Hypothesis Testing.pdf

Unit 3
HypothesisTesting
10 June 2021 Kassa T. (PhD) 1
KassaT. (PhD, Associate Professor)
Dept of Dev’t Economics & Mgt
Email: ktshager@yahoo.com
Tel: +251911346214

Contents:
• Introduction
• Forms of hypothesis Testing
• ParametricVs Non- parametric tests
 Parametric tests
 Non-parametric tests

Unit Objectives:
After completing this chapter, the students
should be able to:
– Differentiate the parametric and non-
parametric tests
– Apply appropriate tests in quantitative
research

Hypothesis testing
• Hypothesis is a claim/premise or statement about the
value of single population characteristics or values of
several population characteristics that we want to test.
• A test of hypothesis is a method that uses sample data
to decide two competing claims (hypothesis) about a
population characteristics.
• Null hypothesis (Ho), is a claim about a population
characteristic that initially assumed to be true.
• Alternative hypothesis (Ha), is the competing claim.

We have two types/forms of hypotheses:
A. The null hypothesis (H0) is often established
as:
 No significant association between two or several items
 No significant difference between two or several items
 No significant influence of one item on another
 No significant treatment effect
 Note: Its mathematical presentation always
includes the equality sign.

b) The alternative hypothesis ( H1 or Ha): is the
alternative available when the null hypothesis has to
be rejected.
 In other words, if we have strong evidence
against the null hypothesis, we have to reject it
and conclude something else which we call the
alternative hypothesis.
 The sign used in formulating the alternative
hypothesis is inequality.

• The form of null hypothesis is:
• Ho: population characteristic = hypothesized value.
• The alternative hypothesis will have on of the following
three forms:
• Ha: population characteristic > hypothesized value.
• Ha: population characteristic < hypothesized value.
• Ha: population characteristic ≠ hypothesized value.

• Alternative Hypothesis as a Research Hypothesis
Developing Null and Alternative Hypotheses
• Example 1:
A new teaching method is developed that is
believed to be better than the current method.
• Alternative Hypothesis:
The new teaching method is better.
• Null Hypothesis:
The new method is no better than the old method.

Example 2:
A new drug is developed with the goal of lowering
blood pressure more than the existing drug.
Alternative Hypothesis:
The new drug lowers blood pressure more
than the existing drug.
Null Hypothesis:
The new drug does not lower blood pressure
more than the existing drug.
10 June 2021 Kassa T. (PhD, Associate Professor) 9

• Null Hypothesis as an Assumption to be Challenged
• We might begin with a belief or assumption that
a statement about the value of a population
parameter is true.
• We then use a hypothesis test to challenge the
assumption and determine if there is statistical
evidence to conclude that the assumption is
incorrect.
• In these situations, it is helpful to develop the null
hypothesis first.

Correct
Decision
Type II Error
Correct
Decision
Type I Error
Reject H0
Accept H0
H0True H0 False
Conclusion
Population Condition

 Reject H0 if the p-value < .
The p-value is the probability, computed using the
test statistic, that measures the support (or lack of
support) provided by the sample for the null
hypothesis.
 If the p-value is less than or equal to the level of
significance , the value of the test statistic is in the
rejection region.

Suggested Guidelines for Interpreting
p-Values
• Less than .01
Overwhelming evidence to conclude Ha is true.
• Between .01 and .05
Strong evidence to conclude Ha is true.
• Between .05 and .10
Weak evidence to conclude Ha is true.
• Greater than .10
Insufficient evidence to conclude Ha is true.

Parametric tests
• Parametric tests are statistical tests which make
certain assumptions about the parameters of the full
population from which the sample is taken.
• These tests normally involve data expressed in absolute
numbers (interval or ratio) rather than ranks and
categories (nominal or ordinal).
• Examples: z- test, t- test, Analysis ofVariance
(ANOVA), etc.
10 June 2021 Kassa T (PhD, Associate professor) 24

• Some assumptions for parametric tests
include:
• The observations should be drawn from
normally distributed populations.
• These populations should have equal
variances with the sample variance.

Non parametric tests
• Non-parametric tests are used to test hypotheses
with nominal and ordinal data.
• The use of non-parametric methods may be necessary
when data have a ranking but no clear numerical
interpretation, such as when assessing preferences; in
terms of levels of measurement, for data on an ordinal
scale.
• Such tests are like Chi-Square (X2), Mann-Whitney
Test, kruskal wallis, Friedman,Wilcoxon, etc.

Paired samples
t-test
Wilcoxon
Independent
samples t-test
Mann Whitney
U
ANOVA*
Repeated
measures
Friedman
ANOVA
One way
Kruskal
Wallis
Parent Population
assumed normal
No assumptions made
about parent
Population
Parent Population
assumed normal
No assumptions made
about parent
Population
Parent Population
assumed normal
No assumptions made
about parent Population
Parent
Population
assumed normal
No assumptions made
about parent Population
Same subject
/sample in both
categories
Different subjects
/sample in both
categories/
Different subject
/sample each category
Same subject
/sample in each
category
Continuous
/ordinal data (in
the form of
numbers/ranks)
More than 2
categories
Data from two or
more categories
Chi-squared
test
Nominal data
(in the form
of counts)
2 Categories
Parametric and Non-parametric tests

Hypothesis testing, example 1
• The average IQ for the adult population is 100
with the standard deviation of 15. A researcher
believes that this value has changed.The researcher
decides to test the IQ of 75 randomly selected
adults.The average IQ of the sample is 105.
• Is there enough evidence to suggest the average
IQ has changed?

Steps:
1. State null (H0) and alternative (Ha) hypothesis
2. Choose the level of significance (α)
3. Find critical values
4. Find test statistic
5. Draw a Conclusion

Step 1: State null (H0) and alternative (Ha)
hypothesis
H0: = 100
H1:  100
Two-tailed test

Step 2: Choose the level of significance (α)
 is divided equally between
the two tails of the critical
Region
 = 0.05
0.025
-0.025
0.95

Step 3: Find critical values
• Critical value (Z-value) should be used because population
standard deviation is known
• At 95% confidence, α/2, Z value is 1.96
Z statistics

Conclusion:
• Since Z cal (2.89) > Z α/2 (1.96) , we reject
the null hypothesis and accept the
alternative hypothesis.
• This means that IQ of the adults has changed
significantly

Hypothesis testing, example 2
• The average IQ for the adult population is
100. A researcher believes that the average
IQ of adults is lower. A random sample of 5
adults are tested and scored.The mean
score is 89 ( with S.D = 15.81).
• Is there enough evidence to suggest the
average IQ is lower?

Step 1: State null (H0) and alternative (Ha)
hypothesis
H0: = 100
H1: < 100
one-tailed test

Step 2: Choose the level of significance (α)
α= 0.05 (left tailed)
0.95

Step 3: Find critical values
• Critical value (t-value) should be used because
population standard deviation is unknown and
sample size is less than 30.
• At 95% confidence, α=0.05, df= 4, t value is -2.132

Conclusion:
• Since t cal |-1.56| < t critical, α =0.05 |-
2.132|, we accept the null hypothesis
• This means that IQ of the adults has not
changed significantly

Chi-square (X2)

Example:

Steps:

Expected

Steps:

ThankYou!!

Hypothesis Testing.pdf

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