STATISTICS
STATISTICS
• branch of mathematics that
deals with the process of
gathering, organizing,
summarizing, and analyzing
statistical data in order to
draw valid conclusions and
make reasonable decisions
DESCRIPTIVE STATISTICS
• Statistical procedures
used to summarize,
organize, and describe a
group of numbers from a
research study.
INFERENTIAL STATISTICS
• Statistical procedures
used to make
generalizations about
the populations from the
data collected from the
sample.
BASIC
STATISTICAL
TERMS
• POPULATION: a collection
of ALL possible members of a
set of people or objects that
are being studied
• SAMPLE: a subset of the
population from whom data
are collected
BASIC
STATISTICAL
TERMS
• PARAMETER: a
numerical value that
describes the population
• STATISTIC: a numerical
value that describes the
sample
BASIC
STATISTICAL
TERMS
•VARIABLE: a
characteristic that varies
from one person or
object to another
•DATA: are actual values
of the variable
VARIABLES,
VALUES, SCORES
• VARIABLE: a condition
or characteristic that can
have different values
•VALUE: possible
number or category that
a score can have
VARIABLES,
VALUES, SCORES
• SCORE: a particular
person’s values on a
variable
VARIABLES,
VALUES, SCORES
EXAMPLE: Stress
Rating •Variable: level
of stress •Values: 0 to 10
• Score: 6
VARIABLES
ACCORDING TO TYPE
• CATEGORICAL or
QUALITATIVE: assumes
non-numerical values;
allow for classification of
individuals based on
some attributes
VARIABLES
ACCORDING TO TYPE
• NUMERICAL or
QUANTITATIVE:
assumes numerical
values
VARIABLES
ACCORDING TO TYPE
• DISCRETE: variables
with values in fixed
amounts and cannot be
broken into smaller
amounts
VARIABLES
ACCORDING TO TYPE
• CONTINUOUS:
variables with infinite
number of possible
values that fall between
any two observed values
VARIABLES ACCORDING
TO LEVELS OF
MEASUREMENT •
NOMINAL: measured
by assigning labels or
names to each
observation; the variable
can only take one value
out of the given options
VARIABLES ACCORDING
TO LEVELS OF
MEASUREMENT
• ORDINAL: observations
can be categorized into
specific order; distance
between variables can’t
be calculated
VARIABLES ACCORDING
TO LEVELS OF
MEASUREMENT
• INTERVAL: distance
between observations
does have meaning
• RATIO: zero is
meaningful
VARIABLES ACCORDING
TO LEVELS OF
MEASUREMENT
Nominal
Ordinal
• Sex
• Grades
• Civil
• Satisfacti
on
Status
• Ratings
• Political
Preferen
c
e
• Residenc
e
Interval
• Temperat
ure
• Calendar
years
• Time
Ratio
• Height
• Weight
VARIABLES ACCORDING
TO LEVELS OF
MEASUREMENT
Offers
Nomin
Ordin
Interv
Ratio
The sequence of
variables is established
al -
al Yes
al Yes
Yes
Mode
Yes
Yes
Yes
Yes
Median
-
Yes
Yes
Yes
Mean
-
-
Yes
Yes
Difference
between variables
can be
evaluated
-
-
Yes
Yes
Addition & Subtraction
-
-
Yes
Yes
Multiplication & Division
-
-
-
Yes
Absolute zero
-
-
-
Yes
VARIABLES ACCORDING TO
FUNCTIONAL
RELATIONSHIP
• INDEPENDENT:
Variables presumed to
affect or
influence another variable
• DEPENDENT: Variables
presumed to be affected
by one or more IVs
VARIABLES ACCORDING TO
FUNCTIONAL
RELATIONSHIP
• MODERATING: A secondary
independent variable that
may affect the relationship
between IV and DV
• EXTRANEOUS: IVs that have
not been controlled; may or
may not influence results
EXERCISE 1
1. A father rates his daughter as
a 2 on a 7-point scale (from 1 to
7) of crankiness. Variable:
Value:
Score:
EXERCISE 1
2. What is the difference
between a categorical
and a numerical variable?
