7 Descriptive Statistics_Mposttest scores

Ano n n m n + I t o
[ D E S C R I P T I V E
S T A T I S T I C S ]
Virtual Research Seminar
25 November 2020 | Google
Meet

1. What is the difference between the pre-
test and posttest scores of the learners
after the (title of the intervention)?
2. What is the level of effectiveness of the
(title of the intervention)?
3. What is the relationship between the
academic performance of the learners
and their bmi?
4. How does the learners feel after
the intervention was
implemented?

target |
At the end of the session, you should be able
to:
 compute measures of location and
measures of variability for different types
of variables using computer software;
 calculate a measure of relationship
between variables (e.g. the Pearson
product-moment correlation coefficient);
and
 interpret descriptive statistics as
applied to existing data

Describing Distributions Graphically
FREQUENCY POLYGON
is a line graph that
shows the frequency of
occurrence of each
score. Seeing data in
this format will help
visualize a given data
set.

is a graphical presentation
of data using bars, whose
heights indicate the
frequency of the
occurrence of a score value
or a range of scores.
HISTOGRAM

BAR GRAPH
is similar to a line graph
and histogram, except that
it is used more for
categorical data. It can be
displayed vertically or
horizontally

PIE CHART
is a circular graph divided
into slices to display
numerical proportions. The
arc length, central angle, and
area of each slice are
proportional to the quantity
it represents.

PICTOGRAPH
uses picture symbols to
express relative frequency or
proportion of different levels
of categorical variable.

SCATTER PLOT
is a graph depicting
the relationship
between two variables.
On the X-axis are the values
of one variable (X) and on
the Y-axis are the values of
the other variable (Y).

Describing Groups Statistically
Measures of Location
These measures allow us to describe
data with several different single values
according to the point on the number
line around which groups tend to
converge.
These include mode, median, and
mean.

Mean
µ for population or M for
sample is the arithmetic
average. It is computed
by summing up all the
data and then dividing it
by the number of data
or cases.
M
=

Median
Median is the number
that divides the data set
into two equal parts. It
is also known as the
middlemost point or the
50th percentile

Mode
Mode is the most
frequently occurring value
in a data set. It is
determined simply by
counting how many times
each value appears and
then finding the value with
the highest frequency.

Remember This…
i. Among the three measures of
location, the most stable is the mean
because it takes in all scores. The most
unstable is the mode because it simply
relies on frequency of occurrence of a
single value.

Remember This…
ii. The mean is the most sensitive to
outliers. These are extreme values, either
extremely high or extremely low. It is a
practice to remove outliers from the
analysis since these may lead to faulty
analyses and interpretations.

Remember This…
iii. Not all measures of location are
suitable for all types of data.

Describing Groups Statistically
Measures of Variability
These measures allow us to describe data
with several different single values
according to the extent to which they are
alike or are different.
These include range, variance, and
standard deviation.

Range
Range (R), the
simplest of the three
measures of
variability, is
computed by finding
the difference
between the highest
value and the lowest
value.
R = 6

Variance
Variance (σ2 for population or
s2 for sample) is the average
squared deviation. This
means that we have to first
get the deviations (X-M) for
each score and then square
these (X-M)^2.

Standard Deviation (σ for population or s for
sample)
Is simply the square root of variance. The
standard deviation is considered the most
stable and the most suitable measure of
variability since it takes into consideration all
score values and is expressed in the original
unit of measurement of the variable.

DESCRIBING DATA USING CORRELATION COEFFICIENT
Correlation coefficient is a
descriptive statistic that is applied
when we want to depict the nature
of the relationship between
variables.

DESCRIBING DATA USING
CORRELATION COEFFICIENT
0.1 to 0.3 - weak relationship
0.4 to 0.6 - moderate
relationship
0.7 to 0.9 - strong relationship

examples of data sets that can be used
1. Formative and summative scores in
certain subjects
2. Enrollment and dropout data
3. School teachers’ profile (gender, age, years
of teaching experience)
4. Students’ profile (gender, grade level,
age, SHS track) 5 Assessment data (e.g.,
NAT scores)

0.1 to 0.3 – weak relationship
0.4 to 0.6 – moderate
relationship
0.7 to 0.9 – strong relationship

Australian Bureau of Statistics. n.d. “Measures of Shape.” Australian Bureau of Statistics (website).
Accessed May 12, 2018.
http://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language+-
+measures+of+shape.
Australian Bureau of Statistics. n.d. “Measures of Central
Tendency.” Australian Bureau of Statistics (website). Accessed
May 12, 2018.
http://www.abs.gov.au/websitedbs/a3121120.nsf/home/stati
stical+language+-
+measures+of+central+tendency.
Campbell, Michael J., David Machin, and Stephen J. Walters. (1990) 2007. Medical Statistics:
A Commonsense Approach. Chichester, England: Wiley-Blackwell.
Center for Innovation in Research and Teaching. n.d. Type of Experimental Research. Arizona:
Grand Canyon University. Accessed May12, 2018.
https://cirt.gcu.edu/research/developmentresources/research_ready/experimental/
design_types.
Center Grove Community School Corporation. n.d. “Module 7: Measures of Central Tendency.”
Canvas (website). Accessed May 12, 2018.
https://centergrove.instructure.com/courses/1823759/pages/module-7-measures-of-central-
tendency.
Complete Dissertation. n.d. Experimental Research Designs. Statistics Solution.
AccessedMay12,2018. http://www.statisticssolutions.com/experimentalresearchdesigns/.
Fraenkel, Jack R. and Norman E. Wallen. (1990) 2008. How to Design and Evaluate Research
in Education. Boston: McGraw Hill.
Levin, Jack A., James Alan Fox, and David R. Forde. (2003) 2013. Elementary Statistics in
Social
Research. New York: Pearson.

M A R K G A L L A N O
Policy, Planning, & Research Division
DepEd Regional Office VIII
(053) 323-5869 |
mark.gallano002@deped.gov.ph
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