Hypothesis testing

HYPOTHESIS TESTING

Quantitative Analysis / Statistical Techniques

Madhuranath RMBA 2012 | Cohort-7Asian Institute of Management

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)

OVERVIEW

Madhuranath R © 2012

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

HYPOTHESIS


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

DefinitionThe process of proving assertions false using a test of observed data (sample data) is called Hypothesis Testing

HYPOTHESIS TESTING


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

TYPES OF HYPOTHESIS


EXAMPLES OF HYPOTHESES

Null HypothesisHo : Mean Sea Level trend is 5.38 mm / year

Alternate HypothesisHa : 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


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

TYPES OF ERRORS


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

α, β AND THE INTER-RELATIONSHIP


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

INTERPRETING RESULTS


Hypothesis testing

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