The document discusses hypothesis testing in quantitative analysis, defining key concepts such as null and alternate hypotheses, and the process of determining these hypotheses through statistical evidence. It outlines the importance of type I and type II errors, including their probabilities (α and β), and how they impact decision-making regarding the null hypothesis. Additionally, it explains the interpretation of p-values in assessing the strength of evidence against the null hypothesis.

1. HYPOTHESIS
TESTING
Quantitative Analysis / Statistical Techniques
Madhuranath R
MBA 2012 | Cohort-7
Asian Institute of Management

2. OVERVIEW
 Hypothesis
 Hypothesis Testing
 Types of Hypotheses – Null, Alternate
 Example of Hypotheses
 Type I & Type II Errors (Level of Significance)
 α, β and the inter-relationship
 Interpreting Results (Weight of evidence from p-value)

3. HYPOTHESIS
What do you mean by a Hypothesis?
A hypothesis is a proposition that is –
 assumed as a premise in an argument / claim
 set forth as an explanation for the occurrence of some
specified group of phenomena

4. HYPOTHESIS TESTING
Why do we make hypotheses?
 The practice of science traditionally involves
formulating and testing hypotheses
 Hypotheses are assertions that are capable of being
proven false using a test of observed data
Definition
The process of proving assertions false using a test of
observed data (sample data) is called Hypothesis Testing

5. TYPES OF HYPOTHESIS
Null Hypothesis
 The null hypothesis typically corresponds to a general or
default position
 Making this assertion will make no difference and hence
cannot be proven positively
Alternate Hypothesis
 An alternate hypothesis asserts a rival relationship between
the phenomena measured by the null hypothesis
 It need not be a logical negation of the null hypothesis as it
only helps in rejecting or not rejecting the null hypothesis

6. EXAMPLES OF HYPOTHESES
Null Hypothesis
Ho : Mean Sea Level trend is
5.38 mm / year
Alternate Hypothesis
Ha : Mean Sea Level trend is
not 5.38 mm / year
The α in this case maybe
assumed as 0.05 to reject the
Null Hypothesis with a 95%
confidence level

7. TYPES OF ERRORS
What are errors in Hypothesis Testing?
The purpose of Hypothesis Testing is to reject or not reject the Null
Hypothesis based on statistical evidence
Hypothesis Testing is said to have resulted in an error when the
decision regarding treatment of the Null Hypothesis is wrong
Type-I Error (Ho right but rejected)
When Null Hypothesis is rejected despite the test on data showing
that the outcome was true
Type-II Error (Ho wrong but not rejected)
When Null Hypothesis is not rejected despite the test on data
showing that the outcome was false

8. α, β AND THE INTER-RELATIONSHIP
During the Hypothesis Testing,
α – is the probability of occurrence of a Type-I Error
β – is the probability of occurrence of a Type-II Error
Relationship between α and β
 For a fixed sample size, the lower we set value of α, the
higher is the value of β and vice-versa
 In many cases, it is difficult or almost impossible to
calculate the value of β and hence we usually set only α

9. INTERPRETING RESULTS
Interpreting the weight of evidence against the
Null Hypothesis for rejecting / not rejecting Ho
If the p-value for testing Ho is less than –
 < 0.10, we have some evidence that Ho is false
 < 0.05, we have strong evidence that Ho is false
 < 0.01, we have very strong evidence that Ho is false
 < 0.001, we have extremely strong evidence that Ho is false

10. To be continued …