1 Statistical-Tests
1 Statistical-Tests
1 Statistical-Tests
April 2, 2024
Research
STATISTICS
STATISTICS
Collect
Organize
Present
Analyze
Interpret
STATISTICS
➢ is a branch of applied Mathematics
that deals with the collection,
organization, presentation, analysis
and interpretation of data in order to
provide a meaningful information to the
people or organizations that will use
these data.
Concept Map of Statistics
•STATISTICS
•includes
Data
Data Presentation •Use of
Collection
•through Descriptive
Measures:
•Text Mean,
Median, &
•using •Tables, Mode
•Primary Frequency
Sources Distribution •Use of
Inferential
•Secondary •Graphs, Measures;
Sources Frequency t, Z, F, r
Histogram
Data presentation
Categories of Statistics
GROUP 1 GROUP 2
80 90
Measures of
Variability
Range
Standard Deviation
Variance
Sources of Data
▪ POPULATION, it represents the totality
of all individuals or objects from which the
required information is to be obtained.
▪SAMPLE, it is a subset of the population,
from which information about the population
is desired.
Types of
Inferential Tests
▪ tests of group differences
- determine whether two populations differ with respect to
their mean scores on some response variable
▪ tests of association (relationship)
- there is a single population of individuals, and you want to
know whether there is a relationship between two or more
variables within this population.
Kinds of Inferential Tests
1. Parametric Test
- are tests that require normal distribution, the level of
measurements of which are express in an interval or ratio
data.
2. Nonparametric Tests
- are tests that do not require a normal distribution and
utilizes both nominal and ordinal data.
Types of Statistical Tests:
Parametric
• Parametric tests require scale (interval/ratio)
• And, also:
• The sample must be representative of the target population so that the
variables being measured fall within the normal distribution for that
population
• The variables must have been measured in a manner that generates
interval or ratio data
• The subjects in the two groups being examined need to be either
randomly assigned to each group or each group must be matched
according to the respondents’ age, sex, etc 21
Use of Parametric Tests
1. Numerical Data
2. Normal Distribution
3. Number of Samples
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Types of Statistical Tests:
Non-Parametric
• When parametric tests conditions are not met, then non
parametric tests are used, so where:
• The sample is not considered representative of the
population and the variables selected are probably not
normally distributed (i.e. random selection has not
occurred)
• The variables have been measured in a way that
generates categorical or ordinal data
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Parametric Tests
➢ TEST OF DIFFERENCE
t-test for Independent Samples
t-test for Correlated Samples
z-test, for Two Sample Means
z-test, for One Sample Group
f-test (ANOVA)
➢TEST OF RELATIONSHIP
r (Pearson Product Moment Coefficient of
Correlation)
HYPOTHESIS
TESTING
What is a
Hypothesis?
A hypothesis is an
assumption about the
population parameter.
HYPOTHESIS TESTING
DEFINITION
Hypothesis testing is an
objective method of making
decisions or inferences from
sample data (evidence).
HYPOTHESIS TESTING
DEFINITION
Hypothesis testing is the process of
making an inference or generalization
on population parameters based on the
results of the study on samples.
NULL VS ALTERNATIVE
HYPOTHESIS
NULL HYPOTHESIS (H0) – an assertion we hold
as true unless we have sufficient statistical
evidence to conclude otherwise.
M1 = M 2 M1 < M 2
TEST OF
SIGNIFICANCE
A N T
I F I C
IG N
S
SIGNIFICANCE LEVEL
The probability of rejecting
the null hypothesis when it
is true, also known as the
type I error.
SIGNIFICANCE LEVEL
This is decided by the researcher
but is normally set at 5% which
means that there is a 1 in 20
chance of rejecting the null when it
is true.
TYPES OF ERROR
DECISION
SITUATION
Do not Reject
Reject H0 H0
Type I Correct
H0 is true Decision
error
Correct Type II
H0 is false Decision error
On a Sunday night, Migs who is taking
Research 1 is thinking whether his teacher
will give a quiz or not. The null hypothesis
is that “the teacher will not give a quiz on
Monday morning”. The teacher gave a quiz
and Migs got a zero for the quiz, which he
could have answered if he had only
studied. What type of error did Migs
commit?
TEST STATISTIC
• It is a value calculated from a
sample to decide whether to
reject or not the null hypothesis
(H0) and varies between tests.
Decision Rule
P-Value Approach
If the computed test value is less than the p-
value, reject the Null hypothesis.