Lecture 1 Introduction to Social Statistics.pdf

This power point presentation is all about Introduction to Social Statistics

1. INTRODUCTION TO SOCIAL
STATISTICS
Lecture 1
Dumisani Namakhwa, BEng(Hon), MSc
[email protected]
[email protected]
0997223338

2. INTRODUCTION
▪Social statistics is the use of statistics to study human behavior and social
environments.
▪Statistics is the discipline that concerns the collection, organization, analysis,
interpretation, and presentation of data.
▪divided into two main categories:
a)Descriptive Statistics
➢This is mainly concerned with collecting and summarizing data and presenting the results in
appropriate tables and charts.
➢For example, measures of central tendency (mean, mode, and median), measures of dispersion
(variance, standard deviation, range)…..
b)Statistical Inference
➢This is concerned with analyzing 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.
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3. VARIABLES
▪A variable is any characteristic, number, or quantity that can be measured or
counted.
▪Age, sex, business income and expenses, country of birth, capital expenditure,
class grades, eye color and vehicle type are examples of variables.
▪It is called a variable because the value may vary between data units in a
population and may change in value over time.
▪For example; 'income' is a variable that can vary between data units in a population
(i.e., the people or businesses being studied may not have the same incomes) and
can also vary over time for each data unit (i.e., income can go up or down).
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4. TYPES OF VARIABLES
▪Numeric variables
➢Numeric variables have values that describe a measurable quantity as a number,
like 'how many' or 'how much’.
➢Therefore, numeric variables are quantitative variables.
➢Numeric variables may be further described as either continuous or discrete:
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Numeric variables
continuous discrete

5. TYPES OF VARIABLES: NUMERIC VARIABLES
▪Continuous variable
▪ Observations can take any value between a certain set of real numbers.
▪The value given to an observation for a continuous variable can include values
as small as the instrument of measurement allows.
▪Examples of continuous variables include height, time, age, and temperature.
▪Discrete variable
▪ Observations can take a value based on a count from a set of distinct whole
values.
▪A discrete variable cannot take the value of a fraction between one value and the
next closest value.
▪Examples of discrete variables include the number of registered cars, number of
business locations, and number of children in a family, all of which measured as
whole units (i.e. 1, 2, 3 cars).
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6. TYPES OF VARIABLES
▪Categorical variables
➢Categorical variables have values that describe a 'quality' or 'characteristic' of
a data unit, like 'what type' or 'which category’.
➢Categorical variables fall into mutually exclusive (in one category or in
another) and exhaustive (include all possible options) categories.
➢Therefore, categorical variables are qualitative variables and tend to be
represented by a non-numeric value.
➢Categorical variables may be further described as ordinal or nominal:
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Categorical variables
ordinal Nominal

7. TYPES OF VARIABLES: CATEGORICAL VARIABLES
▪Ordinal variable
➢Observations can take a value that can be logically ordered or ranked.
➢The categories associated with ordinal variables can be ranked higher or lower than
another, but do not necessarily establish a numeric difference between each category.
➢ Examples of ordinal categorical variables include academic grades (i.e. A, B, C), clothing
size (i.e. small, medium, large, extra large) and attitudes (i.e. strongly agree, agree,
disagree, strongly disagree).
▪Nominal variable
➢Observations can take a value that is not able to be organized in a logical sequence.
➢ Examples of nominal categorical variables include sex, business type, eye color, religion
and brand.
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8. 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:
a)Nominal Scale
b)Ordinal Scale
c)Interval Scale
d)Ratio Scale
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9. MEASUREMENT SCALES
▪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.
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10. MEASUREMENT SCALES
▪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 belongs, the
numbers measure the degree of agreement with the statement and tell us whether
one respondent agrees more or less than another respondent.
➢However, since the ordinal scale has no units of measurement, we cannot say that the
difference between 1 and 2 (i.e., between disagreeing strongly and just disagreeing)
is the same as the difference between 4 and 5 (i.e., between agreeing and agreeing
strongly).
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11. MEASUREMENT SCALES
▪Interval Scale
➢An interval scale is one where there is order and the difference between two values is
meaningful.
➢There is no true zero point or fixed beginning. They do not have a true zero even if one of
the values carry the name “zero.”
➢Interval data examples:
1.Date
2.Temperature, in degrees Fahrenheit or Celsius
3.Age is also a variable that is measurable on an interval scale, like 1, 2, 3, 4, 5 years and etc.
4.Time
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“If anxiety were measured on an interval scale, then a difference
between a score of 15 and a score of 30 would represent the same
difference in anxiety as would a difference between a score of 45 and a
score of 60. But they do not have a zero point. For the anxiety scale, it
would not be valid to say that a person with a score of 30 was twice as
anxious as a person with a score of 15.”

