data <- read.csv("/Users/alicia/Downloads/Maglio and Polman 2014 Experiment 1.csv")

Lab 1:

data$orientation <- as.factor(data$orientation)
data$station <- as.factor(data$station)
model <- aov(subjective_distance ~ orientation * station, data = data)
summary(model)
##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## orientation           1   0.71   0.713   0.664    0.416    
## station               3  75.16  25.053  23.349 6.01e-13 ***
## orientation:station   3  52.41  17.471  16.283 1.77e-09 ***
## Residuals           194 208.15   1.073                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Orientation: p > 0.05. Not statistically significant Station: p < 0.001, statistically significant Orientation x Station:p < 0.001, statisically significant.

Orientation does not affect the subjective distance across all stations

interaction.plot(
  x.factor = data$station,
  trace.factor = data$orientation,
  response = data$subjective_distance,
  type = "b",
  legend = TRUE,
  xlab = "Station",
  ylab = "Mean Subjective Distance",
  trace.label = "Orientation"
)

TukeyHSD(model, which = "orientation:station")
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = subjective_distance ~ orientation * station, data = data)
## 
## $`orientation:station`
##                  diff        lwr          upr     p adj
## 2:1-1:1 -1.013846e+00 -1.9029477 -0.124744584 0.0134437
## 1:2-1:1 -8.846154e-01 -1.7649571 -0.004273649 0.0479420
## 2:2-1:1 -2.013846e+00 -2.9029477 -1.124744584 0.0000000
## 1:3-1:1 -2.045151e+00 -2.9537457 -1.136555349 0.0000000
## 2:3-1:1 -1.461538e+00 -2.3418802 -0.581196726 0.0000233
## 1:4-1:1 -8.846154e-01 -1.7649571 -0.004273649 0.0479420
## 2:4-1:1  3.461538e-01 -0.5429477  1.235255416 0.9331329
## 1:2-2:1  1.292308e-01 -0.7598708  1.018332339 0.9998387
## 2:2-2:1 -1.000000e+00 -1.8977759 -0.102224063 0.0174823
## 1:3-2:1 -1.031304e+00 -1.9483895 -0.114219192 0.0157349
## 2:3-2:1 -4.476923e-01 -1.3367939  0.441409262 0.7830703
## 1:4-2:1  1.292308e-01 -0.7598708  1.018332339 0.9998387
## 2:4-2:1  1.360000e+00  0.4622241  2.257775937 0.0001692
## 2:2-1:2 -1.129231e+00 -2.0183323 -0.240129199 0.0033704
## 1:3-1:2 -1.160535e+00 -2.0691303 -0.251939964 0.0031076
## 2:3-1:2 -5.769231e-01 -1.4572648  0.303418658 0.4790897
## 1:4-1:2  4.440892e-16 -0.8803417  0.880341735 1.0000000
## 2:4-1:2  1.230769e+00  0.3416677  2.119870801 0.0008846
## 1:3-2:2 -3.130435e-02 -0.9483895  0.885780808 1.0000000
## 2:3-2:2  5.523077e-01 -0.3367939  1.441409262 0.5501808
## 1:4-2:2  1.129231e+00  0.2401292  2.018332339 0.0033704
## 2:4-2:2  2.360000e+00  1.4622241  3.257775937 0.0000000
## 2:3-1:3  5.836120e-01 -0.3249831  1.492207193 0.5060133
## 1:4-1:3  1.160535e+00  0.2519400  2.069130270 0.0031076
## 2:4-1:3  2.391304e+00  1.4742192  3.308389504 0.0000000
## 1:4-2:3  5.769231e-01 -0.3034187  1.457264812 0.4790897
## 2:4-2:3  1.807692e+00  0.9185907  2.696793878 0.0000001
## 2:4-1:4  1.230769e+00  0.3416677  2.119870801 0.0008846

A two way ANOVA examining the efects od orientation and station on subjecctive distance revealed a significant interaction between orientation and station. This indicates that the effect of orientation on perceived distance differed depending on the station.

The post-hoc Tukey comparisons showed multiple significant differences between specific orientation x station combinations.