Slide Presentation Srivijaya Universitas.pdf

USING EDUCATIONAL
STATISTICS AT
DEVELOPMENT RESEARCH
DR. PHOONG SEUKYEN
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE AND MATHEMATICS,
UNIVERSITI PENDIDIKAN SULTAN IDRIS

ABOUT ME
• phoong@fsmt.upsi.edu.my
• Expertise:
• Mathematics Education
• Applied Statistics
• Time Series
2

USING EDUCATIONAL
STATISTICS AT

WHAT IS EDUCATIONAL STATISTICS?
• Educational Statistics is defined as the study of the collection, organization,
analysis, interpretation, and presentation of data specifically meant for the
education sector.
4

TYPES OF STATISTICS
i) Descriptive statistics
• Consists of the collection, organization, summarization, and presentation of the data.
ii) Inferential statistics
• Consists of generalizing from samples to populations, performing estimations and
hypothesis tests, determining relationships among variables, and making prediction.
5

DEFINITIONS
Population
The collection of all outcomes,
responses, measurements, or counts
that are of interest.
Sample
The collection of data from a subset of the
population.
6

What is Data?
• The responses, counts, measurements, or observations
that have been collected.
• Data can be classified as one of 2 types:
1. Qualitative Data
2. Quantitative Data
7

QUALITATIVE DATA
➢Non-numerical measurements.
➢Variables that can be placed into distinct categories, according
to some characteristic or attribute.
➢Examples:
➢gender (Male or Female)
➢Geographic locations
➢Education level (Diploma, Degree, Master, PhD)
➢Color
➢etc
8

QUANTITATIVE DATA
➢Numerical measurements and can be ordered or ranked.
➢Examples:
➢Age
➢Weights
➢Temperature
➢Heights
➢Monthly salary
➢Agreement Level (1 – Strongly Disagree, 2 – Disagree, 3 – Agree, 4 – Strongly
Agree)
➢Satisfaction Level (1 – Strongly Dissatisfied, 2 – Dissatisfied, 3 – Satisfied, 4 –
Strongly Satisfied)
9

QUANTITATIVE DATA:
DISCRETEVS. CONTINUOUS
Discrete data:
❑finite number of possible data values: 0, 1, 2, 3, 4….
❑Ex: Number of classes a student is taking
Continuous data:
❑ infinite number of possible data values on a continuous
scale.
❑ Often include fractions and decimals.
❑ Ex: Weight of a baby
10

IT’S TIME TO PLAY !!!
• Kahoot link :
https://kahoot.it/
11

METHODS OF COLLECTING DATA
• Observational study
• Survey
• Experiment
• Simulation
12

Observational study
• A researcher observes or measures characteristics of interest of part of a
population but does not change any existing conditions.
Experiment
• A treatment is applied to part of a population and responses are observed.
13

Survey
• An investigation of one or more characteristics of a population, usually
be asking people questions.
• Commonly done by interview, mail, or telephone.
Simulation
• Uses a mathematical or physical model to reproduce the conditions of a
situation or process. Often involves the use of computers.
14

WHY EDUCATIONAL STATISTICS IS IMPORTANT?
• Provide the tools and techniques necessary for collecting, analyzing, and interpretating data related to
student performance and educational outcomes.
• Providing valuable data and insights that inform decision-making, policy development, and
improvements in the education system.
• Here are some of the key reasons for the importance of educational statistics:
i. Data-Driven Decision Making
ii. Assessment and Evaluation
iii. Resource Allocation
iv. Accountability
v. Policy Development
vi. Identifying Achievement Gaps
vii. Research and Innovation
viii. Long-Term Planning
ix. Parent and Student Involvement
x. Continuous Improvement
15

IMPORTANCE OF EDUCATIONAL STATISTICS
1. Data-Driven Decision Making
help educational institutions, policymakers, and administrators make informed decisions.
By analyzing data on student performance, attendance, and other metrics, schools can
identify areas that require improvement and allocate resources more effectively.
2. Assessment and Evaluation
essential for assessing the effectiveness of educational programs and interventions. By
measuring outcomes and evaluating the impact of various teaching methods, educators
can make evidence-based changes to their curriculum and teaching strategies.
16

3. Resource Allocation
Schools, colleges, and universities must allocate their resources, including budgets and
personnel, wisely. Educational statistics can help identify areas of need and areas of
excellence, enabling administrators to allocate resources more efficiently.
4. Accountability
play a vital role in holding educational institutions accountable for their performance.
Standardized testing, graduation rates, and other data allow for transparency and
accountability in the education system, which is important for parents, students, and the
public.
17