12. MEASUREMENT SCALES
▪Ratio scale
➢The ratio scale has a constant unit of measurement and an absolute zero point. So, this is
the scale used to measure values, lengths, weights and other characteristics where there
are well-defined units of measurement and where there is an absolute zero where none of
the characteristic is present.
➢For example, in values measured in Malawi kwacha, we know (all too well) that a zero
balance means no money.
➢Allow ratio comparisons of measurements.
➢We can also say that £30 is twice as much as £15, and this would be true whatever
currency were used as the unit of measurement.
➢Other examples of ratio scale measurements include the average petrol consumption of a
car, the number of votes cast at an election, the percentage return on an investment, the
profitability of a company, and many others.
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13. SUMMARY: MEASUREMENT SCALES
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14. POPULATION
▪The entire group of individuals is called the population.
▪For example, a researcher may be interested in the relation between class size
(variable 1) and academic performance (variable 2) for the population of third-
grade children.
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15. SAMPLE
▪Usually, populations are so large that a researcher cannot examine the entire group.
Therefore, a sample is selected to represent the population in a research study.
The goal is to use the results obtained from the sample to help answer questions
about the population.
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17. DATA
▪The measurements obtained in a research study are called the data.
▪The goal of statistics is to help researchers organize and interpret the data.
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18. ▪Most data can be put into the following categories:
➢quantitative - data are observations that are measured on a
numerical scale (distance traveled to college, number of
children in a family, etc.)
➢Qualitative - data measurements that each fall into one of
several categories (hair color, ethnic groups and other
attributes of the population).
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CONT.…

19. QUANTITATIVE DATA
▪Quantitative data are always numbers and are the result of counting or measuring
attributes of a population.
▪Quantitative data can be separated into two subgroups:
➢Discrete (if it is the result of counting (the number of students of a given ethnic group in a class,
the number of books on a shelf, …)
➢Continuous (if it is the result of measuring (distance traveled, weight of luggage, …)
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20. QUALITATIVE DATA
▪ Qualitative data are generally described by words or letters.
▪They are not as widely used as quantitative data because many numerical
techniques do not apply to the qualitative data.
▪For example, it does not make sense to find an average hair color or blood
type.
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21. NOTATION
▪The individual measurements or scores obtained for a research participant will be
identified by the letter X (or X and Y if there are multiple scores for each
individual).
▪The number of scores in a data set will be identified by N for a population or n for a
sample.
▪Summing a set of values is a common operation in statistics and has its own
notation. The Greek letter sigma, Σ, will be used to stand for "the sum of." For
example, ΣX identifies the sum of the scores.
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22. ORDER OF OPERATIONS
1.All calculations within parentheses are done first.
2.Squaring or raising to other exponents is done second.
3.Multiplying, and dividing are done third, and should be completed in order
from left to right.
4.Summation with the Σ notation is done next.
5.Any additional adding and subtracting is done last and should be completed in
order from left to right.
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23. THANK YOU
STAT 2202N: Social Statistics 8/6/202423