Basics of Statistics

Jobayer Hossain, PhD
Larry Holmes, Jr, PhD,DrPH, FACE
October 2, 2008
Class Structure
Course Website:
Classes: 8
Contact Hours: 2 hours
– 3 Take-home
– To be assigned in week 3, 5, and 6
– Due in week 4, 6,and 8
1 Take-home final exam/assignment
– Assigned in week 8 -- return for final comments
via e-mail.
Class Participation
Default dataset
– 60 subjects
– 3 or 4 groups
– Several measures of different types
(Nominal, Ordinal, Interval, Ratio)
Contributed datasets - (bring your own)
Areas of special interest
– Let us know yours!
Course objectives
At the end of the course participants are expected to:
– Understand the basic notion of statistics in research
– Know designs used to conduct research
– Understand some key elements in research such as-
selection of criteria of subjects, variables, measurement
scales of variables, and hypothesis
– Learn various statistical techniques used to analyze data
– Be able to interpret results and draw conclusion
– Learn the tools used in the analysis of data – Excel and
Research Design and Methodology
Research is the process of investigating scientific questions
Steps in Research process– Defining the problem and conceptualizing the study
– Designing and conducting study
Collecting data
Analyzing data
– Making sense of data
Defining the problem and
conceptualizing the study
Review relevant previous research and identify– The problem (s) and causes of the problem (s)
– State outcomes of previous research on the problem
– State clearly what you are planning for the proposed
– Form careful research questions and hypotheses
– Identify variables needed to achieve the objective (s)
Defining the problem and
conceptualizing the study
Review relevant…identify
– Identify scales to measure the variables
– Assess the feasibility of study objectives i.e. assess if it
is measurable what you want to measure
– Identify the target populations and define the eligibility
Research Question
Example – Does smoking increase the risk of renal carcinoma?
– Is oral inhaler effective in controlling asthma among
Hypothesis statement
Example – Smoking increases the risk of renal carcinoma in
pediatric patient
– Oral inhaler is effective in controlling asthma among
Study Objective
The purpose or aim of the study
Example– To assess the risk of renal carcinoma associated with
smoking among pediatric patients (primary objective)
– To determine the race and gender disparities in the
prevalence of smoking (secondary objective)
Study variable
Refers to measurement that changes from one individual to
Example- age, gender, BMI, Systolic blood pressure,
Outcome vs independent variable
Response/outcome variable: Measures the outcome of the study
treatment, or experimental manipulation
Examples– Renal carcinoma incident among children
– Asthma control in pediatric asthmatic patients
Independent/ predictor/explanatory variable: Explains or influences
changes in a response variable.
Examples– Smoking
– Oral inhaler
Scale of variable/output measurement
Nominal - Categorical variables without any order or
ranking sequence such as names or classes (e.g., gender).
Binary- two categories, multinomial- more than two
Ordinal - Variables with an inherent rank or order, e.g.
mild, moderate, severe. Can be compared for equality, or
greater or less, but not how much greater or less.
Scale of variable/output measurement
Interval - Values of the variable are ordered as in Ordinal, and
additionally, differences between values are meaningful, however, the
scale is not absolutely anchored. Calendar dates and temperatures on
the Fahrenheit scale are examples. Addition and subtraction, but not
multiplication and division are meaningful operations.
Ratio - Variables with all properties of Interval plus an absolute, nonarbitrary zero point, e.g. age, weight, temperature (Kelvin). Addition,
subtraction, multiplication, and division are all meaningful operations.
Measurement bias
Bias arises due to measurement error
Example– Suppose, In the case of remission of Asthma, the possible
outcomes are complete remission, partial remission and no
remission. If we measure the outcome variable as only remission
and non-remission, basically we are committing an error by putting
partial remission in the non-remission group (type II error).
Designing the study
A study design is a careful advance plan of data collection
and the analytic approach needed to answer the research
question under investigation in a scientific way.
