Hypothesis testing
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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.
Hypothesis testing
- 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 …