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hypothesis testing


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hypothesis testing

  1. 1. RAMESH DEBUR Hypothesis testing
  2. 2. The Way Back <ul><li>Formulate a research Question </li></ul><ul><li>Develop a research Methodology </li></ul><ul><li>Collected Data </li></ul><ul><li>Sorted Data </li></ul>
  3. 3. The Way Forward <ul><li>Introduction </li></ul><ul><li>GENERATE A HYPOTHESIS </li></ul><ul><ul><li>NULL HYPOTHESIS </li></ul></ul><ul><ul><li>ALTERNATIVE HYPOTHESIS </li></ul></ul><ul><li>Significance </li></ul><ul><ul><li>The p Value </li></ul></ul><ul><li>Errors </li></ul><ul><ul><li>TYPE 1 </li></ul></ul><ul><ul><li>TYPE 2 </li></ul></ul><ul><li>ACCEPT OR REJECT HYPOTHESIS </li></ul><ul><li>INFERENCE & PRESENTATION OF THE DATA </li></ul>
  4. 4. Hypothesis Testing <ul><li>Scientific Hypothesis testing – A Deductive method of accepting or rejecting a hypothetical statement </li></ul>
  5. 5. Definition <ul><li>A hypothesis consists either of a suggested explanation for a phenomenon </li></ul><ul><li>Eg: Gastric Juices produces Hunger </li></ul><ul><li>or </li></ul><ul><li>A reasoned proposal suggesting a possible correlation between multiple phenomena </li></ul><ul><li>Eg: People who smoke more cigarettes are at a higher risk of developing lung cancer </li></ul>
  6. 6. Therefore….. <ul><li>Hypothesis testing implies either accepting or rejecting a certain statement. </li></ul><ul><li>Generating a Hypothesis </li></ul><ul><ul><li>In Scientific Research the hypothesis is an offshoot of the research question </li></ul></ul><ul><ul><li>Eg: Do people who smoke more cigarettes increase their risk of developing Lung Cancer </li></ul></ul>
  7. 7. The Logic of Hypothesis Testing <ul><li>All hypothesis are false until proven true </li></ul><ul><li>The farther away from falsification the truer is the hypothesis </li></ul><ul><li>A Hypothesis is NEVER a Fact. We accept a hypothesis as true until it is falsified </li></ul><ul><li>Eg: </li></ul><ul><ul><li>Columbus wants to discover a route to India </li></ul></ul><ul><ul><li>Columbus Discovers America </li></ul></ul><ul><ul><li>Every body he sees are called Indian – Hypothesis </li></ul></ul><ul><ul><li>Later learns they are not Indian – Hypothesis falsified </li></ul></ul>
  8. 8. The NULL Hypothesis <ul><li>The exact opposite of the perceived effect or change </li></ul><ul><li>Eg: </li></ul><ul><ul><li>Gastric Juices DOES NOT cause Hunger </li></ul></ul><ul><ul><li>Smoking DOES NOT Increase the risk of Developing Lung Cancer </li></ul></ul>
  9. 9. The Alternate Hypothesis <ul><li>The Exact opposite of the NULL Hypothesis </li></ul><ul><li>Called alternate because the falsification is the primary logic of hypothesis testing </li></ul><ul><ul><li>Gastric Juices DOES NOT cause Hunger </li></ul></ul><ul><ul><li>Smoking DOES NOT Increase the risk of Developing Lung Cancer </li></ul></ul><ul><li>Easier to Falsify things than prove facts????? </li></ul>
  10. 10. Disproving Null Vs Proving the Alternate Null Alternate
  12. 12. Probability (prob·a·bil·i·ty) <ul><li>Similar to Chance: </li></ul><ul><li>Derived from the Noun Probable </li></ul><ul><li>What is a probability : </li></ul><ul><li>The chance of a event occurring at any given time </li></ul><ul><li>The likelihood of an event having a particular outcome </li></ul><ul><li>Eg: Flipping a coin </li></ul><ul><li>All probability is between 0 and 1 </li></ul>
  13. 13. Flip a coin <ul><li>Likelihood of getting only 1 head in </li></ul><ul><ul><li>1 flip = 0.5 </li></ul></ul><ul><ul><li>2 flips = 0.34 </li></ul></ul><ul><ul><li>4flips = 0.24 </li></ul></ul><ul><ul><li>10 = 0.01 </li></ul></ul><ul><ul><li>100=0.00001 </li></ul></ul><ul><li>Likelihood of getting atleast 1 head in </li></ul><ul><ul><li>1 flip = 0.5 </li></ul></ul><ul><ul><li>2 flips = 0.66 </li></ul></ul><ul><ul><li>4flips = 0.76 </li></ul></ul><ul><ul><li>10 = 0.99 </li></ul></ul><ul><ul><li>100=0.999999 </li></ul></ul>
  14. 14. Probability as related to hypothesis testing <ul><li>The p value </li></ul><ul><li>The likelihood that the data collected is equal to or more extreme than the null hypothesis </li></ul><ul><ul><li>(logic: The Null hypothesis is the extreme value of an experiment) </li></ul></ul><ul><li>Alternatively: The probability that the expected outcome occurred purely by chance </li></ul>
  15. 15. Significance - Definition <ul><li>The significance level of a test is the probability that the test statistic will reject the null hypothesis when the [hypothesis] is true . </li></ul>
  16. 16. IN REAL TERMS <ul><li>Get Test statistic (outcome of research ) </li></ul><ul><li>Null hypothesis – test statistic </li></ul><ul><li>if > chance : accept test and reject null </li></ul><ul><li>If ≤ chance : reject test </li></ul><ul><li>Generally the significance is kept at 0.05 or 1 chance in 100 or 0.001( 1 in 1000) </li></ul>
  17. 17. Errors of Hypothesis testing α is also called as the significance value and is determined by the investigator Stastical Decision True state of the Null Hypothesis True H O False H O Reject H O Type 1 ( α ) Correct Do Not Reject H O Correct Type II ( β )
  18. 18. <ul><li>A type 1 error is considered much more serious than a type 2 error </li></ul><ul><li>Why? EG. A new drug is introduced into the market which can potentially cure hypertension but can also cause sudden death. Evaluate the chances of sudden death by the drug </li></ul>Statistical Decision True state of the Null Hypothesis True H O NO Death False H O Death Reject H O Type 1 ( α ) (Accept drug) Correct (Reject drug) Do Not Reject H O Correct (Accept Drug) Type II ( β ) (Reject Drug)