The basic elements of a study design– Selecting an appropriate sample size for a specified
level of power and level of significance
– Selecting methods of sampling, data collection, and
analysis appropriate to the study's objectives
Clinical/Experimental versus Observational design
The Lancet. 2002, Vol 359
Clinical/Experimental vs Observational
The choice of a design mainly depends on the research
question (s) and type of research conduct ( experimental
or observational)
Experimental/ Interventional: The investigator controls
the experimental environment in which the hypothesis is
tested. The randomized double-blind clinical trial is the
gold standard.
Clinical/Experimental vs Observational
Non-experimental/Observational: The population is
observed without any interference by the investigator.
For example, in a study to see the effect of smoking, it is
impossible for an investigator to assign smoking to the subjects.
Instead, investigator can study the effect by choosing a control
group and find the cause and relation effect. Some examples are– Cross-sectional study
– Cohort study
– Case-control study
Randomized control design
Random allocation of subjects to different interventions (or
treatments) for the purpose of comparing/determining the
efficacy of the study treatment (s).
– E.g. placebo or standard medication (active control) can
be used as a control
– Patients with cancer or painful disease can not receive
placebo as a control
Randomized control design
Blindness: Reduces the bias due to the preconception or
personal bias.
– Open trial: Investigator and subject know the full details of the
– Single-blind trial: Investigator knows about the treatment but
subject does not.
– Double-blind: Both investigator and subject do not know about
the treatment
– Triple-blind: Sponsor, investigator, and subject do not know about
the treatment.
Distribution of a variable
Distribution - (of a variable) tells us what values the
variable takes and how often it takes these values. E.g.
distribution of some 26 pediatric patients of ages 1 to 6
at AIDHC are as followsAge
Science of data collection, summarization, analysis
and interpretation
Descriptive versus Inferential Statistics:
– Descriptive Statistic: Data description
(summarization) such as center, variability and
– Inferential Statistic : Drawing conclusion beyond
the sample studied, allowing for prediction.
A Taxonomy of Statistics
How does statistics help us?
Ages (in month) of the 60 patients in our data set 1 are- 71,
127, 65, 82, 140, 53, 114, 56, 84, 65, 67, 134, 64, …., 91, 51
By simply looking at the data, we fail to produce any informative
account to describe the data, how ever, statistics produce a quick
insight in to data using graphical and numerical statistical tools
Age Distribution
Distribution of age
Number of Subjects
Age (month)
Standard Error
Standard Deviation
Sample Variance
Age in Month
Statistical Description of Data
Statistics describes a numeric set of data by its
Center (mean, median, mode etc)
Variability (standard deviation, range etc)
Shape (skewness, kurtosis etc)
Statistics describes a categorical set of data by
Frequency, percentage or proportion of each
Statistical Inference
Statistical Inference
Statistical inference is the process by which we acquire information
about populations from samples.
Two types of estimates for making inferences:
– Point estimation.
– Interval estimate.
Population and sample
Population: The entire collection of individuals or
measurements about which information is desired.
Sample: A subset of the population selected for study.
– Primary objective is to create a subset of population
whose center, spread and shape are as close as that of
– Methods of sampling: Random sampling, stratified
sampling, systematic sampling, cluster sampling,
multistage sampling, area sampling, qoata sampling etc.
Parameter vs Statistics
– Any statistical characteristic of a population.
– Population mean, population median, population
standard deviation are examples of parameters.
– Parameter describes the distribution of a population
– Parameters are fixed and usually unknown
Parameter vs Statistics
Statistic: Any statistical characteristic of a sample.
– Sample mean, sample median, sample standard
deviation are some examples of statistics.
– Statistic describes the distribution of population
– Value of a statistic is known and is varies for different
– Are used for making inference on parameter
Parameter vs Statistics
Statistical Issue: To describe the distribution of a
population through census or making inference on
population distribution/ population parameter using sample
distribution/ statistic.
E.g. sample mean is an estimate of the population mean
Hypothesis Testing
Null hypothesis and Alternative hypothesis
e Reject Ho
s Accept Ho
Real Situation
Ho is true
Ho is false
Type I
error (α)
Type II
Error ()
(1- α)
Elements/Steps in hypothesis
Hypothesis testing steps:
– 1. Null (Ho) and alternative (H1)hypothesis specification
– 2. Selection of significance level (alpha) - 0.05 or 0.01
– 3. Calculating the test statistic –e.g. t, F, Chi-square
– 4. Calculating the probability value (p-value) or
confidence Interval?
