#!/usr/bin/env python

# ----------------------------------------------------------------------------------- #
#
#  ROOT macro for exercise on planning experiment.
#
#  You are planning the "Lady Tasting Tea" experiment, serving 10 cups of tea (or
#  whatever you're testing). However, you are wondering, if you experiment is good
#  enough, and would like to improve on it (also beyond simply tasting tea).
#
#  Author: Troels C. Petersen (NBI)
#  Email:  petersen@nbi.dk
#  Date:   21st of October 2013
#
# ----------------------------------------------------------------------------------- #

from ROOT import *
from array import array

# Setting what to be shown in statistics box:
gStyle.SetOptStat("emr")
gStyle.SetOptFit(1111)

verbose = True
Nverbose = 10

r = TRandom3()
r.SetSeed(93)

SaveFigures = false

Nexperiments = 100
Ntests = 10
Hist_Ncorrect  = TH1F("Hist_Ncorrect",  "Hist_Ncorrect", Ntests+1, -0.5, Ntests+0.5)



# ------------------------------------------------------------------ #
# Loop over number of experiments and make random choices:
# ------------------------------------------------------------------ #

for iexp in range (Nexperiments) :
    
    # Make Ntests tests of a random number:
    Ncorrect = 0
    for itest in range (Ntests) :
        if (r.Uniform() > 0.5) : Ncorrect += 1
        
    Hist_Ncorrect.Fill(Ncorrect)



# ------------------------------------------------------------------ #
# Show the distribution of results:
# ------------------------------------------------------------------ #

c0 = TCanvas("c0","", 20, 50, 600, 400)
    
Hist_Ncorrect.GetXaxis().SetTitle("Number of correct answers")
Hist_Ncorrect.GetYaxis().SetTitle("Frequency")
Hist_Ncorrect.SetLineWidth(2)
Hist_Ncorrect.SetLineColor(2)
Hist_Ncorrect.Draw()

c0.Update()
if (SaveFigures) : c0.SaveAs("TestResult.png")





raw_input( ' ... Press enter to exit ... ' )

# ----------------------------------------------------------------------------------- #
# 
#  Before starting looking at the program, sit down and calculate (either in hand, or
#  as a section in the beginning of this program) the probabilities of the outcome of
#  a 10-cup lady-tasting-tea experiment. Such a calculation is always healthy to get
#  a feel for the sensitivity of the experiment.
#
#  Questions:
#  ----------
#   1) What is the chance that a person choosing at random gets all 10 tastings correct?
#      And given that this actually happens once in the above program, would you claim,
#      that I chose the "random" seed deliberately and not at random?
#
#   2) In the above example, each test is random, and there is no knowledge of how many
#      of each sample is being tested. How does the test change, when it is known, that
#      half of the samples are of one type and the other half of the opposite type?
# 
#   3) Imagine that you are now conducting a beer tasting! You friend made the (drunk?)
#      claim, that he could always recognize a "Groen Tuborg". You decide to design an
#      experiment that can test this hypothesis. How would you do this?
#       - How sure do you want to be on the result? (i.e. p-value of all correct)
#       - How many types of beer would you use?
#       - What if you want to allow for one (or more) wrong identifications?
#       - How many times should your friend taste a beer sample?
#       - Will you tell him ahead of time, how many of each sample there are?
# 
#   4) Imagine a prominent professor at NBI making a similar claim about sushi? You
#      can only ask him to taste 12 times (that is a full lunch, and you can not
#      afford more). If you get three samples, four from each restaurant, and you
#      allow for up to one misidentification, how sure can you be, that his claim is
#      reasonable? I.e. what is the p-value for a random guess to get 11 or 12 correct?
#      Calculate this both analytically and using a Monte Carlo simulation.
# 
# ----------------------------------------------------------------------------------- #