source('utils.R')

# Section 3; Question 1 (EPage 668):
#
source('chap_14_sect_3_question_1_data.R')

d = DF$Winter - DF$Summer
ad = abs(d)
r = rank( ad, ties.method='average' )
z = rep( 0, length(d) )
z[ d > 0 ] = 1
w = sum( z * r )
n = length(d)
max_d_value = n*(n+1)/2

max_d_value - w 
p_value = sum( c( 1, 1, 2, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1) )/2^n
print( sprintf( 'w= %d; p_value= %.6f', w, p_value ) )


# Section 3; Question 2:
#
n = 5
pw = c( 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1 )/2^n # P_W(W=w)
print( cumsum( rev(pw) ) )


# Section 3; Question 3 (EPage 676):
#
source('chap_14_sect_3_question_3_data.R')

d = DF$High - DF$Moderate
ad = abs(d)
r = rank( ad, ties.method='average' )
z = rep( 0, length(d) )
z[ d > 0 ] = 1
w = sum( z * r )
n = length(d)
m = n*(n+1)/4 # expected mean under H_0
v = n*(n+1)*(2*n+1)/24 # expected variance under H_0
z = ( w - m ) / sqrt(v)
p_value = 2*(1-pnorm(abs(z)))
print( sprintf( 'w= %d; p_value= %.6f', w, p_value ) )


# Section 3; Question 4 (EPage 676):
#
source('chap_14_sect_3_question_4_data.R')

res = signed_rank(DF$Score[-8]) # drop the eigth sample
p_value = 2*(1-pnorm(abs(res$z)))
print( sprintf( 'w= %d; p_value= %.6f', res$w, p_value ) )


# 3.5:
#
source('../Chapter5/chap_5_sect_3_question_2_data.R')
res = signed_rank(DF$Ratio - 0.8)
p_value = pnorm(res$z)
print( sprintf( 'w= %d; p_value= %.6f', res$w, p_value ) )


# 3.6:
#
source('../Chapter13/case_study_13_3_1_data.R')
res = signed_rank(DF$After - DF$Before)
p_value = 2*(1-pnorm(abs(res$z)))
print( sprintf( 'w= %d; p_value= %.6f', res$w, p_value ) )


# 3.8:
#
source('../Chapter8/chap_8_sect_2_question_6_data.R')
res = signed_rank(DF$Mothered - DF$Unmothered)
p_value = 2*(1-pnorm(abs(res$z)))
print( sprintf( 'w= %d; p_value= %.6f', res$w, p_value ) )

t.test( DF$Mothered, DF$Unmothered ) # gives the same conclusion as the signed rank test above


# 3.9:
#
source('../Chapter9/chap_9_sect_2_question_6_data.R')
x = DF[ DF$Alcohol==1, ]$Age
y = DF[ DF$Alcohol==0, ]$Age
res = rank_sum( x, y )
p_value = pnorm(res$z) # a one sided test expect mean(x) < mean(y)
print( sprintf( 'w_prime= %.2f; p_value= %.6f', res$w_prime, p_value ) )

t.test( x, y, alternative='less' )


# 3.10
#
source('../Chapter9/table_9_3_1.R')
x = DF$Non_Confined
y = DF$Confined
res = rank_sum( x, y )
p_value = 2*(1-pnorm(abs(res$z)))
print( sprintf( 'w_prime= %.2f; p_value= %.6f', res$w_prime, p_value ) )

t.test( x, y )