Uploaded by Mark Joseph D Landingin

# Statistics - complete slides

```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
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
• 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
-
-
Yes
Yes
Multiplication &amp; 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?
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
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
3.
Give
the
level
of
measurement of each of
the following variables:
a. Nominal
b. Nominal
c. Interval
d. Ordinal
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
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?
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
4. A grouped frequency table
groups the frequencies of
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?
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,
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
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
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
```