Module 1 - Statistics
Module 1 – Introduction to Statistics
Module Overview:
1) Overview of Statistics
2) Branches of Statistics.
3) Population and Sample, Parameter and Statistic.
4) Types of Data
5) Level of Measurements
6) Sampling Methods
SECTION 1.1: Overview of Statistics
Overview of Statistics
Students who are studying Social and Natural Sciences such as Psychology, Economics, Sociology, or
Business are often surprised to learn how much of the curriculum in their field focuses on understanding
and learning how to analyze data. Because statistics is an essential part of these fields, students need to
understand how to use statistics and how to interpret statistical results.
1
,Module 1 - Statistics
The science of statistics provides students with guidelines for describing data and for interpreting patterns
of differences that may occur within certain groups of data or between different groups. Statistics also
provides sound and scientifically rigorous techniques for handling and analyzing data when making
inferences from numerical results. Statistics has the power to transform data into knowledge that can be
used to understand and solve real world problems.
Definition:
Statistics is the science of collecting, organizing, summarizing data and drawing conclusions for the
population based on those results. Alternative Definition:
Statistics is a collection of methods for decision making in the face of uncertainty on the basis of numerical
data and calculated risks.
The two major branches of statistics are Descriptive and Inferential Statistics; these statistics are not
mutually exclusive, but rather, build on one another. They are presented below:
Descriptive Statistics
Descriptive statistics are statistical procedures that are used to describe characteristics of data sets.
Descriptive statistics refers to the measurement of data that is presently occurring within all subjects. This
type of statistic involves methods of organizing, picturing, and summarizing information from samples or
populations so that we can communicate our results as accurately and completely as possible. For example,
one of the first things that we would want to do with our data is to graph them, to calculate means,
(averages) and other measures, and to look from extreme scores or oddly shaped distribution of scores.
These procedures are called descriptive statistics because they are primarily aimed at describing the data. It
also allows us to simplify large quantities of data in an understandable and logical manner.
Definition:
The branch of statistics which deals with collecting, organizing, summarizing and graphing a data set is
called descriptive statistics.
Inferential Statistics
Once we have described our data in detail and are satisfied that we understand what the numbers have to
say on a superficial level, we will employ the use of Inferential Statistics. Inferential statistics refers to
2
, Module 1 - Statistics
assessing the likelihood of something happening at some point in the future (probability) or testing a
sample of the population in order to generalize to the entire population. Perhaps one of the simplest
inferential tests is used when you want to compare the average performance of two groups on a single
measure to see if there is a difference. You might want to know whether sixth-grade boys and girls differ in
math test scores or whether a program group differs on the outcome measure from a control group. Most of
this book will deal with inferential statistics as it allows us to draw conclusions about a population based on
the data in our sample.
Definition:
The branch of statistics which deals with drawing conclusions based on information collected from the
sample is called inferential statistics.
Population
In most statistical investigations, the target group is known as the population. A population is not a group of
people, but a set of responses from a group. For example, if we are interested in the effect that watching
Sesame Street has on preschool children’s vocabulary scores, the population of interest is preschool
children’s vocabulary scores. In a second case, if we are interested in differences in cooking abilities
between men and women, our population of interest is differences in cooking abilities of men and women.
As you can see, the population of interest is dependent on the research question itself. In most statistical
studies, the population can be too large, making it difficult or sometimes even impossible to try to extract
information from the population. Fortunately, statistics has allowed us to draw conclusions about an entire
population by studying only a subset (sample) of responses drawn from that population.
Definition:
A population is the entire collection of outcomes, measurements, and counts to be studied.
Sample
A sample is a subset or part of the population that is being examined. It is important that the data sample we
examine is representative of the population of interest. This means that the sample must possess the same
important qualities and characteristics that are in the population. For example, if the population of interest
is preschool children’s vocabulary scores, our sample responses should be reflective of the wide range of
possible vocabulary scores found in the population. If our sample consisted of only the vocabulary scores
of preschoolers from higher socio-economic status families who have had extensive experience in high-
3
Module 1 – Introduction to Statistics
Module Overview:
1) Overview of Statistics
2) Branches of Statistics.
