# The raw data:
#
DF = data.frame(
    student=as.factor( 1:15 ),
    waking=c( 18, 19, 16, 21, 16, 20, 20, 14, 11, 22, 19, 29, 16, 27, 15 ),
    hypnotic=c( 25, 20, 26, 26, 20, 23, 14, 18, 18, 20, 22, 27, 19, 27, 21 )
)

# Convert this dataframe into a form that the R aov command can directly use:
#
if( FALSE ){
    #
    # "by hand"
    #
    block=c( DF$student, DF$student )
    measurement=c( DF$waking, DF$hypnotic )
    type=c( rep( 0, length(DF$waking) ), rep( 1, length(DF$hypnotic) )  )
    DF_melt = data.frame( measurement=measurement, block=block, type=type )
}else{
    #
    # Using melt.
    #
    library(reshape2)
    DF_melt = melt(DF, id.vars=c('student'), value.name='n_correct', variable.name='state')
}