearson's Chi-squared test

data:  Confusion_Matrix
X-squared = 6.7431, df = 1, p-value = 0.009411

table(LandBpracdata2023Nomissing$InstructionCond, LandBpracdata2023Nomissing$Strategy) 

              
               Yes, strategy No strategy
  Naturalistic           104          64
  Analytic                67          75

Hypotheses 4: The relationship between individual difference and experimental measures: 4a: Scores on the Drake and the Everyday beliefs about control scale will be positively associated with a greater experimental illusion of control.

4b: Scores on the Drake and the Everyday beliefs about control scale will be positively associated with a greater number of presses.

plot(LandBpracdata2023Nomissing$Drake, LandBpracdata2023Nomissing$Taskrating)

plot(LandBpracdata2023Nomissing$EverydayIllusions, LandBpracdata2023Nomissing$Taskrating)

plot(LandBpracdata2023Nomissing$Drake, LandBpracdata2023Nomissing$Controlrating)

plot(LandBpracdata2023Nomissing$EverydayIllusions, LandBpracdata2023Nomissing$Controlrating)

plot(LandBpracdata2023Nomissing$Drake, LandBpracdata2023Nomissing$Presses)

plot(LandBpracdata2023Nomissing$EverydayIllusions, LandBpracdata2023Nomissing$Presses)

cor.test(LandBpracdata2023Nomissing$Controlrating, LandBpracdata2023Nomissing$Drake)

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$Controlrating and LandBpracdata2023Nomissing$Drake
t = 0.82057, df = 309, p-value = 0.4125
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.0649244  0.1570326
sample estimates:
       cor 
0.04662962 

cor.test(LandBpracdata2023Nomissing$Taskrating, LandBpracdata2023Nomissing$Drake)

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$Taskrating and LandBpracdata2023Nomissing$Drake
t = 0.59589, df = 309, p-value = 0.5517
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.07763032  0.14455216
sample estimates:
       cor 
0.03387951 

cor.test(LandBpracdata2023Nomissing$Presses, LandBpracdata2023Nomissing$Drake)

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$Presses and LandBpracdata2023Nomissing$Drake
t = 2.2999, df = 309, p-value = 0.02212
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.01878618 0.23752267
sample estimates:
      cor 
0.1297324 

cor.test(LandBpracdata2023Nomissing$Controlrating, LandBpracdata2023Nomissing$EverydayIllusions)

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$Controlrating and LandBpracdata2023Nomissing$EverydayIllusions
t = 3.9296, df = 309, p-value = 0.000105
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.1096043 0.3215770
sample estimates:
      cor 
0.2181622 

cor.test(LandBpracdata2023Nomissing$Taskrating, LandBpracdata2023Nomissing$EverydayIllusions)

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$Taskrating and LandBpracdata2023Nomissing$EverydayIllusions
t = 2.5366, df = 309, p-value = 0.01169
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.03211299 0.25006548
sample estimates:
      cor 
0.1428202 

cor.test(LandBpracdata2023Nomissing$Presses, LandBpracdata2023Nomissing$EverydayIllusions)

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$Presses and LandBpracdata2023Nomissing$EverydayIllusions
t = 3.2795, df = 309, p-value = 0.001159
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.07368587 0.28872825
sample estimates:
      cor 
0.1834002 

Hypotheses 5: Association between experimental measures 5a: The number of button presses will be higher for those who report having found a strategy.

t.test(Presses ~ Strategy, data=LandBpracdata2023Nomissing)

    Welch Two Sample t-test

data:  Presses by Strategy
t = 1.349, df = 282.77, p-value = 0.1784
alternative hypothesis: true difference in means between group Yes, strategy and group No strategy is not equal to 0
95 percent confidence interval:
 -34.52567 184.93337
sample estimates:
mean in group Yes, strategy   mean in group No strategy 
                   462.1319                    386.9281 

cohensD(Presses ~ Strategy, LandBpracdata2023Nomissing)

[1] 0.1555362

5b:The two experimental measures of control (Is it controllable AND did the person’s rating of control) should be higher for those who reported finding a strategy.

t.test(Controlrating ~ Strategy, data=LandBpracdata2023Nomissing)

    Welch Two Sample t-test

data:  Controlrating by Strategy
t = 7.7525, df = 303.09, p-value = 1.376e-13
alternative hypothesis: true difference in means between group Yes, strategy and group No strategy is not equal to 0
95 percent confidence interval:
 15.92227 26.75517
sample estimates:
mean in group Yes, strategy   mean in group No strategy 
                   34.30994                    12.97122 

cohensD(Controlrating ~ Strategy, data=LandBpracdata2023Nomissing)

[1] 0.8559567

t.test(Taskrating~ Strategy, data=LandBpracdata2023Nomissing)

    Welch Two Sample t-test

data:  Taskrating by Strategy
t = 5.5632, df = 303.93, p-value = 5.814e-08
alternative hypothesis: true difference in means between group Yes, strategy and group No strategy is not equal to 0
95 percent confidence interval:
 10.92355 22.88082
sample estimates:
mean in group Yes, strategy   mean in group No strategy 
                   34.45614                    17.55396 

cohensD(Taskrating ~ Strategy, data=LandBpracdata2023Nomissing)

[1] 0.6292935

Hypothesis 6:Measure validity: Scores on the two illusion of control measures (i.e., Drake and Everyday Illusions) will be positively correlated.

cor.test(LandBpracdata2023Nomissing$Drake, LandBpracdata2023Nomissing$EverydayIllusions)

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$Drake and LandBpracdata2023Nomissing$EverydayIllusions
t = 2.1074, df = 309, p-value = 0.03589
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.00792127 0.22724266
sample estimates:
      cor 
0.1190337 

plot(LandBpracdata2023Nomissing$Drake, LandBpracdata2023Nomissing$EverydayIllusions)