Package install

library(nlme)
library(car)

Data import

d1<- read.csv("/Users/koho0/Desktop/1st ANOVA stats/Fig 1_2hr interval_mEPSC freq_5day.csv")

Data structure

str(d1)

## 'data.frame':    52 obs. of  4 variables:
##  $ subject   : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ sex       : Factor w/ 2 levels "female","male": 2 2 2 2 2 2 2 2 2 2 ...
##  $ group     : Factor w/ 2 levels "con","sevo2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ mEPSC_freq: num  0.0417 0.1333 0.1417 0.1083 0.0667 ...

Variance component analysis

Data Conversion to groupdedData

d1.gr=groupedData(d1[,4]~group|sex, data=d1)

Varicance component analysis using plot

plot(d1.gr, outer=~sex*group)

Two Way ANOVA analysis

Modleing with interaction

md1=aov(d1[,4]~group*sex, data=d1)

Model summary

summary(md1)

##             Df Sum Sq Mean Sq F value Pr(>F)  
## group        1 0.0199 0.01988   2.738 0.1045  
## sex          1 0.0442 0.04420   6.088 0.0172 *
## group:sex    1 0.0008 0.00080   0.111 0.7408  
## Residuals   48 0.3485 0.00726                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

According to the results,

Model diagnostics

par(mfrow=c(2,2))
plot(md1)

comma <- function(x) format(x, digits = 4)
SWT=shapiro.test(residuals(md1))
LT=leveneTest(md1)
Pswt=comma(SWT$p.value)
Plt=comma(LT[1,3])

Accoring to the results, the p value of Shapiro-Wilk test is 1.963e-05, which is smaller than 0.05, so normality assumption can’t be accepted. The p-value of Levene test is 0.556, which is greater than 0.05, so equal variances can be assumed.

Post hoc test with nested model

We use nested model for post hoc test(to compare group within each sex). There are only one test, so we do not use p-value adjustment.

nest=summary(lm(d1[,4]~sex/group, data=d1))
nest$coefficients

##                        Estimate Std. Error  t value    Pr(>|t|)
## (Intercept)          0.07500000 0.02459656 3.049207 0.003727391
## sexmale              0.05059524 0.03351946 1.509429 0.137744303
## sexfemale:groupsevo2 0.03571429 0.03351946 1.065479 0.291989518
## sexmale:groupsevo2   0.05148810 0.03351946 1.536066 0.131088395