Module 4 data analysis

Data Analysis Module
ILRI Graduate Fellows skills training
Nairobi 4th December 2013

Session Objectives
To be able to;
• Answer the research questions:
What results do you need to show and in what format
(tables, graphs, charts etc.)
Selection of data analysis methods (principles and concepts)
• Identify, evaluate and apply data analysis packages – software
available, open source
• Plan analysis of own data and carry out exploratory analysis
• Carry out formal data analysis using different tools and methods
e.g. R

Research Process
• Problem definition
• Literature review
• Objective & hypothesis
• Study design
• Sampling
• Data collection
• Data management
• Formal analysis
• Reporting
• Publication
• Data archiving or
publication
Project development implementation Communicating findings
Definition of problem
domain & how the
specific problem fits in
Identification of gaps,
appropriate methods &
theory
Research will approve or
disapprove the hypothesis
Research strategy to be
used, sample size,
sampling frame
 Sample selection
 Data collection tools
 Database development and
data cleaning
 Exploration, description,
modelling & interpretation
of statistical outputs
 Choice of reporting
media & format
 Advise on presentation
of results
 Data sharing media

Data Analysis – Guiding Principles
Translating Research Questions / Objectives / Hypotheses into an
‘analysis plan’
• Used our research questions / objectives / hypotheses to design
the study – experiment or survey, questions to ask & data to
collect
• We use them again to plan the analysis – what differences do I
need to show, what are my response variables, what types of
model may I need to use etc.
• This is often a good time to draft tables and graphs which you
think will help answer the questions

Data Analysis – Multi-level Data Structures
• Many studies are designed at different levels and collect data at these
multiple levels
• E.g. in experiments this could be animals or plots → blocks and for survey this
may be animal → household → village → district.
• Another aspect of ‘levels’ is repeated measurements over time.
• These levels must not be forgotten when we reach analysis stage –
which level do we summarise each variable at? What is our ‘unit of
analysis’?
• For formal analysis then there are advanced methods that allow the
data to be analysed in a way that allows for the multi-level data
structure (including variation).
• The analysis can often be simplified into fewer dimensions by
summarising particular aspects
• e.g. means between two points in time, the slope of the trend between two
points, the value reached at the end.

Data Analysis – Response & Explanatory
variables
Terms are discipline specific:
Response ≡ Dependent variable ≡ y
Explanatory ≡ Independent variable ≡ x’s
• Explanatory variables can be continuous or discrete
• In epidemiology they can be ‘confounding’ or biological
‘interacting’*
• In economics they can be exogenous or endogenous
*Note that statistical confounding and interactions have different
interpretations

Data Analysis – Variable Types
• Variables can be:
CONTINUOUS or DISCRETE
• In analysis we may sometimes convert continuous data to discrete
• Both Response and Explanatory variables can be continuous or
discrete.

Data Analysis – Aim of Exploratory Analysis
• Data exploration is the first stage to any analysis of the data –
people often jump straight to formal analysis and models but it
is at this stage where you will identify patterns and ‘odd’ data
• In some cases this may be 90% of the analysis you do on the
data (e.g. Case Study 11)
• The more complicated the data set the more interesting and
necessary the exploratory phase becomes.
• With some expertise in data management we can highlight the
important patterns within the data and list the types of
statistical models and their forms that need to be fitted at the
next stage.

Data Analysis – Activities of Exploratory Analysis

Data Analysis – Exploratory Analysis Methods
(Continuous & Discrete Variables)
 Tools for exploratory analysis:
• Means & ranges Case Study 2
• 1 & 2-way tables of means Case Study 3
• Frequency tables Case Study 3 & Case Study 8 – use of Excel pivot tables!
• Histograms Case Study 11
• Scatterplots Case Study 1 & Case Study 3
• Boxplots Case Study 3
• Bar charts & pie charts Case Study 11
• Trend graphs, survival curves Case Study 3
 Identify patterns and unusual variables – e.g. outliers, zeros
 Measures of variation – variance, standard deviation, confidence interval,
standard error, CV
 Transformation of variables?

Data Analysis – Confirmatory / Formal Analysis
Exploratory analysis was the first part of the analysis of our
research data – to gain initial understanding of patterns that
exist in the data and suggest further analysis needs
By the time we reach Confirmatory / Formal analysis we
have refined our objectives and these should clearly define
exactly what type of further statistical analysis we need (and
which models to use)
In exploratory analysis it is difficult to look at many variables
at the same time – formal analysis allows us to do this and be
able to see which variables are more important and others.

