Example Analysis

This example is taken from https://crumplab.github.io/statisticsLab/lab-10-factorial-anova.html#r-10. The data file is stroop_stand.csv, and can be found here https://github.com/CrumpLab/statisticsLab/tree/master/data

Load the data and libraries you will use

library(data.table)
library(dplyr)
library(ggplot2)
all_data <- fread("data/stroop_stand.csv")

Pre-processing

Pre-processing can include many steps. Here, we convert the data from wide to long format, and make a new data frame.

RTs <- c(as.numeric(unlist(all_data[,1])),
         as.numeric(unlist(all_data[,2])),
         as.numeric(unlist(all_data[,3])),
         as.numeric(unlist(all_data[,4]))
         )

Congruency <- rep(rep(c("Congruent","Incongruent"),each=50),2)
Posture <- rep(c("Stand","Sit"),each=100)
Subject <- rep(1:50,4)

stroop_df <- data.frame(Subject,Congruency,Posture,RTs)

Checks

It is important to check the data you are analyzing before you analyze. The checks you make depend on the questions you are trying to answer. Here we check the number of subjects in each condition.

This is a 2x2 repeated measures design, each subject should have 4 means

num_subjects <- stroop_df %>%
                  group_by(Subject) %>%
                  summarise(counts = length(Subject))
total_subjects <- length(num_subjects$Subject)
total_has_four <- num_subjects$counts == 4
sum(total_has_four) == total_subjects

## [1] TRUE

Are there any subjects with huge mean RTs? Could indicate something weird happened.

hist(stroop_df$RTs)

Exclusion

If you are going to exlcude subjects from analysis, then justify your exclusion criterion, and then eliminate subject data from the data frame. We will not exlcude any subjects here.

# no exclusions

Analysis

Now you can begin analysis. This experiment asked whether the Stroop effect (difference between mean incongruent and mean congruent), depends on whether people are sitting or standing. Let’s get the means, make a tbale, then plot the data.

table of 2x2 means

overall_means <- stroop_df %>%
                  group_by(Posture,Congruency) %>%
                  summarise(meanRT = mean(RTs),
                            SEMRT = (sd(RTs)/sqrt(length(RTs))))

# make a table of overall means
knitr::kable(overall_means)

Posture	Congruency	meanRT	SEMRT
Sit	Congruent	821.9232	16.60384
Sit	Incongruent	940.7855	17.91041
Stand	Congruent	807.9599	14.93521
Stand	Incongruent	903.9131	15.34939

plot of 2x2 means

ggplot(overall_means, aes(x=Posture,
                          y=meanRT, 
                          group=Congruency,
                          fill=Congruency))+
  geom_bar(stat="identity",position="dodge")+
  theme_classic(base_size=12)+
  ylab("Mean Reaction Time (ms)")+
  geom_errorbar(aes(ymin=meanRT-SEMRT,
                    ymax=meanRT+SEMRT),
                position=position_dodge(width=0.9),
                width=.2,
                color="black")+
  coord_cartesian(ylim=c(750,1000))

Repeated measure ANOVA

# Make sure Subjecdt is  a factor
stroop_df$Subject <-  as.factor(stroop_df$Subject)

aov_out <- aov(RTs~Posture*Congruency + Error(Subject/(Posture*Congruency)), stroop_df)
#print summary of ANOVA table
summary(aov_out)

## 
## Error: Subject
##           Df  Sum Sq Mean Sq F value Pr(>F)
## Residuals 49 2250739   45933               
## 
## Error: Subject:Posture
##           Df Sum Sq Mean Sq F value  Pr(>F)   
## Posture    1  32303   32303    7.33 0.00931 **
## Residuals 49 215948    4407                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Error: Subject:Congruency
##            Df Sum Sq Mean Sq F value Pr(>F)    
## Congruency  1 576822  576822   342.5 <2e-16 ***
## Residuals  49  82535    1684                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Error: Subject:Posture:Congruency
##                    Df Sum Sq Mean Sq F value  Pr(>F)   
## Posture:Congruency  1   6560    6560   8.964 0.00431 **
## Residuals          49  35859     732                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# prints a nicer ANOVA table
summary_out <- summary(aov_out)
library(xtable)
knitr::kable(xtable(summary_out))

	Df	Sum Sq	Mean Sq	F value	Pr(>F)
Residuals	49	2250738.636	45933.4416	NA	NA
Posture	1	32303.453	32303.4534	7.329876	0.0093104
Residuals1	49	215947.614	4407.0942	NA	NA
Congruency	1	576821.635	576821.6349	342.452244	0.0000000
Residuals	49	82534.895	1684.3856	NA	NA
Posture:Congruency	1	6560.339	6560.3389	8.964444	0.0043060
Residuals	49	35859.069	731.8177	NA	NA

# prints means for each effect
print(model.tables(aov_out,"means"), format="markdown")

## Tables of means
## Grand mean
##          
## 868.6454 
## 
##  Posture 
## Posture
##   Sit Stand 
## 881.4 855.9 
## 
##  Congruency 
## Congruency
##   Congruent Incongruent 
##       814.9       922.3 
## 
##  Posture:Congruency 
##        Congruency
## Posture Congruent Incongruent
##   Sit   821.9     940.8      
##   Stand 808.0     903.9

Example Write-Up

We submitted the mean reaction times for each subject in each condition to a 2 (Congruency: congruecnt vs. incongruent) x 2 (Posture: Standing vs. Sitting) repeated measures ANOVA.

There was a main effect of Congruency, F (1, 49) = 342.45, MSE = 1684.39, p < 0.001. Mean reaction times were slower for incongruent (922 ms) than congruent groups (815 ms).

There main effect of Posture was significant, F (1, 49) = 7.33, MSE = 4407.09, p =.009. Mean reaction times were slower for sitting (881 ms) than standing groups (855 ms).

The two-way interaction between Congruency and Posture was significant, F (1, 49) = 8.96, MSE = 731.82, p < 0.004. The Stroop effect was 23 ms smaller in the standing than sitting conditions.