hypothesis testing basics

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