Data Analysis – Confirmatory / Formal
Analysis (Some options…)
(Non-parametric equivalents
for small samples)
Response / Dependent Variable(s)
Discrete Continuous
Explanatory /
Independent
Variable(s)
Discrete
Chi-square/ Regression
(Logistic – binary;
Poisson - count)
T-Test / Analysis of
Variance (/ Regression)
Continuous
Regression (Logistic –
binary; Poisson - count)
Correlation / Linear
Regression
Both
Regression (Logistic –
binary; Poisson - count)
ANOVA / Linear
Regression

(Some advanced options…)
• Mixed-effects models (REML) – incorporates random effects
including spatial & temporal repeated measurements; better at
managing data with many levels of hierarchy; used a lot in
epidemiology, animal/plant genetics.
• Survival models.
• Multivariate (> 1 y) methods– can be both parametric & non-
parametric).
• Proportional-odds models when categorical response with both
than 2 categories.

Concepts
The underlying concept in formal statistical modeling is:
Data = Pattern + Residual
 ‘Data’ are the raw data (responses) that you collected, or sometimes may be
summaries derived from the raw data*. They could also be transformed
values*
 ‘Pattern’ is all the variables (continuous or discrete) that are in the design of
the study (e.g. treatment) or have been selected in your exploratory analysis
as explaining some of the differences in the ‘Data’
 ‘Residual’ is the variation we can’t explain by the ‘Pattern’.
The aim of our formal analysis is to put as much of the
variation as possible into the ‘Pattern’ while keeping the
model as simple as possible…easy 
*See earlier slides

Data Analysis – Confirmatory / Formal Analysis:
Correlation & simple Linear Regression 1
 We will use correlation & fitting a
straight line to data to explain the
concepts of statistical modeling:
• The simplest way of looking at the
relationship between an x-variable
and a y-variable is with the
CORRELATION.
• An extension of this is to use a
LINEAR REGRESSION model to fit a
straight line through the points (Case
study 3)
• To look at how well this model is
fitting we use an ‘analysis of
variance’ – the amount of variation in
the Pattern vs. in the Residual

 Linear regression and similar models present the analysis in an
‘analysis of variance’ table that looks like (Section 3.2):
 In this example the p-value will tell you if the slope of the line is
significantly different from 0 (i.e. a flat line) (Section 5)
 Models such as Logistic for binary data and proportions or
Poisson for counts give a similar table but it is now the ‘analysis
of deviance’ with similar interpretations (Section 10.2
Source of
variation
d.f. s.s. m.s. v.r (F-value) p-value
Slope of line 1
Residual (error) N-2
Total N-1

 A key aspect of any
model is the ‘model
checking’ – part of this is
done through
examination of the
residuals.
 For all regression models
which assume that
either the data or the
residuals are ‘normal’
then we use the same
assumptions of
independence,
randomness and normal
distribution

Parameter Estimates & Least Square Means
 We also look at the parameter estimates and their standard
errors – for the linear regression example the parameter estimate
is the slope (and intercept). For more complex models and those
with discrete explanatory variable we will use the parameter
estimates to compare levels of the discrete variables (Case Study 3
for examples & discussion).
 For models containing discrete variables as explanatory /
independent variables we will often want to present Means and
Standard Errors and compare these (with t-test if comparing 2 or
multiple comparison tests) (Section 6).

Exercise
 Identify what sort of model you may use in your research (check
the Statistical Modeling Teaching Guide) – e.g. linear regression
(section 3), designed experiment (section 4), response data which
are proportions or binary (section 10), count response data
(section 11), survival data (section 12).
 Which parameters may be included in your model as the Pattern
 Draw a pretend analysis of variance / deviance or parameter
estimates table of what you may expect to see in the analysis

Features Excel Stata SPSS SAS R
Learning curve Gradual/flat Steep/gradual Gradual/flat Pretty steep Pretty steep
User interface Point-and-click Programming/point-
and-click
Mostly point-and-
click
Programming Programming
Data
manipulation
Weak/moderate Very strong Moderate Very strong Very strong
Data analysis Modest Powerful Powerful Powerful/versatile Powerful/versatile
Graphics Very good Very good Very good Good Excellent
Cost
Part of MS office Affordable
(perpetual
licenses, renew
only when
upgrade)
Expensive (with
annual license
renewal )
Expensive
Annual Renewal
Open source
(free)
Data Analysis – Application (Statistical Software
Packages)

