coursework/week2/power-effect-replication.R at master · navanizard/coursework · GitHub

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library(tidyverse)

####################################################################################
# IST Chapter 12, Exercise 12.1
magnets <- read_csv("http://pluto.huji.ac.il/~msby/StatThink/Datasets/magnets.csv")

#  Consider a medical condition that does not have a standard
# treatment. The recommended design of a clinical trial for a new treatment
# to such condition involves using a placebo treatment as a control. A placebo
# treatment is a treatment that externally looks identical to the actual treatment
# but, in reality, it does not have the active ingredients. The reason for using
# placebo for control is the “placebo effect”. Patients tend to react to the fact that
# they are being treated regardless of the actual beneficial effect of the treatment

# As an example, consider the trial for testing magnets as a treatment for pain
# that was described in Question 9.1. The patients that were randomly assigned
# to the control (the last 21 observations in the file “magnets.csv”) were treated
# with devices that looked like magnets but actually were not. The goal in this
# exercise is to test for the presence of a placebo effect in the case study “Magnets
# and Pain Relief” of Question 9.1 using the data in the file “magnets.csv”.


# 1. Let X be the measurement of change, the difference between the score of
#   pain before the treatment and the score after the treatment, for patients
#   that were treated with the inactive placebo. Express, in terms of the
#   expected value of X, the null hypothesis and the alternative hypothesis
#   for a statistical test to determine the presence of a placebo effect. The null
#   hypothesis should reflect the situation that the placebo effect is absent

# ANSWER:
    # H0 (Null Hypothesis): X = 0
    # HA (Alternative Hypothesis): X > 0

# 2. Identify the observations that can be used in order to test the hypotheses.
placebo_change <- magnets$change[30:50]

# 3. Carry out the test and report your conclusion. (Use a significance level of
#    5%.)
results <- t.test(placebo_change, alternative = "greater", mu = 0)
p_val <- results$p.value
p_val < 0.05 # TRUE, so reject the null. We have sufficient evidence to support the claim
#              that there is an observed difference in pain levels for the treament and control groups.

####################################################################################
# IST Chapter 13, Exercise 13.1

magnets <- read_csv("http://pluto.huji.ac.il/~msby/StatThink/Datasets/magnets.csv")
#  In this exercise we would like to analyze the results of the
# trial that involves magnets as a treatment for pain. The trial is described in
# Question 9.1. The results of the trial are provided in the file “magnets.csv”

# Patients in this trial were randomly assigned to a treatment or to a control.
# The responses relevant for this analysis are either the variable “change”, which
# measures the difference in the score of pain reported by the patients before and
# after the treatment, or the variable “score1”, which measures the score of pain
# before a device is applied. The explanatory variable is the factor “active”.
# This factor has two levels, level “1” to indicate the application of an active
# magnet and level “2” to indicate the application of an inactive placebo.

# In the following questions you are required to carry out tests of hypotheses.
# All tests should conducted at the 5% significance level:
# 1. Is there a significance difference between the treatment and the control
#    groups in the expectation of the reported score of pain before the application of the device?

# ANSWER:
    # H0 (Null Hypothesis): Xtrt - Xctrl = 0
    # HA (Alternative Hypothesis): Xtrt - Xctrl != 0

control_score1 <- magnets$score1[30:50]
treatment_score1 <- magnets$score1[1:29]

results <- t.test(control_score1, treatment_score1, mu = 0)
p_val <- results$p.value
p_val < 0.05 # FALSE, so fail to reject the null. We do not have sufficient evidence to support
#              the claim that there isn't an observed difference in the expected value of the
#              initial pain levels for the treament and control groups before the application
#              of the device.


# 2. Is there a significance difference between the treatment and the control
#    groups in the variance of the reported score of pain before the application
#    of the device?

control_score1 <- magnets$score1[30:50]
treatment_score1 <- magnets$score1[1:29]

results <- var.test(control_score1, treatment_score1)
p_val <- results$p.value
p_val < 0.05 # FALSE, so fail to reject the null. We do not have sufficient evidence to support
#              the claim that there isn't an observed difference in the variance of the
#              initial pain levels for the treament and control groups before the application
#              of the device.

# 3. Is there a significance difference between the treatment and the control
#    groups in the expectation of the change in score that resulted from the
#    application of the device?

# ANSWER:
    # H0 (Null Hypothesis): Xtrt - Xctrl = 0
    # HA (Alternative Hypothesis): Xtrt - Xctrl != 0

control_change <- magnets$change[30:50]
treatment_change <- magnets$change[1:29]

results <- t.test(control_change, treatment_change, mu = 0)
p_val <- results$p.value
p_val < 0.05 # TRUE, so reject the null. We have sufficient evidence to support
#              the claim that there is an observed difference in the expected value of the
#              pain levels for the treament and control groups after the application
#              of the device.

# 4. Is there a significance difference between the treatment and the control
#    groups in the variance of the change in score that resulted from the application of the device?

control_change <- magnets$change[30:50]
treatment_change <- magnets$change[1:29]

results <- var.test(control_change, treatment_change)
p_val <- results$p.value
p_val < 0.05 # TRUE, so reject the null. We have sufficient evidence to support
#              the claim that there is an observed difference in the variance of the
#              pain levels for the treament and control groups after the application
#              of the device.