ED 502:
EDUCATIONAL STATISTICS
TESTS OF RELATIONSHIP
STATISTICAL
TREATMENT
Pearson - r
Spearman RankOrder Correlation /
Spearman Rho
FUNCTION USE
LEVEL/SCALE OF
MEASUREMENT
It is used to determine if there is
a correlation or relationship
between two variables of the
interval or ratio type.
Interval / Ratio
It is used to determine if there is
a correlation or relationship
between two variables of the
ordinal type.
Ordinal
* product-moment correlation
Independence
It is used to determine if there is
a correlation or relationship
between two variables of the
nominal type.
Scores, Grades, Ratings
Ex.
 Reading Comprehension
 Personality
* nonparametric statistics
(distribution free statistics)
Chi-Square Test of
SAMPLE DATA
Nominal
SAMPLE PROBLEM
Is there a positive correlation between
Reading Comprehension and
Personality of PNU graduate students?
Is there a significant relationship
between the Student Academic
Achievement in Math II and
Instructional Level among PNU
undergraduate students?
Ranks, Non-numeric
scales
Is there a correlation between
Motivation and Self-Concept?
Ex.
 Satisfaction
 Happiness
 Motivation
 Self-concept
 Discomfort
What type of affective need is
addressed by the type of management
of emotions?
Categorical /
Classificatory Variables
50 Male high school students and 50 Female
high school students were asked about their
color preferences. Among the Male students,
20 preferred light colors, 15 preferred bright
and 15 preferred dark. Of the 50 Female
students, 15 preferred light colors, 15
preferred bright and 20 preferred dark colors.
Ex.
 Sex
 Drink Preference
 Color Preference
Is sex related to color preferences?
TESTS OF DIFFERENCE
STATISTICAL
TREATMENT
One Population
Z - Test
FUNCTION USE
LEVEL/SCALE OF
MEASUREMENT
SAMPLE DATA
It is used to determine if the
given sample mean was drawn
from the population with no
parameters or if a given group
represent the population.
Interval / Ratio
2 groups – single interval
variable
Ex.
 Group of Teachers
(sample mean) from the
University (population)
 Group of Teenagers
(sample mean) from the
Metro Manila
(population)
* random / purposive sampling
Z - Test of
Independent
Proportions
It is used to determine if there is
a significant difference between
two independent / different
groups or situations that call
for two types of responses
(dichotomous).
* include issues in which you are
only asked whether you agree
or disagree
Nominal
Frequencies converted to
Proportions
(2 groups – 2 responses)
Ex.
 Yes and No
 Agree and Disagree
 In Favor and Against
SAMPLE PROBLEM
The given population obtained a mean of 120
and the standard deviation is 20. A sample of
100 was drawn from the population and it
obtained a mean of 119.
Test the hypothesis that the sample
mean of 119 was drawn from the
population whose mean is 120.
50 Male graduate students and 50 Female
graduate students were asked whether they
are in favor or against same sex marriage.
Among Male respondents, 25 are in favor and
25 are against. Among Female respondents,
20 are in favor and 30 are against.
Is there a significant difference between
Male and Female graduates who are
in favor of same sex marriage?
90 Ph.D candidates in Educ. Mgt. and 80
Ph.D candidates in Math respond to an item
concerning the usefulness of Foreign
Language requirement for the Ph.D. 30
Educational Mgt. candidates and 55 Math
candidates agree with the statement.
Is there a significant difference between
the proportions in each group that
responded In Favor?
Z - Test of
Dependent
Proportions
It is used to determine if there is
a significant difference between
pair of observations from a
single group.
Nominal
Pair of Observations
Ex.
 Before and After
 In Favor and Against
 Passed and Failed
* response to a question given in
two different occasions
Is there a significant difference in the
responses of the 50 voters before and
after the Meeting de Avance?
Consider the test items A and B. In a sample
of 100 children, 30 pass item A fail item B,
whereas 20 fail item and pass item B.
Are the proportions of children
passing the two items significantly
different from each other?
T - Test of
Independent /
Uncorrelated
Means
It is used to determine if there is
a difference between two
groups using dependent
independent variables.
Interval / Ratio
2 groups – Control and
Experimental Group
Ex.
 Method of Teaching
 Achievement
 IQ Scores
* comparison of two groups
Is there a significant difference between
the experimental and control group in
terms of achievement in Statistics?
A survey was conducted on attitude toward
mentally impaired children. A random
sample of teachers and administrators were
selected and asked to respond to an attitude
toward mentally impaired children scale.
Is there a significant difference between
teachers and school administrators in
terms of attitude toward mentally
impaired children?
T - Test of
Dependent /
Correlated Means
It is used to determine if there is
a significant difference between
two sets or two groups of
correlated scores or measures.
Interval / Ratio
2 groups – Pre-test and
Post-test
Ex.
 Scores
Is there a significant difference between
the Pre-test and Post-test in Statistics
of the Experimental Group?
Is there a difference in the Pre-test and
Post-test scores in the Math
Achievement test of Grade IV pupils
when exposed to traditional method?
calculator-integrated method?
Chi-Square Test of
Goodness of Fit
One-Way Analysis
of Variance
(ANOVA I)
It is used to determine if there is
difference between the
observed (hypothetical /
theoretical) distribution and
expected (predetermined)
distribution.
It is used to determine if there is
a significant difference between
two or more groups in terms of
means (achievement, weight, IQ).
Nominal
Ex.
 Responses
Strongly Agree (SA)
Agree (A)
No Opinion (NO)
Strongly Disagree (SD)
Disagree (D)
Interval / Ratio
of Variance
(ANOVA II)
It is used to determine if there is
an interaction / combined
effect between or among two or
more independent variables
(ex. method of teaching, medium
of instruction) to the dependent
variable (ex. achievement test).
* can answer 3 questions
2 or more groups
Ex.
 Method of Teaching:
I – Discovery Approach
II – Distance-Learning
III – Instructional-TV
* extension of T-test / inspects
an independent variable
Two-Way Analysis
Frequencies, Scale,
Opinion, Response
Interval / Ratio
2 or more groups
Ex.
 Effect of Method of
Teaching and Medium
of Instruction to
Achievement
100 students were asked about their opinion
about Pacquiao’s candidacy. 23 strongly
agreed, 21 agreed, 5 expressed no opinion, 25
disagreed and 26 strongly disagreed.
Is there a significant difference between
the observed distribution and
expected distribution of the students’
responses on the said issue?
Are the observed frequencies the same
as an expected set of frequencies? (Ex.
Are the number of workplace accidents
the same for each hour of the day?)
Do the three groups of graduate
students (discovery approach, distance
learning, instructional TV) differ
significantly in terms of achievement in
Statistics?
A researcher was interested in whether an
individual's interest in politics was influenced
by their level of education and gender.
Therefore, the dependent variable was
"interest in politics", and the two independent
variables were "gender" and "level of
education".
Is there an interaction between
education level and gender / was the
effect of level of education on interest in
politics different for males and females?
LEVELS OF MEASUREMENT
NOMINAL
ORDINAL
INTERVAL
STATISTICAL
Chi-Square Test of Independence
Spearman Rank-Order
Pearson - r
TREATMENTS
Z - Test of Independent Proportions
Correlation / Spearman Rho
One Population Z - Test
TO BE USED
RATIO
Z - Test of Dependent Proportions
T - Test of Independent / Uncorrelated Means
Chi-Square Test of Goodness of Fit
T - Test of Dependent / Correlated Means
One-Way Analysis of Variance (ANOVA I)
Two-Way Analysis of Variance (ANOVA II)
STATISTICS /
 proportions
 percentage
MEASURES
 Median
 Quartile Deviation
PRE-TEST POST-TEST CONTROL GROUP DESIGN:
EXPERIMENTAL GROUP
Pre-test
Post-test
CONTROL GROUP
Pre-test
T - Test of Independent Means
Means
LEVEL OF SIGNIFICANCE
∝ .05  you have 5 chances (Type I Error) out of 100 that you are wrong with your
decision and 95% that you’re correct; rejecting the null hypothesis when it should
be accepted; has smaller Region of Acceptance and bigger Region for Rejection (
any computed Z-value or absolute value 1.96, reject Ho )
∝ .01  you have 1 chance (Type II Error) of being wrong and 99% that you’re
correct; accepting the null hypothesis when it should be rejected; has bigger Region
of Acceptance and smaller Region for Rejection ( any computed Z-value or absolute
value 2.58, reject Ho)
DECISION – INTERPRETATION OF HYPOTHESIS
Significant