EXERCISE 1
3. Give the level of measurement
of each of the following
variables:
a. A person’s nationality
b. A person’s sex
c. A person’s score on a standard
IQ test
d. A person’s place on a waiting
list (first, second)
EXERCISE 1
4. What is the difference
between a discrete and a
continuous variable?
EXERCISE 1 (Answers)
1. A father rates his daughter as
a 2 on a 7-point scale (from 1 to
7) of crankiness. Variable:
CRANKINESS
Value: 1 to 7
Score: 2
EXERCISE 1 (Answers)
2. Numerical: values that are
numbers that tell you the
degree or extent of what
the variable measures
Categorical: values that are
different categories; no
particular numerical order
EXERCISE 1 (Answers)
3.
Give
the
level
of
measurement of each of
the following variables:
a. Nominal
b. Nominal
c. Interval
d. Ordinal
EXERCISE 1 (Answers)
4. Discrete: has specific
values and has no values
between the specific
values
Continuous: an infinite
number
of
values
between any two values
FREQUENCY TABLES
How stressed have you been
in the last 2.5 weeks, on a
scale of 0 to 10, with 0 being
not at all stressed and 10
being as stressed as
possible?
HOW TO MAKE A
FREQUENCY TABLE 1.
Make a list down the page of
each possible values, from
lowest to highest.
2. Go one by one through the
scores, making a mark for
each next to its value on
your list.
HOW TO MAKE A
FREQUENCY TABLE 3.
Make a table showing how
many times each value on
your list is used. 4. Figure the
percentage of scores for
each value.
FREQUENCY TABLES
FREQUENCY
TABLES
CUMULATIVE
FREQUENCY • tells how
many scores are accumulated
up to this point on the table
GROUPED
FREQUENCY TABLES
• combined category: a
range of values that
includes these two values |
called an interval
GROUPED
FREQUENCY TABLES
GROUPED FREQUENCY
TABLES
GROUPED FREQUENCY
TABLES
GROUPED FREQUENCY
TABLES
EXERCISE 2
1. What is a frequency table?
2. Why would a researcher
want
to
make
a
frequency table?
EXERCISE 2
3. Make a frequency table for
the following scores: 5, 7,
4, 5, 6, 5, 4
4. What does a grouped
frequency table group?
EXERCISE 2 (Answers)
1. A frequency table is a
systematic listing of the
number of scores (the
frequency) of each value in
the group studied.
2. A frequency table makes it
easy to see the pattern in a
large group of scores.
EXERCISE 2
(Answers)
4. A grouped frequency table
groups the frequencies of
adjacent values into
intervals.
HISTOGRAMS
HISTOGRAMS
HISTOGRAM
• bar-like graph of a
frequency distribution in
which the values are plotted
along the horizontal axis
and the height of each bar is
the frequency of that value
HOW TO MAKE A
HISTOGRAM
1. Make a frequency table (or
a grouped frequency
table).
2. Put the values along the
bottom of the page, from
left to right, from lowest
to highest.
HOW TO MAKE A
HISTOGRAM
3.
Make a scale of
frequencies along the left
edge of the page that
goes from 0 at the
bottom to the highest
frequency for any value.
HOW TO MAKE A
HISTOGRAM
4. Make a bar above each
value with a height for
the frequency of that
value.
BAR GRAPH
• When you have a nominal
variable, the histogram is
called a bar graph.
BAR GRAPH
EXERCISE 3
1. How is a histogram based
on a nominal variable
different
from
a
histogram based on
numeric equal-interval
variable?
EXERCISE 3
2. What values can be found
at the:
a. bottom,
b. left,
c. above each value
in a histogram?
EXERCISE 3 (Answer)
1. A histogram based on a
nominal variable has
gaps between the bars
and is called a bar graph.