– 5. Describing the result and statistic in an understandable
Point Estimation
• A point estimate draws inference about a
population by estimating the value of an unknown
parameter using a single value or a point.
Population distribution
Sample distribution
Point estimator
Interval Estimation
• An interval estimator draws inferences about a population by
estimating the value of an unknown parameter using an interval.
Population distribution
Interval estimator
Sample distribution
P-Value versus the Confidence Interval
Two main ways to assess study precision and the role of
chance in a study.
– P value measures ( in probability) the evidence against
the null hypothesis.
– An interval within which the value of the parameter lies
with a specified probability
– E.g. 95% CI implies that if one repeats a study 100
times, the true measure of association will lie inside the
CI in 95 out of 100 measures
Procedures for sample size
Selection of primary variables of interest and formulation
of hypotheses
Information of standard deviation ( if numeric) or
proportion (if categorical)
A tolerance level of significance ()
Selection of reasonable test statistic
Power or Confidence level
A scientifically or clinically meaning effect/ difference
Brief concept of Statistical Software
There are many software packages to perform statistical
analysis and visualization of data. Some of them are– System for Statistical Analysis (SAS), S-plus, R, Matlab, Minitab,
BMDP, STATA, SPSS, StatXact, Statistica, LISREL, JMP, GLIM,
HIL, MS Excel etc. We will discuss MS Excel and SPSS in brief .
useful websites (a free but powerful statistical software)
Microsoft Excel
A Spreadsheet Application. It features calculation, graphing tools, pivot tables
and a macro programming language called VBA (Visual Basic for Applications).
There are many versions of MS-Excel. Excel XP, Excel 2003, Excel 2007 are
capable of performing a number of statistical analyses.
Starting MS Excel: Double click on the Microsoft Excel icon on the desktop or
Click on Start --> Programs --> Microsoft Excel.
Worksheet: Consists of a multiple grid of cells with numbered rows down the
page and alphabetically-tilted columns across the page. Each cell is referenced
by its coordinates. For example, A3 is used to refer to the cell in column A and
row 3. B10:B20 is used to refer to the range of cells in column B and rows 10
through 20.
Microsoft Excel
Opening a document: File  Open (From a existing workbook). Change the
directory area or drive to look for file in other locations.
Creating a new workbook: FileNewBlank Document
Saving a File: FileSave
Selecting more than one cell: Click on a cell e.g. A1), then hold the Shift key
and click on another (e.g. D4) to select cells between and A1 and D4 or Click on a
cell and drag the mouse across the desired range.
Creating Formulas: 1. Click the cell that you want to enter the
formula, 2. Type = (an equal sign), 3. Click the Function Button, 4.
Select the formula you want and step through the on-screen
Microsoft Excel
Entering Date and Time: Dates are stored as MM/DD/YYYY. No need to enter
in that format. For example, Excel will recognize Jan 9 or jan-9 as 1/9/2007
and Jan 9, 1999 as 1/9/1999. To enter today’s date, press Ctrl and ; together.
Use a or p to indicate am or pm. For example, 8:30 p is interpreted as 8:30
pm. To enter current time, press Ctrl and : together.
Copy and Paste all cells in a Sheet: Ctrl+A for selecting, Ctrl +C for copying
and Ctrl+V for Pasting.
Sorting: Data  Sort Sort By …
Descriptive Statistics and other Statistical methods: ToolsData Analysis
Statistical method. If Data Analysis is not available then click on Tools Add-Ins and
then select Analysis ToolPack and Analysis toolPack-Vba
Microsoft Excel
Statistical and Mathematical Function: Start with ‘=‘ sign and then select
function from function wizard f x .
Inserting a Chart: Click on Chart Wizard (or InsertChart), select
chart, give, Input data range, Update the Chart options, and Select
output range/ Worksheet.
Importing Data in Excel: File open FileType Click on File Choose Option (
Delimited/Fixed Width) Choose Options (Tab/ Semicolon/ Comma/ Space/ Other)
 Finish.
