L & B Practical 2023

Descriptive Statistics

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    
hist(LandBpracdata2023Nomissing$Age)

describe(LandBpracdata2023Nomissing)
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 
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 
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.

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 beliefs and the Everyday illusions scales will be positively associated with a greater experimental illusion of control (taskrating and controlrating).

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

describeBy(LandBpracdata2023Nomissing, group=LandBpracdata2023Nomissing$Strategy)

 Descriptive statistics by group 
group: Yes, strategy
---------------------------------------------------- 
group: No 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

Exploratory Analysis

Gender differences

Females will score higher in drakes and Everyday illusions than males

t.test(Drake ~ Gender, data=LandBpracdata2023Nomissing)

    Welch Two Sample t-test

data:  Drake by Gender
t = -1.0202, df = 304.99, p-value = 0.3085
alternative hypothesis: true difference in means between group Male and group Female is not equal to 0
95 percent confidence interval:
 -3.999860  1.268551
sample estimates:
  mean in group Male mean in group Female 
            30.27673             31.64238 
cohensD(Drake ~ Gender, data=LandBpracdata2023Nomissing)
[1] 0.1154691
t.test(EverydayIllusions ~ Gender, data=LandBpracdata2023Nomissing)

    Welch Two Sample t-test

data:  EverydayIllusions by Gender
t = 0.044391, df = 307.62, p-value = 0.9646
alternative hypothesis: true difference in means between group Male and group Female is not equal to 0
95 percent confidence interval:
 -1.339023  1.400833
sample estimates:
  mean in group Male mean in group Female 
            35.66667             35.63576 
cohensD(EverydayIllusions ~ Gender, data=LandBpracdata2023Nomissing)
[1] 0.005032788

Females will press more times than males

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

    Welch Two Sample t-test

data:  Presses by Gender
t = 0.072192, df = 307.81, p-value = 0.9425
alternative hypothesis: true difference in means between group Male and group Female is not equal to 0
95 percent confidence interval:
 -104.4161  112.3696
sample estimates:
  mean in group Male mean in group Female 
            429.7582             425.7815 
cohensD(Presses ~ Gender, data=LandBpracdata2023Nomissing)
[1] 0.008197438

Females will score higher on taskrating than males

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

    Welch Two Sample t-test

data:  Taskrating by Gender
t = -1.3672, df = 302.72, p-value = 0.1726
alternative hypothesis: true difference in means between group Male and group Female is not equal to 0
95 percent confidence interval:
 -10.633130   1.914899
sample estimates:
  mean in group Male mean in group Female 
            24.52830             28.88742 
cohensD(Taskrating~ Gender, data=LandBpracdata2023Nomissing)
[1] 0.1556825

Females will score higher on controlrating than males

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

    Welch Two Sample t-test

data:  Controlrating by Gender
t = -0.77365, df = 307.47, p-value = 0.4397
alternative hypothesis: true difference in means between group Male and group Female is not equal to 0
95 percent confidence interval:
 -8.433123  3.673241
sample estimates:
  mean in group Male mean in group Female 
            23.42138             25.80132 
cohensD(Controlrating~ Gender, data=LandBpracdata2023Nomissing)
[1] 0.08788667

Gender and strategy

Confusion_Matrix2 <- table(LandBpracdata2023Nomissing$Gender, LandBpracdata2023Nomissing$Strategy)
prop.table(Confusion_Matrix2, margin=2) 
        
         Yes, strategy No strategy
  Male       0.5294118   0.4964029
  Female     0.4705882   0.5035971
chisq.test(Confusion_Matrix2,correct=FALSE)

    Pearson's Chi-squared test

data:  Confusion_Matrix2
X-squared = 0.33358, df = 1, p-value = 0.5636
table(LandBpracdata2023Nomissing$Gender, LandBpracdata2023Nomissing$Strategy) 
        
         Yes, strategy No strategy
  Male              90          69
  Female            80          70

Age differences-Correlations

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

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$Controlrating and LandBpracdata2023Nomissing$Age
t = 0.98837, df = 309, p-value = 0.3237
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.05542545  0.16631684
sample estimates:
       cor 
0.05613792 
cor.test(LandBpracdata2023Nomissing$Taskrating, LandBpracdata2023Nomissing$Age)

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$Taskrating and LandBpracdata2023Nomissing$Age
t = 0.80154, df = 309, p-value = 0.4234
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.06600095  0.15597786
sample estimates:
       cor 
0.04555073 
cor.test(LandBpracdata2023Nomissing$Presses, LandBpracdata2023Nomissing$Age)

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$Presses and LandBpracdata2023Nomissing$Age
t = -0.48956, df = 309, p-value = 0.6248
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.13862740  0.08363697
sample estimates:
       cor 
-0.0278393 
cor.test(LandBpracdata2023Nomissing$Drake, LandBpracdata2023Nomissing$Age)

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$Drake and LandBpracdata2023Nomissing$Age
t = -1.5133, df = 309, p-value = 0.1312
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.19512471  0.02569373
sample estimates:
        cor 
-0.08576868 
cor.test(LandBpracdata2023Nomissing$EverydayIllusions, LandBpracdata2023Nomissing$Age)

    Pearson's product-moment correlation

data:  LandBpracdata2023Nomissing$EverydayIllusions and LandBpracdata2023Nomissing$Age
t = -3.0989, df = 309, p-value = 0.002121
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.27943741 -0.06362703
sample estimates:
       cor 
-0.1736158 
t.test(Age~ Strategy, data=LandBpracdata2023Nomissing)

    Welch Two Sample t-test

data:  Age by Strategy
t = -1.0365, df = 297.86, p-value = 0.3008
alternative hypothesis: true difference in means between group Yes, strategy and group No strategy is not equal to 0
95 percent confidence interval:
 -5.397268  1.673258
sample estimates:
mean in group Yes, strategy   mean in group No strategy 
                   31.90058                    33.76259 
cohensD(Age~ Strategy, data=LandBpracdata2023Nomissing)
[1] 0.118081
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