Data Analysis tools - Week 1 - Running an analysis of variance

The week 1 assignment asks to run an analysis of variance and then analyze and interpret post hoc paired comparisons in instances where the original statistical test was significant, and examining more than two groups (i.e. more than two levels of a categorical, explanatory variable).

I have analysed the gapminder dataset. In the analysis I look at the relationship between the income per person (incomecategory) as the explanatory variable and the oil consumption per person (oilperperson) as the response variable.

Program

LIBNAME mydata "/courses/d1406ae5ba27fe300 " access=readonly;

DATA new; set mydata.gapminder;

/*
Formatting for income, armed forces and oil
*/

format oilcategory $35.;  
format incomecategory $20.;
format armedforcescategory $20.;

/*
Oil categorisation
*/

if /*oilperperson = .  then oilcategory='Missing';*/
oilperperson lt 2  then  oilcategory= 'Less than 2 tonnes per year';
else if oilperperson lt 4  then  oilcategory= '2 to 4 tonnes per year';
else if oilperperson lt 6  then  oilcategory= '4 to 6 tonnes per year';
else if oilperperson lt 8  then  oilcategory= '6 to 8 tonnes per year';
else if oilperperson gt 8  then  oilcategory= 'Greater than 8 tonnes per year';

/*
Income per person categorisation
*/

if  /*incomeperperson = .   then  incomecategory='Missing'; */
incomeperperson lt 5000  then  incomecategory = 'Less than $5000';
else if incomeperperson lt 10000  then  incomecategory = '$5000 to $10000';
else if incomeperperson lt 15000  then  incomecategory = '$10000 to $15000';
else if incomeperperson lt 20000  then  incomecategory = '$15000 to $20000';
else if incomeperperson lt 30000  then  incomecategory = '$20000 to $30000';
else if incomeperperson gt 30000  then  incomecategory = '$30000 and higher';

/*
Armed forces categorisation
*/

if /*armedforcesrate= . then  armedforcescategory='Missing'; */
armedforcesrate lt 1  then  armedforcescategory = 'Less than 1%';
else if armedforcesrate lt 2  then  armedforcescategory = '1% to 2%';
else if armedforcesrate lt 4  then  armedforcescategory = '2% to 4%';
else if armedforcesrate lt 6  then  armedforcescategory = '4% to 6%';
else if armedforcesrate lt 8  then  armedforcescategory = '6% to 8%';
else if armedforcesrate gt 8  then  armedforcescategory = 'greater than 8%';

/*
Insert meaningful lables to the variables
*/

label  country   =  "country"
 oilperperson  =  "Oil per person"
 incomeperperson  =  "Income per person ($)(based on 2010 dollar exchange rate)"
 incomecategory  =  "Income category"
 polityscore  =  "Democracy score"
 armedforcesrate  =  "Armed forces personnel (% of total labor force)"
 incomecategory  =  "Income category"
 armedforcescategory =  "Armed forces category"
 oilcategory  =  "Oil category";

run;

proc sort data=new; by country;

proc anova data=new; class incomecategory;
model oilperperson=incomecategory;
means incomecategory/duncan;

run;

ANOVA Analysis

Interpretation

The means of the oil consumption variable is generally in an increasing order with the income per person. This basically gives an idea that there must be some positive relationship between the two variables.

From the data I can see that the p value is less than the 5% level which means that the test is statistically significant. So I must reject the null Hypothesis that there is no relation between the income and the oil consumption. This rejection also makes sense as higher income could be used to explain the higher oil consumption.

From the Duncan post hoc test it seems that the mean oil consumption of the highest income category "$30000 and higher" is statistically different to the mean oil consumption of the lower income categories "Less than $5000" , "$5000 to $10000" and "$10000 to $20000" because the groupings have distinctly separate alphabets. 

In my view though ideally each income category should have had their own group. The details of how the Duncan test works needs to be thoroughly understood.