LECTURE 1 AND 2 Introduction to Statistics
Statistics
Statistics" (preferably with a capital letter) to refer to the academic discipline concerned
with the collection, description, analysis and interpretation of numerical data. As such,
the subject of Statistics may be divided into two main categories:
(a) Descriptive Statistics
This is mainly concerned with collecting and summarising data, and presenting the
results in appropriate tables and charts. For example, companies collect and
summarise their financial data in tables (and occasionally charts) in their annual
reports, but there is no attempt to go "beyond the data".
(b) Statistical Inference
This is concerned with analysing data and then interpreting the results (attempting
to go "beyond the data"). The main way in which this is done is by collecting data
from a sample and then using the sample results to infer conclusions about the
population.
For example, prior to general elections in the Kenya and many other countries,
statisticians conduct opinion polls in which samples of potential voters are asked
which political party they intend to vote for. The sample proportions are then used
to predict the voting intentions of the entire population.
Of course, before any descriptive statistics can be calculated or any statistical inferences
made, appropriate data has to be collected. We will start the course, therefore, by seeing
how we collect data. This study unit looks at the various types of data, the main sources
of data and some of the numerous methods available to collect data.
B. MEASUREMENT SCALES AND TYPES OF DATA
Measurement Scales
Quantitative methods use quantitative data which consists of measurements of various
kinds. Quantitative data may be measured in one of four measurement scales, and it is
important to be aware of the measurement scale that applies to your data before
commencing any data description or analysis. The four measurement scales are:
(a) Nominal Scale
The nominal scale uses numbers simply to identify members of a group or category.
For example, in a questionnaire, respondents may be asked whether they are male
or female and the responses may be given number codes (say 0 for males and 1 for
females). Similarly, companies may be asked to indicate their ownership form and
again the responses may be given number codes (say 1 for public limited
companies, 2 for private limited companies, 3 for mutual organizations, etc.). In
these cases, the numbers simply indicate the group to which the respondents
belong and have no further arithmetic meaning.
(b) Ordinal Scale
The ordinal scale uses numbers to rank responses according to some criterion, but
has no unit of measurement. In this scale, numbers are used to represent "more
than" or "less than" measurements, such as preferences or rankings. For example, it
is common in questionnaires to ask respondents to indicate how much they agree
with a given statement and their responses can be given number codes (say 1 for
"Disagree Strongly", 2 for "Disagree", 3 for "Neutral", 4 for "Agree" and 5 for "Agree
Strongly"). This time, in addition to indicating to which category a respondent
1| Jeff Arodi
Statistics
Statistics" (preferably with a capital letter) to refer to the academic discipline concerned
with the collection, description, analysis and interpretation of numerical data. As such,
the subject of Statistics may be divided into two main categories:
(a) Descriptive Statistics
This is mainly concerned with collecting and summarising data, and presenting the
results in appropriate tables and charts. For example, companies collect and
summarise their financial data in tables (and occasionally charts) in their annual
reports, but there is no attempt to go "beyond the data".
(b) Statistical Inference
This is concerned with analysing data and then interpreting the results (attempting
to go "beyond the data"). The main way in which this is done is by collecting data
from a sample and then using the sample results to infer conclusions about the
population.
For example, prior to general elections in the Kenya and many other countries,
statisticians conduct opinion polls in which samples of potential voters are asked
which political party they intend to vote for. The sample proportions are then used
to predict the voting intentions of the entire population.
Of course, before any descriptive statistics can be calculated or any statistical inferences
made, appropriate data has to be collected. We will start the course, therefore, by seeing
how we collect data. This study unit looks at the various types of data, the main sources
of data and some of the numerous methods available to collect data.
B. MEASUREMENT SCALES AND TYPES OF DATA
Measurement Scales
Quantitative methods use quantitative data which consists of measurements of various
kinds. Quantitative data may be measured in one of four measurement scales, and it is
important to be aware of the measurement scale that applies to your data before
commencing any data description or analysis. The four measurement scales are:
(a) Nominal Scale
The nominal scale uses numbers simply to identify members of a group or category.
For example, in a questionnaire, respondents may be asked whether they are male
or female and the responses may be given number codes (say 0 for males and 1 for
females). Similarly, companies may be asked to indicate their ownership form and
again the responses may be given number codes (say 1 for public limited
companies, 2 for private limited companies, 3 for mutual organizations, etc.). In
these cases, the numbers simply indicate the group to which the respondents
belong and have no further arithmetic meaning.
(b) Ordinal Scale
The ordinal scale uses numbers to rank responses according to some criterion, but
has no unit of measurement. In this scale, numbers are used to represent "more
than" or "less than" measurements, such as preferences or rankings. For example, it
is common in questionnaires to ask respondents to indicate how much they agree
with a given statement and their responses can be given number codes (say 1 for
"Disagree Strongly", 2 for "Disagree", 3 for "Neutral", 4 for "Agree" and 5 for "Agree
Strongly"). This time, in addition to indicating to which category a respondent
1| Jeff Arodi
