introduction to statistical analysisqmgcw.in/pdf/hsce.pdfintroduction to statistical analysis dr. n....
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INTRODUCTION TO STATISTICAL
ANALYSIS
Dr. N. SowmyaM.Sc, M.Phil, Ph.D,
Associate Professor & Head,
Department of Home Science,
Quaid-E-Millath Govt. College for Women,
Chennai-02
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CONTENTS
Descriptive and inferential statistics
Types of Variables
Analysis of Data
Parametric and non - parametric tests
t-test, ANOVA, Correlation and linear regression
analysis
Demonstration of the above analyses using SPSS
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STATISTICS-AN OVERVIEW
An area of Science concerned with extraction
of information from numerical data and its
use in making inferences about the
population from which it is obtained.
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VARIABLESA characteristic that varies from one subject
to another or from one unit to another.
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ANALYSIS OF DATA
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POINTS TO REMEMBER
Standard deviation (S.D.) is a measure of variability
& explains how far each observation deviates from
the mean
In a normal distribution ,S.D should be <1/2 mean.
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INFERENTIAL STATISTICS
Hypothesis testing - A way of organising & presenting evidence that helps
to reach a conclusion
PARAMETRIC TESTS
They assume certain properties of the population like normal
distribution, equal mean & variance etc.
Powerful statistical tests.
Important tests-t test, F test (ANOVA), Pearson correlation and linear
regression
When the dependent variable is continuous, parametric tests can be used.
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NON-PARAMETRIC TESTS
Do not make any assumptions about the
population
Used when the distribution is not a normal
distribution (skewed)
When the dependent variable is categorical or
ordinal, non parametric tests can be used
Ex-Chi-square test,Mann-whitney U test,
Kruskal wallis test
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t-TEST
Used to compare the means of groups
TYPES
• One sample test
• T-test for 2 independent samples (uncorrelated)
• T-test for paired samples (correlated)
• One sample t test-compare the means of a single group of observations
with a specified value.Ex. Compare the mean dietary intake with RDA
• Student’s t test- to compare means of 2 independent samples.
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Independent variable-one nominal variable with 2 levels -
ex.boys/girls, smoking/non-smoking workers
Dependent variable-ex.marks obtained by the students , BMI/blood
Glucose etc
Assumptions
The 2 pairs should be independent.
The independent variable is categorical & contains only 2 levels.
It is a normal distribution.
VARIABLES FOR INDEPENDENT SAMPLE t - TEST
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PAIRED t-TEST
Same individuals are studied more than once in
different circumstances.
Ex-measurements made on the same people before
and after intervention.
Condition- outcome variable should be
continuous, normal distribution.
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ANOVA
ANOVA or F statistics are actually ratios of estimate of
variance.
Used to compare the means of more than 2 groups.
Examines the difference among groups.
Considers the variation across all groups at once
It is called ANOVA because although means are compared,
the comparisons are made using estimates of variance.
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TYPE OF DATA REQUIRED
Independent variable- one nominal variable >2 levels Ex -
income level - Low/medium/high
Dependent variable- continuous variable Ex.height,weight
Assumptions
-The samples are random & independent of each other.
-The independent variable is categorical & contains more than
2 levels.
-Normal distribution
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ANOVA separates the variation in all the data into 2
parts
The variation between each group mean & overall mean
for all the groups ie. Between group variability
The variation between each study participant &
participants group mean (the within group variability).
If the between group variability is much > than within
group variability) there are likely to be differences
between group means.
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MEASURES OF RELATIONSHIP
CORRELATION
Bivariate data-where 2 variables are measured from each subject. Ex.
Height & Age
The relationship between such variables is called Correlation.
Represented as “r” & ranges from -1 to 1(Pearson’s Coefficient of
correlation)
REGRESSION
Describes the relation between the values of 2 variables.
Can predict the value of one variable using the value of the other variable.
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CORRELATION
• Correlation analysis is used to determine if there is
a relationship between 2 variables - ex. Weight &
blood glucose levels and the strength of association
between them.
• Correlation analysis also determines the direction
of relationship - whether it is positive or negative
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LINEAR REGRESSION
Used when the relationship between variables is linear
Simple linear regression-one independent & one
dependent variable - ex age and height.
Multiple linear regression-more than one independent
variable - ex Age, height and BMI on BP levels.
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Describes the relation between 2 variables
Indicates the impact of the independent
variable
Predicts the value of one variable using the
value of the other variable for an individual.
ex. Given a value of age, corresponding
cholesterol levels can be predicted
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TO SUM UP
• Statistics can be used to describe the
population characteristics and for
making inferences
• For normal distributions, parametric
tests like t- test and ANOVA are used
• Statistical methods like correlation
and regression are used to study
relationship between variables
• SPSS can be used effectively for all the
above analysis
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