Limitations: Excel uses algorithms that are vulnerable to rounding and truncation
errors and may produce inaccurate results in extreme
Statistics Package
for the Social Science (SPSS)
A general purpose statistical package SPSS is widely used in the social
sciences, particularly in sociology and psychology.
SPSS can import data from almost any type of file to generate tabulated
reports, plots of distributions and trends, descriptive statistics, and
complex statistical analyzes.
Starting SPSS: Double Click on SPSS on desktop or ProgramSPSS.
Opening a SPSS file: FileOpen
• Data Editor
Various pull-down menus appear at the top of the Data Editor window. These
pull-down menus are at the heart of using SPSSWIN. The Data Editor menu
items (with some of the uses of the menu) are:
Statistics Package
for the Social Science (SPSS)
used to open and save data files
used to copy and paste data values; used to find data in a
file; insert variables and cases; OPTIONS allows the user to
set general preferences as well as the setup for the
Navigator, Charts, etc.
user can change toolbars; value labels can be seen in cells
instead of data values
select, sort or weight cases; merge files
Compute new variables, recode variables, etc.
Statistics Package
for the Social Science (SPSS)
perform various statistical procedures
create bar and pie charts, etc
add comments to accompany data file (and other,
advanced features)
these are features not currently installed (advanced
statistical procedures)
switch between data, syntax and navigator windows
to access SPSSWIN Help information
Statistics Package
for the Social Science (SPSS)
Navigator (Output) Menus
When statistical procedures are run or charts are created, the output will appear
in the Navigator window. The Navigator window contains many of the pull-down
menus found in the Data Editor window. Some of the important menus in the
Navigator window include:
used to insert page breaks, titles, charts, etc.
for changing the alignment of a particular portion of the output
Statistics Package
for the Social Science (SPSS)
• Formatting Toolbar
When a table has been created by a statistical procedure, the user can edit the
table to create a desired look or add/delete information. Beginning with version
14.0, the user has a choice of editing the table in the Output or opening it in a
separate Pivot Table (DEFINE!) window. Various pulldown menus are activated
when the user double clicks on the table. These include:
undo and redo a pivot, select a table or table body (e.g., to
change the font)
used to insert titles, captions and footnotes
used to perform a pivot of the row and column variables
various modifications can be made to tables and cells
Statistics Package
for the Social Science (SPSS)
Importing tab-delimited data
In SPSSWIN click on FILE ⇒ OPEN ⇒ DATA. Look in the appropriate location for
the text file. Then select “Text” from “Files of type”: Click on the file name and then
click on “Open.” You will see the Text Import Wizard – step 1 of 6 dialog box.
You will now have an SPSS data file containing the former tab-delimited data. You
simply need to add variable and value labels and define missing values.
Exporting Data to Excel
click on FILE ⇒ SAVE AS. Click on the File Name for the file to be exported. For
the “Save as Type” select from the pull-down menu Excel (*.xls). You will notice the
checkbox for “write variable names to spreadsheet.” Leave this checked as you will
want the variable names to be in the first row of each column in the Excel
spreadsheet. Finally, click on Save.
Statistics Package
for the Social Science (SPSS)
• Additional menus
used to edit a graph
used to edit the text in a syntax window
• Show or hide a toolbar
Click on VIEW ⇒ TOOLBARS ⇒ 􀀻to show it/ to hide it
• Move a toolbar
Click on the toolbar (but not on one of the pushbuttons) and then drag the toolbar to
its new location
• Customize a toolbar
Statistics Package
for the Social Science (SPSS)
Importing data from an EXCEL spreadsheet:
Data from an Excel spreadsheet can be imported into SPSSWIN as follows:
1. In SPSSWIN click on FILE ⇒ OPEN ⇒ DATA. The OPEN DATA FILE Dialog
Box will appear.
2. Locate the file of interest: Use the "Look In" pull-down list to identify the folder
containing the Excel file of interest
3. From the FILE TYPE pull down menu select EXCEL (*.xls).
4. Click on the file name of interest and click on OPEN or simply double-click on
the file name.
