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

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

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.

VARIABLESA characteristic that varies from one subject

to another or from one unit to another.

ANALYSIS OF DATA

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.

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.

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

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.

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

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.

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.

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

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.

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.

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

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.

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

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