3) Population and Sample, Parameter and Statistic.
4) Types of Data
5) Level of Measurements
6) Sampling Methods
SECTION 1.1: Overview of Statistics
Overview of Statistics
Students who are studying Social and Natural Sciences such as Psychology, Economics, Sociology, or
Business are often surprised to learn how much of the curriculum in their field focuses on understanding
and learning how to analyze data. Because statistics is an essential part of these fields, students need to
understand how to use statistics and how to interpret statistical results.
1
,Module 1 - Statistics
The science of statistics provides students with guidelines for describing data and for interpreting patterns
of differences that may occur within certain groups of data or between different groups. Statistics also
provides sound and scientifically rigorous techniques for handling and analyzing data when making
inferences from numerical results. Statistics has the power to transform data into knowledge that can be
used to understand and solve real world problems.
Definition:
Statistics is the science of collecting, organizing, summarizing data and drawing conclusions for the
population based on those results. Alternative Definition:
Statistics is a collection of methods for decision making in the face of uncertainty on the basis of numerical
data and calculated risks.
The two major branches of statistics are Descriptive and Inferential Statistics; these statistics are not
mutually exclusive, but rather, build on one another. They are presented below:
Descriptive Statistics
Descriptive statistics are statistical procedures that are used to describe characteristics of data sets.
Descriptive statistics refers to the measurement of data that is presently occurring within all subjects. This
type of statistic involves methods of organizing, picturing, and summarizing information from samples or
populations so that we can communicate our results as accurately and completely as possible. For example,
one of the first things that we would want to do with our data is to graph them, to calculate means,
(averages) and other measures, and to look from extreme scores or oddly shaped distribution of scores.
These procedures are called descriptive statistics because they are primarily aimed at describing the data. It
also allows us to simplify large quantities of data in an understandable and logical manner.
Definition:
The branch of statistics which deals with collecting, organizing, summarizing and graphing a data set is
called descriptive statistics.
Inferential Statistics
Once we have described our data in detail and are satisfied that we understand what the numbers have to
say on a superficial level, we will employ the use of Inferential Statistics. Inferential statistics refers to
2
, Module 1 - Statistics
assessing the likelihood of something happening at some point in the future (probability) or testing a
sample of the population in order to generalize to the entire population. Perhaps one of the simplest
inferential tests is used when you want to compare the average performance of two groups on a single
measure to see if there is a difference. You might want to know whether sixth-grade boys and girls differ in
math test scores or whether a program group differs on the outcome measure from a control group. Most of
this book will deal with inferential statistics as it allows us to draw conclusions about a population based on
the data in our sample.
Definition:
The branch of statistics which deals with drawing conclusions based on information collected from the
sample is called inferential statistics.
Population
In most statistical investigations, the target group is known as the population. A population is not a group of
people, but a set of responses from a group. For example, if we are interested in the effect that watching
Sesame Street has on preschool children’s vocabulary scores, the population of interest is preschool
children’s vocabulary scores. In a second case, if we are interested in differences in cooking abilities
between men and women, our population of interest is differences in cooking abilities of men and women.
As you can see, the population of interest is dependent on the research question itself. In most statistical
studies, the population can be too large, making it difficult or sometimes even impossible to try to extract
information from the population. Fortunately, statistics has allowed us to draw conclusions about an entire
population by studying only a subset (sample) of responses drawn from that population.
Definition:
A population is the entire collection of outcomes, measurements, and counts to be studied.
Sample
A sample is a subset or part of the population that is being examined. It is important that the data sample we
examine is representative of the population of interest. This means that the sample must possess the same
important qualities and characteristics that are in the population. For example, if the population of interest
is preschool children’s vocabulary scores, our sample responses should be reflective of the wide range of
possible vocabulary scores found in the population. If our sample consisted of only the vocabulary scores
of preschoolers from higher socio-economic status families who have had extensive experience in high-
3