5. Keep the box checked that reads "Read variable names from the first row of
data". This presumes that the first row of the Excel data file contains variable
names in the first row. [If the data resided in a different worksheet in the Excel
file, this would need to be entered.]
6. Click on OK. The Excel data file will now appear in the SPSSWIN Data
Statistics Package
for the Social Science (SPSS)
Importing data from an EXCEL spreadsheet:
7. The former EXCEL spreadsheet can now be saved as an SPSS file (FILE ⇒
SAVE AS) and is ready to be used in analyses. Typically, you would label variable
and values, and define missing values.
Importing an Access table
SPSSWIN does not offer a direct import for Access tables. Therefore, we must follow
these steps:
1. Open the Access file
2. Open the data table
3. Save the data as an Excel file
4. Follow the steps outlined in the data import from Excel Spreadsheet to SPSSWIN.
Importing Text Files into SPSSWIN
Text data points typically are separated (or “delimited”) by tabs or commas.
Sometimes they can be of fixed format.
Statistics Package
for the Social Science (SPSS)
Running the FREQUENCIES procedure
1. Open the data file (from the menus, click on FILE ⇒ OPEN ⇒ DATA) of
2. From the menus, click on ANALYZE ⇒ DESCRIPTIVE STATISTICS ⇒
3. The FREQUENCIES Dialog Box will appear. In the left-hand box will be a listing
("source variable list") of all the variables that have been defined in the data file. The
first step is identifying the variable(s) for which you want to run a frequency analysis.
Click on a variable name(s). Then click the [ > ] pushbutton. The variable name(s)
will now appear in the VARIABLE[S]: box ("selected variable list"). Repeat these
steps for each variable of interest.
4. If all that is being requested is a frequency table showing count, percentages
(raw, adjusted and cumulative), then click on OK.
Statistics Package
for the Social Science (SPSS)
Descriptive and summary STATISTICS can be requested for numeric variables. To
request Statistics:
1. From the FREQUENCIES Dialog Box, click on the STATISTICS... pushbutton.
2. This will bring up the FREQUENCIES: STATISTICS Dialog Box.
3. The STATISTICS Dialog Box offers the user a variety of choices:
The DESCRIPTIVES procedure can be used to generate descriptive statistics
procedure offers many of the same statistics as the FREQUENCIES procedure,
but without generating frequency analysis tables.
Statistics Package
for the Social Science (SPSS)
Requesting CHARTS
One can request a chart (graph) to be created for a variable or variables included in
a FREQUENCIES procedure.
1. In the FREQUENCIES Dialog box click on CHARTS.
2. The FREQUENCIES: CHARTS Dialog box will appear. Choose the intended chart
(e.g. Bar diagram, Pie chart, histogram.
Pasting charts into Word
1. Click on the chart.
2. Click on the pulldown menu EDIT ⇒ COPY OBJECTS
3. Go to the Word document in which the chart is to be embedded. Click on EDIT ⇒
4. Select Formatted Text (RTF) and then click on OK
5. Enlarge the graph to a desired size by dragging one or more of the black squares
along the perimeter (if the black squares are not visible, click once on the graph).
Statistics Package
for the Social Science (SPSS)
1. From the ANALYZE pull-down menu, click on DESCRIPTIVE STATISTICS ⇒
2. The CROSSTABS Dialog Box will then open.
3. From the variable selection box on the left click on a variable you wish to
designate as the Row variable. The values (codes) for the Row variable make up
the rows of the crosstabs table. Click on the arrow (>) button for Row(s). Next,
click on a different variable you wish to designate as the Column variable. The
values (codes) for the Column variable make up the columns of the crosstabs
table. Click on the arrow (>) button for Column(s).
4. You can specify more than one variable in the Row(s) and/or Column(s). A cross
table will be generated for each combination of Row and Column variables
Statistics Package
for the Social Science (SPSS)
Limitations: SPSS users have less control over data manipulation and
statistical output than other statistical packages such as SAS, Stata etc.
SPSS is a good first statistical package to perform quantitative research
in social science because it is easy to use and because it can be a good
starting point to learn more advanced statistical packages.