5. Policy Development
Policymakers use educational statistics to develop and implement policies that can address
the challenges and needs of the education system. These policies can cover issues like
curriculum development, teacher training, and funding allocation.
6. Identifying Achievement Gaps
can reveal achievement gaps among various demographic groups, such as those based on
race, socioeconomic status, or gender. This information is crucial for addressing inequalities
and working towards a more equitable education system.
18

7. Research and Innovation
provide a rich source of data for researchers studying various aspects of education.
This research, in turn, contributes to innovation and improvement in teaching
methods, curriculum design, and educational technology.
8. Long-Term Planning
By analyzing trends and patterns in educational data, institutions and governments
can engage in long-term planning. This includes forecasting future enrollment,
teacher recruitment, and infrastructure needs.
19

9. Parent and Student Involvement
Access to educational statistics can empower parents and students to make informed
decisions about their educational choices. It helps them understand the strengths and
weaknesses of different schools and programs.
10. Continuous Improvement
support a culture of continuous improvement in education. By monitoring data over time,
educational institutions can track progress, set goals, and make adjustments to improve
overall quality.
20

WHY EDUCATIONAL STATISTICS IS IMPORTANT TO
DEVELOPMENT RESEARCH?
1. Measuring Progress and Impact
provide data on literacy rates, school enrollment, completion rates, and educational
attainment. Researchers can use this data to assess the progress and impact of
development programs and policies related to education.
2. Identifying Educational Barriers
can reveal barriers to education, such as gender disparities, socio-economic
inequalities, and access issues. Researchers can analyze this data to identify specific
challenges that need to be addressed to promote inclusive and equitable
development.
21

3. Policy Evaluation
Development researchers can use educational statistics to evaluate the effectiveness
of education-related policies and interventions. This helps in determining whether
these initiatives are achieving their intended outcomes and where improvements are
needed.
4. Targeted Interventions
can inform the design of targeted interventions. By identifying areas with low
educational attainment or high dropout rates, researchers can recommend strategies
and resources to improve educational outcomes in specific regions or among certain
populations.
22

5. Economic Development
Education is closely linked to economic development. Researchers can use educational
statistics to examine the relationship between education levels and economic growth,
workforce productivity, and poverty reduction. This information is vital for crafting
development strategies that promote economic well-being.
6. Health and Social Development
Education has a significant impact on health outcomes and social development.
Research that uses educational statistics can explore correlations between education
and factors such as healthcare utilization, family planning, and social inclusion.
23

7. Human Capital Development
Education is a key component of human capital development. Research in this area relies
on educational statistics to measure the stock of human capital within a country or region,
helping policymakers understand the potential for future growth and development.
8. Long-Term Planning
can support long-term planning in development projects. Researchers can use these
statistics to anticipate future workforce needs, plan infrastructure development, and
ensure a well-educated population for a prosperous future.
24

9. Sustainable Development Goals (SDGs)
The United Nations' Sustainable Development Goals include targets related to
education (SDG 4: Quality Education). Educational statistics are essential for tracking
progress toward these goals and ensuring that education is a central part of the
development agenda.
10. International Comparisons
Researchers often compare educational statistics across countries to identify best
practices and learn from the successes and challenges in different regions. These
cross-country comparisons inform international development efforts.
25

FACTORS AFFECT EDUCATIONAL STATISTICS IN
• Educational statistics in development research can be influenced by a wide range of
factors that need to be considered when analyzing and interpreting the data.
• These factors can impact the accuracy and relevance of educational statistics and
understanding them is crucial for effective research.
• Some of the key factors affecting educational statistics in development research include:
1. Data Quality
2. Data Availability
4. Socioeconomic Factors
5. Cultural and Societal Norms
6. Political Factors
7. Access to Education
8. Teacher Quality and Training
9. Parental Involvement
10. Technology and Infrastructure
11. Data Collection Methods
26

1. Data Quality
The quality and accuracy of data collection methods can significantly affect
educational statistics. Errors in data collection, recording, and reporting can lead to
misleading statistics. It's essential to ensure that data collection procedures are
reliable and consistent.
2. Data Availability
The availability of educational data can vary from one region or country to another.
Some areas may lack comprehensive or up-to-date educational statistics, making it
challenging to conduct research and make informed decisions.
27

Resource allocation within the education system can impact statistics. Unequal
distribution of resources, such as funding, qualified teachers, and educational
infrastructure, can lead to disparities in educational outcomes.
4. Socioeconomic Factors
Socioeconomic factors, such as poverty, income inequality, and parental
education, can influence educational statistics. Children from disadvantaged
backgrounds may face more barriers to accessing quality education and
achieving positive educational outcomes.
28

5. Cultural and Societal Norms
In some cultures, gender bias may limit educational opportunities for girls,
while in others, traditional beliefs and practices may impact school attendance
and curriculum.
6. Political Factors
Political decisions and government policies can influence educational statistics.
Changes in education policies, funding, and curriculum can have a direct
impact on enrollment, attendance, and educational outcomes.
29

FACTORS AFFECT EDUCATIONAL
STATISTICS IN DEVELOPMENT
RESEARCH
30
7. Access to Education
The availability and accessibility of educational institutions, especially
in rural or remote areas, can affect enrollment rates. Limited access to
schools or transportation can impact educational statistics.