Data Analysis – Application (Using
R)
Outline
• Installing R
• R Environment
 Command prompt
 RStudio
 Setting your workspace
• Loading and installing R packages
• Importing data into R - *.csv/*.xls
• Saving R data
• Data exploration – summary statistics
• Graphing in R - boxplot
• Data analysis – T-test/linear & logistic regression

Introduction to R
Installing R
- Download R from http://cran.r-project.org
CRAN – Comprehensive R Archive Network
R version changes over time, the current one is E-
2.15.0
- Installing RStudio
- Setting up the work environment

Introduction to R
R Environment
Command prompt
R is primarily a command driven software where instructions are typed at
the command prompt (> )
R is case sensitive
Rstudio
Rstudio has limited set of commands that can be selected and executed from
the menu
Setting your workspace
It is important to set R preferences to suit your work environment, one such
setting is the working directory.
Working directory is set using the command setwd
setwd("D:/My Documents/R course") or from File->change dir on the menu
Take note of / R will not recognize when specifying subdirectories

Introduction to R
Loading and installing R packages
Modules or sets of functions are referred to as PACKAGES in R. Some packages
are part of the base installation while others have to be installed separately.
There are several user-contributed packages.
Type library() to view installed packages
To view functions within a package type
library(help=“packagename”) e.g. library(help=stats) – no quotes
Install packages using the menu Packages->Install package(s) ….
Use find(“item”) command to identify the package containing an item of
interest
e.g. find(“plot”), if you are sure of the exact name otherwise use
apropos(“item”)

Introduction to R
Importing data into R - *.csv/*.xls
Although it is possible to enter data directly into R, importing data in a spreadsheet format is more
efficient.
Use:
i. Read.table – to import space separated data with column headings (*.txt)
prod1 <- read.table("D://My Documents/R course/PROD2B.txt", header=T, sep=",")
ii. Read.csv – to import comma separated data with column headings (*.csv)
prod2 <- read.csv("D://My Documents/R course/PROD2B.csv", header=T)
To save the file in R
write.table(prod2, file="D://My Documents/R course/proddata2", quote=FALSE)
i. odbcConnectExcel() - to import excel worksheet
prod3<-"D://My Documents/R course/PROD2B.xls“
datachannel<-odbcConnectExcel(prod3)
outprod3 <-sqlFetch(channel= datachannel, sqtable="prod3")
write.table(outprod3, file="D://My Documents/R course/proddata3", quote=FALSE)

Introduction to R
Data exploration – summary statistics
One can get summary statistics on all numeric variables in the dataset
using summary(datasetname)
eg. summary(outprod3)
It is also possible to get summary statistics on a particular variable, use
$ to attach variable to the data table
e.g. summary(outprod3$WEIGHT)
Use aggregate to get summary statistics by group/category
e.g. aggregate(data.frame(WEIGHT), by=list(herd=HERD,sex=SEX), mean)
It is advisable to attach a data file to avoid having to specify the data file
all the time particularly for long summaries such as aggregate
attach(outprod3)

Introduction to R
Graphing in R – boxplot
- R has powerful graphing features that can be used in data
exploration, such as histograms, boxplot, scatterplot, etc.
histogram(~PCV, n=30, xlab="Packed Cell Volume")
boxplot(PCV, ylab="Packed Cell Volume")
boxplot(PCV~HERD, color="orange", ylab="Packed Cell Volume",
xlab="Herd")
xyplot(PCV~WEIGHT, color="orange", ylab="Packed Cell Volume",
xlab="Weight")

Introduction to R
Data analysis – T-test
- t.test(prod2$WEIGHT~prod2$SEX)
Data analysis – Linear Regression
- output1<-lm(PCV~WEIGHT)
- Remember to attach the dataset to make it active
- attach(prod2)
Data analysis – Logistic Regression
-

References
 Research Methods & Biometrics Teaching Resource – Case Study 1 & 4 have R,
Case Study 2 has ANOVA: many others used in this session as examples. The study
guides are useful for reference material on Explanatory and Formal Analysis.
 Take home:
 Analysis the Data & Models Chapters in Green Book
 Good Statistical Practice for Natural Resources Research – Part IV
 R Intro Course Notes – Nicholas Ndiwa
 Reading University SSC – Approaches to Analysis of Survey Data; Confidence &
Significance: Key Concepts of Inferential Statistics; Modern methods of analysis;
Analysis of Experimental Data

Module 4 data analysis

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