Analysis fixes

* ANOVA table built and used correctly
* Influence calculated as Niccolo did
* ANOVA uses trial data instead of summary

AdvisorChoice/analysis/AdvisorChoice.R

@@ -30,8 +30,8 @@ if(!exists("getMatlabData", mode="function")) {
 } 
 
 
-#acPth <- "C:/Users/mj221/Filr/My Files/Results/AdvisorChoice"
-acPth <- "D:/Users/MJ/Filr/My Files/Results/AdvisorChoice"
+acPth <- "C:/Users/mj221/Filr/My Files/Results/AdvisorChoice"
+#acPth <- "D:/Users/MJ/Filr/My Files/Results/AdvisorChoice"
 
 raw_study <- getMatlabData(acPth)  # get some data from the path defined for convenience in mat2R
 
@@ -162,49 +162,81 @@ print('## 3) ANOVA investigating influence #####################################
 # since it will come in handy for looking at influence on subsets of trials
 # later. Below, we run an ANOVA using the influence data.
 
-# TODO: change this to match Niccolo's definiton of influence/sway
-
 print('Calculating influence on each trial')
 # Calculate the influence of the advisor on each trial
-trial_influence <- vector('list',length(study))
+trial_influence <- data.frame(pId=integer(),
+                              tId=integer(),
+                              block=integer(), 
+                              advisorId=integer(), 
+                              adviceType=integer(), #  1=Agree-in-confidence; 2=Agree-in-uncertainty
+                              choiceAllowed=integer(), #  F=forced; T=choice
+                              agree=integer(), #  F=disagree; T=agree
+                              initialAnswerRight=integer(), #  F=left; T=right
+                              initialConfidenceCategory=integer(), # whether initial answer was low/med/high confidence
+                              shift=integer(),  #  amount the confidence changes
+                              influence=integer()) #  amount the confidence changes in the direction of the advice
 for(p in seq(length(study))) {
-  p_data <- data.frame('id'=integer(), 'direction'=integer(), 'influence'=integer())
-  trials <- study[[p]]$trials
+  # skip practice trials
+  trials <- study[[p]]$trials[which(study[[p]]$trials[,"practice"]==FALSE),]
+  advisorIds <- as.numeric(study[[p]]$cfg$advisor[seq(1,length(study[[p]]$cfg$advisor),6)])
+  advisorAdviceTypes <- as.numeric(study[[p]]$cfg$advisor[seq(2,length(study[[p]]$cfg$advisor),6)])
   for(t in seq(dim(trials)[1])) {
-    # store the index of this trial in the master trial list
+    # store basic trial information 
     tid <- trials[t, "id"]
+    aT <- advisorAdviceTypes[as.numeric(trials[t,"advisorId"])]
+    cA <- lapply(trials[t,"choice"],mean)>1
+    t_data <- data.frame(pId=p,
+                         tId=tid,
+                         block=trials[t,"block"],
+                         advisorId=trials[t,"advisorId"],
+                         adviceType=aT,
+                         choiceAllowed=cA,
+                         agree=trials[t,"agree"],
+                         initialAnswerRight=trials[t,"cj1"]>0,
+                         initialConfidenceCategory=NA)
     if(is.nan(trials[[t,"advisorId"]])) {
       # trials without an advisor are entered as NA
-      p_data <- rbind(p_data, data.frame(id=tid,direction=NA,influence=NA))
-      next 
-    }
-    # calculate the influence of the advice
-    cj1 <- trials[[t,"cj1"]]+55 # rescale from [-55 55] to [0 110]
-    cj2 <- trials[[t,"cj2"]]+55
-    sway <- cj2 - cj1 # +ve values indicate increasingly right-oriented response
-    if((trials[[t,"agree"]] && trials[[t,"cj1"]]<0) ||
-       (!trials[[t,"agree"]] && trials[[t,"cj1"]]>=0)) {
-      # Advice was 'target is on the left' so we need to reverse the sway
-      sway = sway * -1
-      direction <- 1
+      t_data$shift <- NA
+      t_data$influence <- NA
     } else {
-      # record the advice direction for posterity
-      direction <- 2
+      # calculate the confidence change on this trial ('shift')
+      # shift = Cpost - Cpre
+      # C-values are *-1 if answer was 'left', so
+      # Cpre [1,55]
+      # Cpost [-55,-1]U[1,55]
+      cj1 <- trials[[t,"cj1"]]
+      cj2 <- trials[[t,"cj2"]]
+      if(trials[[t,"cj1"]]<0) {
+        # initial response is 'left'
+        cj1 <- cj1 * -1
+        cj2 <- cj2 * -1
+      } 
+      shift <- cj2 - cj1 # +ve values indicate shift towards more confidence in initial response
+      if((trials[[t,"agree"]])) {
+        # on agreement trials shift towards initial response inidicates following advice
+        influence <- shift
+      } else {
+        # on disagreement trials shift AWAY from initial response inidicates following advice
+        influence <- shift * -1
+      }
+      t_data$shift <- shift
+      t_data$influence <- influence
+      # for correct trials record the confidence 'step'
+      if(trials[[t,"cor1"]]) {
+        t_data$initialConfidenceCategory <- trials[t,"step"]
+      }
     }
-    # save this value
-    t_data <- data.frame('id'=tid, 'direction'=direction, 'influence'=sway)
-    p_data <- rbind(p_data, t_data)
+    trial_influence <- rbind(trial_influence, t_data)
   }
-  trial_influence[[p]] <- p_data
 }
 
