This document discusses hypothesis testing and the key concepts involved. It defines a hypothesis as a claim or premise that can be tested. For a hypothesis to be testable, it must be clearly defined, empirically based, specific, relate to available research techniques and theory. Hypotheses can be categorized as null or alternative. The null hypothesis states the claim to be tested, while the alternative challenges it. Tests determine if there is sufficient evidence to reject the null hypothesis based on a pre-defined level of significance (α), which indicates the probability of a Type I error of rejecting a true null hypothesis. Failing to reject a false null hypothesis is a Type II error. The relationship between the two error types and one-tailed versus

1. Hypothesis Testing
presented by
UVISE P M

2. What is a Hypothesis?
 A premise or claim that we want to test
“A hypothesis is a conjectural statement of the relation
between two or more variables”. (Kerlinger, 1956)

3. 1. A Hypothesis must be conceptually clear
- concepts should be clearly defined
- the definitions should be commonly accepted
- the definitions should be easily communicable
2. The hypothesis should have empirical reference
- Variables in the hypothesis should be empirical realities
- If they are not it would not be possible to make the observation and
ultimately the test
3. The Hypothesis must be specific
- Place, situation and operation
Characteristics of a Testable Hypothesis

4. 4. A hypothesis should be related to available techniques of
research
- Either the techniques are already available or
- The researcher should be in a position to develop suitable
techniques
5. The hypothesis should be related to a body of theory
- Hypothesis has to be supported by theoretical argumentation
- It should depend on the existing body of knowledge
In this way
- the study could benefit from the existing knowledge and
- later on through testing the hypothesis could contribute to the reservoir of
knowledge
Characteristics of a Testable Hypothesis

5. Categorizing Hypotheses
Can be categorized in different ways
Based on their formulation
• Null Hypotheses
• Alternate Hypotheses

6. The Null Hypothesis, H0
• States the claim or assertion to be tested
• Is always about a population parameter, not about a sample
statistic
• Begin with the assumption that the null hypothesis is true
– Similar to the notion of innocent until
proven guilty
• Always contains “=” , “≤” or “” sign
• May or may not be rejected
• It states that independent variable has no effect and there
will be no difference b/w the two groups.

7. The Alternative Hypothesis, H1
• Is the opposite of the null hypothesis
• Challenges the status quo
• Never contains the “=” , “≤” or “” sign
• May or may not be proven
• Is generally the hypothesis that the researcher is trying to
prove
• It states that independent variable has an effect and
there will be a difference b/w the two groups.

8. Level of Significance, 
• Defines the unlikely values of the sample statistic if the null
hypothesis is true
• Indicates the percentage of sample means that is outside the cut-off
limits (critical value)
• It is the max. value of probability of rejecting null hypothesis when it
is true.
– Defines rejection region of the sampling distribution
• Is designated by  , (level of significance)
– Typical values are 0.01, 0.05, or 0.10
• Is selected by the researcher at the beginning
• Provides the critical value(s) of the test

9. Level of Significance and the Rejection Region
H0: μ ≥ 3
H1: μ < 3 0
H0: μ ≤ 3
H1: μ > 3


Represents
critical value
Lower-tail test
Level of significance = 
0Upper-tail test
Two-tail test
Rejection
region is
shaded
/ /2
0
/ /2H0: μ = 3
H1: μ ≠ 3

10. Types of Errors…
A Type I error occurs when we reject a true null hypothesis
(i.e. Reject H0 when it is TRUE)
A Type II error occurs when we don’t reject a false null
hypothesis (i.e. Do NOT reject H0 when it is FALSE)
H0 T F
Reject Type I( )
Correct
decision
Fail to Reject
Correct
decision
Type II( )



11. • The probability of a Type I error is denoted as α (Greek
letter alpha). The probability of a type II error is β
(Greek letter beta).
• The two probabilities are inversely related. Decreasing
one increases the other, for a fixed sample size.
• In other words, you can’t have  and β both real small
for any old sample size. You may have to take a much
larger sample size, or in the court example, you need
much more evidence.

12. Type I & II Error Relationship
 Type I and Type II errors cannot happen at the same
time
 Type I error can only occur if H0 is true
 Type II error can only occur if H0 is false
If Type I error probability (  ) , then
Type II error probability ( β )

13. One-Tail Test
• In many cases, the alternative hypothesis focuses on a particular
direction
• Determines whether a particular population parameter is larger or
smaller than some predefined value
• Uses one critical value of test statistic
H0: μ ≥ 3
H1: μ < 3
H0: μ ≤ 3
H1: μ > 3
This is a lower-tail test since the alternative
hypothesis is focused on the lower tail below the
mean of 3
This is an upper-tail test since the alternative
hypothesis is focused on the upper tail above the
mean of 3

15. Two tailed test
• Two-tailed Test
• Determines the
likelihood that a
population parameter
is within certain upper
and lower bounds
• May use one or two
critical values