REJECT

use Alternate Hypothesis
Not Significant
GUIDE IN CHOOSING STATISTICAL TREATMENT:
1) Determine the type of research question to be answered by the statistical analysis.
a. the degree of relationship or dependence among variables (H0 = there is no relationship or dependence,
and the statistical test answers the question as to whether any relationship or dependence found is
sufficiently different from zero that it can be considered “statistically significant”.)
b. the significance of group differences (H0 = there is no difference between groups. The statistical test
answers the question as to whether an observed difference is probably due just to random factors, or is
large enough to be considered “statistically significant” and due to the treatment factor.)
T - Test of Dependent
T - Test of Dependent
Means
Post-test
 Mean
 Standard Deviation

ACCEPT

use Null Hypothesis
2) Determine the nature(s) of the variables under discussion, and whether they meet the assumptions of a
particular test (e.g. the data are normally distributed).
3) Types/levels of data:
NOMINAL – unordered categories; numbers simply express identity/ labeling purposes (e.g. religion;
country of birth; sex; etc.)
ORDINAL – ordered categories; numbers express ranks (e.g. level of agreement on an opinion survey;
proficiency level at a martial art; scale used in determining the hardness of a mineral, academic ranks)
 for nominal and ordinal data, what is usually recorded is the number of occurrences of a particular
result (e.g. number of Christians, number of Buddhists etc. but these numbers are not the values of the
variable. In this case, variable = religion, values = Christian, Buddhist, …and the numbers are the number
of occurrences of a particular value.)
INTERVAL – ordinal + distance between values is of constant size; has equal intervals that is distances
between points are equal starting an arbitrary zero (e.g. temperature; score)
RATIO – interval + (i) there is a meaningful zero and (ii) the ratio between two numbers is meaningful;
zero is absolute; there is absolute value of the variable (e.g. height; weight, distance, number of children)
 ratio and interval data can be either discrete (i.e. there are gaps between values, e.g. number of
children) or continuous (i.e. there are no gaps between values (e.g. weight, height).