 # 2x2x2 ANOVA investigating effects of advisor type
 # (agree-in-confidence/uncertainty), choice (un/forced), and agreement
 # (dis/agree) on influence. These are all within-subjects manipulations.
-
-# First prepare the data by setting a data frame with the relevant information
-# (the participant ID, the factors, and the mean influence for each of those
-# factor combination).
+print('Running ANOVAs')
+anova_output <- aov(formula = influence ~ adviceType * choiceAllowed * agree + Error(pId), data=trial_influence)
+print('>>(anova_output)')
+print(summary(anova_output))
 
 # The bias-sharing advisor and anti-bias advisors differ in their frequency with
 # which they agree with the participant as a  function of participant confidence
@@ -215,76 +247,8 @@ for(p in seq(length(study))) {
 # confidence balance out). This subset only includes trials on which the
 # participant was CORRECT since the step information is not recorded for
 # incorrect trials (where all advisors agree 30% of the time).
-anova_data <- data.frame(pId=integer(),
-                         advice=integer(),
-                         choice=integer(),
-                         agreement=integer(),
-                         influence=double(),
-                         n=integer())
-anova_data_70 <- anova_data
-advisorTypes <- c(1,2) # 1=aic, 2=aiu
-choiceTypes <- c(0,1) # 0=forced, 1=unforced
-agreementTypes <- c(0,1) # 0=disagree, 1=agree
-for(p in seq(length(study))) {
-  p_data <- study[[p]]
-  trials <- p_data$trials
-  trials <- trials[which(trials[,"practice"]==FALSE),]
-  # the _70 variables concern only trials where participant was correct with
-  # middle confidence
-  trials_70 <- trials[which(trials[,"step"]==0),] 
-  advisorIds <- as.numeric(p_data$cfg$advisor[seq(1,length(p_data$cfg$advisor),6)])
-  advisorAdviceTypes <- as.numeric(p_data$cfg$advisor[seq(2,length(p_data$cfg$advisor),6)])
-  # for each advisor type
-  for(aT in advisorTypes) {
-    trials_A <- trials[which(trials[,"advisorId"]==advisorIds[which(advisorAdviceTypes==aT)]),]
-    trials_70_A <- trials_70[which(trials_70[,"advisorId"]==advisorIds[which(advisorAdviceTypes==aT)]),]
-    # for each choice type
-    for(cT in choiceTypes) {
-      # using ...mean>1 here is a huge HACK. It works because the no choice is
-      # represented by 0. So the expected combinations (ignoring NaNs) are 1,0;
-      # 2,0; and 2,1 which average to .5, 1, and 1.5 respectively. Since we only
-      # care about the 2,1 case (a genuine choice between advisors), the hack
-      # works.
-      trials_C <- trials_A[which((as.numeric(lapply(trials_A[,"choice"],mean))>1)==cT),]
-      trials_70_C <- trials_70_A[which((as.numeric(lapply(trials_70_A[,"choice"],mean))>1)==cT),]
-      # for each agreement type
-      for(agT in agreementTypes) {
-        trials_G <- trials_C[which(trials_C[,"agree"]==agT),]
-        trials_70_G <- trials_70_C[which(trials_70_C[,"agree"]==agT),]
-        # calculate the influence and record the value
-        mean_influence <- 
-          mean(trial_influence[[p]][which(trial_influence[[p]][,"id"]%in%trials_G[,"id"]),"influence"])