When making a histogram
from a frequency table
(a) What goes along the
bottom: the values from
lowest to highest
(b) What goes along the left
edge: the frequencies from
0 at the bottom to the
highest frequency of any
value at the top
When making a histogram
from a frequency table
(c) What goes above each
value: above each value is a
bar with a height of the
frequency for that value
BASIC SAMPLING
TECHNIQUES
Probability Sampling • a
process of selecting a
sample in such a way that all
individuals in the defined
population have an equal
chance of being selected for
the sample
BASIC SAMPLING
TECHNIQUES
Non-Probability Sampling •
a process of selecting a
sample that does not involve
random selection
PROBABILITY
SAMPLING
TECHNIQUES
Simple Random Sampling •
a sampling procedure that
assures that each element in
the population has an equal
chance of being selected
PROBABILITY
SAMPLING
TECHNIQUES
Stratified Sampling
• the whole population is
first divided into mutually
exclusive subgroups or
strata and then units are
selected randomly from
each stratum
PROBABILITY
SAMPLING
TECHNIQUES
Cluster Sampling
• subjects are randomly
selected in groups or
clusters
• All of the members have
similar characteristics.
PROBABILITY
SAMPLING
TECHNIQUES
Systematic Sampling
• individuals are selected
from a list by taking every
“kth” name
• The “kth” depends on what
k is.
NON-PROBABILITY
SAMPLING
TECHNIQUES
Convenience Sampling •
selection of units from the
population based on easy
availability
and/or
accessibility
NON-PROBABILITY
SAMPLING
TECHNIQUES Purposive
Sampling
• selection of individuals
from
the
population
depending on the purpose
of the study
NON-PROBABILITY
SAMPLING
TECHNIQUES Quota
Sampling
• non-random selection of
sample according to some
fixed quota
NON-PROBABILITY
SAMPLING
TECHNIQUES Snowball
Sampling
• In snowball sampling, you
begin
by
identifying
someone who meets the
criteria for inclusion in your
study
DATA COLLECTION
Primary Data
• refer to the data obtained
directly from an original
source by means of actual
observations
or
conducting interviews
by
DATA COLLECTION
Secondary Data
• refer to the data or
information that come from
existing records in usable
forms such as surveys,
census, business journals,
etc
DATA
GATHERING
INSTRUMENTS
• Questionnaire
Method • Observation
Method
• Non-participant
Observation • Participant
Observation • Direct or
Interview Method •
Registration Method
• Experimental Method
FREQUENCY
DISTRIBUTIONS
•
show
the
pattern
of
frequencies over the various
values
• UNIMODAL: one high
“tower” in the histogram •
BIMODAL: two fairly equal
high points
FREQUENCY
DISTRIBUTION
S
•
MULTIMODAL:
two or more
high points
•
RECTANGULA
R: distribution
with values of
about the samefrequency
SYMMETRICAL AND
SKEWED
DISTRIBUTIONS •
SYMMETRIC Distribution:
distribution in which the pattern
of frequencies on the left and
right side are mirror images
SYMMETRICAL AND
SKEWED
DISTRIBUTIONS •
SKEWED Distribution:
distribution in which the
scores pile up on one side
of the middle and are
spread out on the other
side
SYMMETRICAL AND
SKEWED
DISTRIBUTIONS •The side
with fewer scores
(the side that looks like a
tail) is considered the
direction of the skew.
SYMMETRICAL AND
SKEWED
DISTRIBUTIONS •
POSITIVELY SKEWED: skewed
to the right
• NEGATIVELY SKEWED:
skewed to the left
SYMMETRICAL AND
SKEWED
DISTRIBUTIONS • FLOOR
EFFECT: situation in
which many scores pile up at
the low end of a distribution
(creating skewness to the
right) because it is not possible
to have any lower score
SYMMETRICAL AND
SKEWED
DISTRIBUTIONS • CEILING
EFFECT: situation in
which many scores pile up at
the high end of a distribution
(creating skewness to the left)
because it is not possible to
have any higher score
NORMAL AND
KURTOTIC
DISTRIBUTION
• NORMAL CURVE: specific,
mathematically defined, bell
shaped frequency distribution that
is symmetrical and unimodal
NORMAL AND
KURTOTIC
DISTRIBUTION
• KURTOSIS: how much the shape of
a distribution differs from a normal
curve in terms of whether its curve in
the middle is more peaked or flat
than the normal curve