8. Teacher Quality andTraining
The qualifications and training of teachers can significantly affect educational outcomes.The
presence of well-qualified teachers can positively impact student achievement and overall
educational statistics.
9. Parental Involvement
The level of parental involvement in a child's education can influence statistics related to student
performance and attendance. Supportive parents can contribute to better educational outcomes.
31

9. Technology and Infrastructure
Access to technology and educational infrastructure can impact educational statistics, especially in the
context of online learning and the digital divide.
10. Data Collection Methods
The methods used for data collection, such as surveys, standardized testing, and administrative records,
can influence the quality and comprehensiveness of educational statistics.
32

EDUCATIONAL STATISTICS ANALYSIS
33

ANALYSIS RELATED TO EDUCATIONAL STATISTICS
• Descriptive Statistics – Demographic Respondents
• Divided into:
1. Measures of Central Tendency
2. Measures of Variation
3. Measures of Position
34

i- Measures of Central Tendency
❖ Mean
❖ Mode
❖ Median
ii- Measures of Variation
❖ Variance
❖ Standard Deviation
iii- Measures of Position
❖ Percentile
❖ Quartile
Data Description
35

MEASURES OF CENTRAL TENDENCY
• A value that represents a typical, or central, entry of a data set.
• Most common measures of central tendency:
• Mean
• Median
• Mode
36

MEASURE OF CENTRAL TENDENCY: MEAN
• Is the sum of all the data entries divided by the number of entries.
• Population mean:
• Sample mean:
x
N


=
x
x
n

=
37

MEASURE OF CENTRAL TENDENCY: MEDIAN
• The value that lies in the middle of the data when the data set is arranged in
order from lowest to highest.
• Measures the center of an ordered data set by dividing it into two equal parts.
• If the data set has an
• odd number of entries: median is the middle data entry.
• even number of entries: median is the mean of the two middle data entries.
- The position of the median can be find using the following formula:
• Position of the median = (n+1)/2 , where n is the sample size.
38

COMPUTING THE MEDIAN
If the data set has an:
• odd number of entries: median is the middle data entry:
• even number of entries: median is the mean of the two middle data entries:
39
2 5 6 11 13
median is the exact middle value:
median is the mean of the by two numbers:
2 5 6 7 11 13
Median = 6
5
.
6
2
7
6
median =
+
=
39

Median for grouped data
- The median for grouped data can be calculated using the
following formula.
Where,
Lm = lower limit of the class containing the median.
wm = width of the class in which the median lies.
fm = frequency in the class containing the median.
n = total number of frequencies.
 fm = cumulative number of frequencies in all the classes
immediately preceding the class containing the median.
** To identify the class of median, we need to find the middle
observation which is determined by n/2.







−
+
= m
m
m
m f
n
f
w
L
Median
2
40

MEASURE OF CENTRAL TENDENCY: MODE
• The data entry that occurs with the greatest frequency.
• If no entry is repeated the data set has no mode.
• If two entries occur with the same greatest frequency, each
entry is a mode (bimodal).
• Examples:
1) 5.40 1.10 0.42 0.73 0.48 1.10
2) 27 27 27 55 55 55 88 88 99
3) 1 2 3 6 7 8 9 10
Mode is 1.10
41
Bimodal -- 27 & 55
No Mode

CATEGORIES OF MODE
No mode Unimodal Bimodal Multimodal
Data set which
each value
occurring once
Data set with one
value that occurs
with highest
frequency
Data set with two
values that occur
with same highest
frequency (2
modes)
More than two
values in a data set
occur with the
same highest
frequency (>2
modes)
42

DISTRIBUTION SHAPES
• The three most important shapes are positively skewed,
symmetric, and negatively skewed.
43

MEASURES OFVARIATION (“SPREAD”)
Another important characteristic of quantitative data is how
much the data varies or is spread out.
The 3 most common method of measuring spread are:
1. Range
2. Standard deviation
3. Variance
44

RANGE
• The difference between the maximum and minimum data
entries in the set.
• The data must be quantitative.
• Range = (Max. data entry) – (Min. data entry)
45

STANDARD DEVIATION ANDVARIANCE
• The standard deviation is the most used measure of dispersion.
• The value of the standard deviation tells how closely the values of a data set
are clustered around the mean.
Formula:
PopulationVariance:
•
Population Standard Deviation:
•
N
X
 −
=
2
2 )
( 