-        if(length(trials_70_G)==dim(trials)[2]) {
-          # only one entry was found for this case, so mean is just the value
-          mean_influence_70 <- trial_influence[[p]][which(trial_influence[[p]][,"id"]==trials_70_G["id"]),"influence"]
-          dim(trials_70_G) <- c(1, dim(trials)[2])
-        } else {
-          mean_influence_70 <- 
-            mean(trial_influence[[p]][which(trial_influence[[p]][,"id"]%in%trials_70_G[,"id"]),"influence"])
-        }
-        r_data <- data.frame(pId=p, 
-                             adviceType=aT, 
-                             choiceAllowed=cT, 
-                             agreement=agT, 
-                             influence=mean_influence, 
-                             n=dim(trials_G)[1])
-        r_data_70 <- data.frame(pId=p,
-                                adviceType=aT,
-                                choiceAllowed=cT,
-                                agreement=agT,
-                                influence=mean_influence_70,
-                                n=dim(trials_70_G)[1])
-        anova_data <- rbind(anova_data, r_data)
-        anova_data_70 <- rbind(anova_data_70, r_data_70)
-      }
-    }
-  }
-}
-# now we can run the anova. Let's build the model:
-anova_output <- aov(formula = influence ~ adviceType * choiceAllowed * agreement + Error(pId), data=anova_data)
-print('>>(anova_output)')
-print(summary(anova_output))
-anova_output_70 <- aov(formula = influence ~ adviceType * choiceAllowed * agreement + Error(pId), data=anova_data_70)
+trial_influence_70 <- trial_influence[which(trial_influence$initialConfidenceCategory==0),]
+anova_output_70 <- aov(formula = influence ~ adviceType * choiceAllowed * agree + Error(pId), data=trial_influence_70)
 print('>>(anova_output_70) Looking at only trials where intial decision was correct and made with middle confidence:')
 print(summary(anova_output_70))
 

README.md

@@ -1,2 +1,6 @@
-# Experiments on trust in feedback and feedback-free scenarios
-This repository contains the scripts used to run the experiments on trust in feedback and no feedback social scenarios, as reported in my PhD thesis (https://ora.ox.ac.uk/objects/uuid:04e42d0e-8133-4a4d-8fc0-27324876bfba). The relative papers are under review or in preparation.
+# Experiments on social influence in decision-making in the absence of feedback
+## Foundation
+This repository is built on top of code produced by [Niccolo Pescetelli](https://github.com/chri4354) during his [PhD thesis](https://ora.ox.ac.uk/objects/uuid:04e42d0e-8133-4a4d-8fc0-27324876bfba), and those original scripts can be found on [his profile](https://github.com/chri4354/nofeedback_trust). The relative papers are under review or in preparation.
+
+## Introduction
+Previous work (see above) identified that, in the absence of objective feedback, people can use their own metacognitive information to evaluate the relative worth of advisors. Under certain circumstances this valuable heuristic approach leads to systematic errors. The code within this repository is for running MATLAB experiments to explore these errors and their consequences.