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# Hypothesis testing

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An attempt to simplify the Hypothesis Testing concepts of Statistical Techniques / Quantitative Analysis.

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### Hypothesis testing

1. 1. HYPOTHESIS TESTINGQuantitative Analysis / Statistical Techniques Madhuranath R MBA 2012 | Cohort-7 Asian Institute of Management
2. 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. 3. HYPOTHESISWhat 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. 4. HYPOTHESIS TESTINGWhy 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 dataDefinition The process of proving assertions false using a test of observed data (sample data) is called Hypothesis Testing
5. 5. TYPES OF HYPOTHESISNull Hypothesis  The null hypothesis typically corresponds to a general or default position  Making this assertion will make no difference and hence cannot be proven positivelyAlternate 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. 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. 7. TYPES OF ERRORSWhat 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 wrongType-I Error (Ho right but rejected) When Null Hypothesis is rejected despite the test on data showing that the outcome was trueType-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. 8. α, β AND THE INTER-RELATIONSHIPDuring the Hypothesis Testing,α – is the probability of occurrence of a Type-I Errorβ – is the probability of occurrence of a Type-II ErrorRelationship 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. 9. INTERPRETING RESULTSInterpreting the weight of evidence against theNull Hypothesis for rejecting / not rejecting HoIf 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. 10. To be continued …