N
X
 −
=
=
2
2 )
( 


46

SampleVariance:
• or
Sample Standard Deviation:
• or
1
)
( 2
2
−
−
=

n
X
X
s
1
)
( 2
2
−
−
=
=

n
X
X
s
s
( )
 
1
2
2
2
−
−
=


n
n
X
X
s
( )
 
1
2
2
−
−
=


n
n
X
X
s
47

❖In general, a lower value of the standard deviation for a
data set indicates that the values of that data set are
spread over a relatively smaller range around the mean.
❖In contrast, a large value of the standard deviation for a
data set indicates that the values of that data set are
spread over a relatively large range around the mean.
48

POPULAR STATISTICAL METHOD USED
IN DEVELOPMENT RESEARCH
• One sample t-test
• Paired sample t-test
• Correlation
49

DIFFERENCES BETWEEN ONE SAMPLE T-TEST AND
PAIREDT-TEST
50
Pre / Before Post / After

ONE SAMPLE T-TEST
• to determine whether an unknown population mean is different from a specific value.
• Assumptions:
i. The data are numeric
ii. Independent (values are not related to one another)
iii. Continuous
iv. the population is assumed to be normally distributed.
51

EXAMPLE
The average score in the statistics test at a
university has been 28 points for years. This
semester a new online statistics tutorial was
introduced. Now the course management
would like to know whether the success of the
studies has changed since the introduction of
the statistics tutorial: Does the online statistics
tutorial have a positive effect on exam results?
Student Score
1 28
2 29
3 35
4 37
5 32
6 26
7 37
8 39
9 22
10 29
11 36
12 38
52

INDEPENDENT SAMPLE T-TEST
• to test the difference between means when the two samples are independent and when
the samples are taken from two normally or approximately normally distributed
populations.
• Assumptions:
i. The data are numeric
ii. Observations are independent of one another (that is, the sample is a simple
random sample and each individual within the population has an equal chance of
being selected)
iii. The sample mean, is normally distributed
iv. Equal variances between groups.
ҧ
𝑥
53

PAIRED SAMPLE T-TEST
• observations in the first sample are directly related to the observations in the second
sample or they occur as pairs of values.
• Assumptions:
• The dependent variable must be continuous (interval/ratio).
• The observations are independent of one another.
• The dependent variable should be approximately normally distributed.
• The dependent variable should not contain any outliers.
54

• Examples of dependent samples:
a) To determine students’ achievement using a new teaching method by
having pre-test and post-test.
b) To investigate the effectiveness of a games on the topic straight-line
for secondary school students.
c) To investigate the students’ interest on different subjects.
55

EXAMPLE
• A physical education director claims by taking a special vitamin, a weightlifter can increase
his strength. Eight athletes are selected and given a test of strength, using the standard
bench press. After 2 weeks of regular training, supplemented with the vitamin, they are
tested again. Test the effectiveness of the vitamin regimen at α=0.05. Each value in these
data represents the maximum number of pounds the athlete can bench-press. Assume
that the variable is approximately normally distributed.
Athlete 1 2 3 4 5 6 7 8
Before (X1) 210 230 182 205 262 253 219 216
After (X2) 219 236 179 204 270 250 222 216
56

CORRELATION
• Correlation is a statistical method used to determine whether a relationship between variables
exists.
• Correlation coefficient is a measure to determine whether two or more variables are related and
also to determine the strength of the relationship.
• There are 2 types of relationship: simple or multiple.
• Simple relationship -- there are only two variables under study
• Multiple relationship -- several variables are under study
• Simple relationships can be either positive or negative.
• A positive relationship exists when both variables increase or decrease at the same time. In a
negative relationship, as one variable increases, the other variable decreases, and vice versa.
57

CORRELATION COEFFICIENT
• The correlation coefficient computed from the sample data measures the
strength and direction of a relationship between two variables.
• The symbol for the sample correlation coefficient is r while the symbol
for the population correlation coefficient is ρ.
58

• The range of the correlation coefficient is from -1 to +1 (-1 ≤ r ≤+1). If there is a strong
positive linear relationship between variables, the value of r will be close to +1. If there is
a strong negative linear relationship between the variables, the value of r will be close to
-1.Where there is no linear relationship or only a weak relationship, the value of r will be
close to 0.
• The formula for the correlation coefficient, r is given below:
( )( )
( ) ( )
  ( ) ( )
 
2
2
2
2
)
(







−
−
−
=
y
y
n
x
x
n
y
x
xy
n
r
59

EXAMPLE OF THE APPLICATION OF
EDUCATIONAL STATISTICS

EXAMPLE OF THE APPLICATION
OF EDUCATIONAL STATISTICS
62

EXAMPLE OF THE APPLICATION
OF EDUCATIONAL STATISTICS
63

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