##### SCA-21
##### 
##### Two-Sample Means Tests
##### 

### This gives a few examples of the analysis process for comparing
### two population means.



### Preamble

# Import extra functionality
source("http://rfs.kvasaheim.com/stat200.R")




### Part I: OPEC Wealth
# 
#   I would like to determine if OPEC members have a different
#   level of wealth than non-members.

dt = read.csv("http://rfs.kvasaheim.com/data/gdp.csv")
attach(dt)

#   To answer this question, I would like to use the two-
#   population t-test because it is the most powerful test
#   available. However, it requires the variables to be
#   Normally distributed in both populations.

shapiroTest(gdpcap~OPEC)

#   According to the Shapiro-Wilk test, neither population is
#   Normal. Because of this, we should use the Mann-Whitney
#   test.

wilcox.test(gdpcap~OPEC, conf.int=TRUE)

#   According to the Mann-Whitney test, there is no significant
#   evidence that OPEC membership is associated with higher -- 
#   or lower -- average wealth levels.

boxplot(gdpcap~OPEC, ylab="GDP per Capita", xlab="OPEC Membership")

detach(dt)




### Part II: OPEC Corruption
# 
#   I would like to determine if OPEC members have a different
#   level of corruption than non-members.

dt = read.csv("http://rfs.kvasaheim.com/data/gdp.csv")
attach(dt)

#   To answer this question, I would like to use the two-
#   population t-test because it is the most powerful test
#   available. However, it requires the variables to be
#   Normally distributed in both populations.

shapiroTest(corruption~OPEC)

#   According to the Shapiro-Wilk test, neither population is
#   Normal. Because of this, we should use the Mann-Whitney
#   test.

wilcox.test(corruption~OPEC, conf.int=TRUE)

#   According to the Mann-Whitney test, there is no significant
#   evidence that OPEC membership is associated with higher -- 
#   or lower -- average corruption levels.

boxplot(corruption~OPEC, ylab="Corruption Level", xlab="OPEC Membership")

detach(dt)





### Part III: OPEC Democracy
# 
#   I would like to determine if OPEC members have a LOWER
#   level of democracy than non-members.

dt = read.csv("http://rfs.kvasaheim.com/data/gdp.csv")
attach(dt)

#   To answer this question, I would like to use the two-
#   population t-test because it is the most powerful test
#   available. However, it requires the variables to be
#   Normally distributed in both populations.

shapiroTest(democracy~OPEC)

#   According to the Shapiro-Wilk test, the non-member population is
#   not Normal. Because of this, we should use the Mann-Whitney
#   test.

wilcox.test(democracy~OPEC, alternative="less", conf.int=TRUE)

#   n.b.: m<n in the alphabet (member < non-member). If the 
#         claim was that non-menbers were less than members, 
#         would use alternative="greater"

#   According to the Mann-Whitney test, there is significant
#   evidence that OPEC membership is associated with lower
#   average democracy levels.
#
#   In fact, we are 95% confident that the average difference
#   is at least 4 points.

boxplot(democracy~OPEC, ylab="Democracy Level", xlab="OPEC Membership")

detach(dt)





### Part IV: Western Democracy
# 
#   I would like to determine if Western States have a HIGHER
#   level of democracy than non-Western States.

dt = read.csv("http://rfs.kvasaheim.com/data/gdp.csv")
attach(dt)

#   To answer this question, I would like to use the two-
#   population t-test because it is the most powerful test
#   available. However, it requires the variables to be
#   Normally distributed in both populations.

shapiroTest(democracy~(region=="Western"))

#   According to the Shapiro-Wilk test, neither population -- 
#   Western or non-Western -- is Normal. Because of this, we 
#   should use the Mann-Whitney test.

wilcox.test(democracy~(region=="Western"), 
                            alternative="less", conf.int=TRUE)

#   n.b.: F<T in the alphabet (FALSE < TRUE). 
#         If the claim was that Western States were LESS than
#         non-Western States, would use alternative="greater"
#         because we would be testing 
#                  FALSE > TRUE 
#            non-Western > Western
#

#   According to the Mann-Whitney test, there is significant
#   evidence that Western States tend to have higher levels of
#   democaracy than non-Western States.
#
#   In fact, we are 95% confident that the average difference
#   is at least 4 points.

boxplot(democracy~(region=="Western"), ylab="Democracy Level", xlab="Western State")

detach(dt)

#####

#   n.b.: Always draw a graphic. Then, make sure the results 
#         shown in the graphic are consistent with the results
#         of your analysis. In that way, the graphic also helps
#         you make sure you did the analysis correctly.