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Presentation 2

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This document discusses hypothesis testing, which is a method used in scientific research to either accept or reject hypotheses. It outlines the key steps: 1) Formulating a research question and hypothesis. The null hypothesis states there is no effect or relationship, while the alternative suggests there is. 2) Collecting and analyzing data. 3) Using a p-value and significance level (typically 0.05) to determine whether to reject the null hypothesis, based on the probability the results occurred by chance. 4) Drawing inferences and presenting the findings. Type 1 and 2 errors in hypothesis testing are also discussed.

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RAMESH DEBUR Hypothesis testing
The Way Back Formulate a research Question Develop a research Methodology Collected Data Sorted Data
The Way Forward Introduction GENERATE A HYPOTHESIS NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS Significance The p Value Errors TYPE 1 TYPE 2 ACCEPT OR REJECT HYPOTHESIS INFERENCE & PRESENTATION OF THE DATA
Hypothesis Testing Scientific Hypothesis testing – A Deductive method of accepting or rejecting a hypothetical statement
Definition A hypothesis consists either of a suggested explanation for a phenomenon Eg: Gastric Juices produces Hunger or A reasoned proposal suggesting a possible correlation between multiple phenomena Eg: People who smoke more cigarettes are at a higher risk of developing lung cancer
Therefore….. Hypothesis testing implies either accepting or rejecting a certain statement. Generating a Hypothesis In Scientific Research the hypothesis is an offshoot of the research question Eg: Do people who smoke more cigarettes increase their risk of developing Lung Cancer
The Logic of Hypothesis Testing All hypothesis are false until proven true The farther away from falsification the truer is the hypothesis A Hypothesis is NEVER a Fact. We accept a hypothesis as true until it is falsified Eg: Columbus wants to discover a route to India Columbus Discovers America Every body he sees are called Indian – Hypothesis Later learns they are not Indian – Hypothesis falsified
The NULL Hypothesis The exact opposite of the perceived effect or change Eg: Gastric Juices DOES NOT cause Hunger Smoking DOES NOT Increase the risk of Developing Lung Cancer
The Alternate Hypothesis The Exact opposite of the NULL Hypothesis Called alternate because the falsification is the primary logic of hypothesis testing Gastric Juices DOES NOT cause Hunger Smoking DOES NOT Increase the risk of Developing Lung Cancer Easier to Falsify things than prove facts?????
Disproving Null Vs Proving the Alternate Null Alternate
THE NEXT QUESTION WHEN DO WE REJECT THE NULL HYPOTHESIS ANSWER : WHEN THE CHANCES OF IT BEING TRUE ARE VERY SLIM ( NON SIGNIFICANT) PROBABILITY TESTING
Probability (prob·a·bil·i·ty) Similar to Chance: Derived from the Noun Probable What is a probability : The chance of a event occurring at any given time The likelihood of an event having a particular outcome Eg: Flipping a coin All probability is between 0 and 1
Flip a coin Likelihood of getting only 1 head in 1 flip = 0.5 2 flips = 0.34 4flips = 0.24 10 = 0.01 100=0.00001 Likelihood of getting atleast 1 head in 1 flip = 0.5 2 flips = 0.66 4flips = 0.76 10 = 0.99 100=0.999999
Probability as related to hypothesis testing The p value The likelihood that the data collected is equal to or more extreme than the null hypothesis (logic: The Null hypothesis is the extreme value of an experiment) Alternatively: The probability that the expected outcome occurred purely by chance
Significance - Definition The significance level of a test is the probability that the test statistic will reject the null hypothesis when the [hypothesis] is true .
IN REAL TERMS Get Test statistic (outcome of research ) Null hypothesis – test statistic if > chance : accept test and reject null If ≤ chance : reject test Generally the significance is kept at 0.05 or 1 chance in 100 or 0.001( 1 in 1000)
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 )
A type 1 error is considered much more serious than a type 2 error 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 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)

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Presentation 2

  • 2. The Way Back Formulate a research Question Develop a research Methodology Collected Data Sorted Data
  • 3. The Way Forward Introduction GENERATE A HYPOTHESIS NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS Significance The p Value Errors TYPE 1 TYPE 2 ACCEPT OR REJECT HYPOTHESIS INFERENCE & PRESENTATION OF THE DATA
  • 4. Hypothesis Testing Scientific Hypothesis testing – A Deductive method of accepting or rejecting a hypothetical statement
  • 5. Definition A hypothesis consists either of a suggested explanation for a phenomenon Eg: Gastric Juices produces Hunger or A reasoned proposal suggesting a possible correlation between multiple phenomena Eg: People who smoke more cigarettes are at a higher risk of developing lung cancer
  • 6. Therefore….. Hypothesis testing implies either accepting or rejecting a certain statement. Generating a Hypothesis In Scientific Research the hypothesis is an offshoot of the research question Eg: Do people who smoke more cigarettes increase their risk of developing Lung Cancer
  • 7. The Logic of Hypothesis Testing All hypothesis are false until proven true The farther away from falsification the truer is the hypothesis A Hypothesis is NEVER a Fact. We accept a hypothesis as true until it is falsified Eg: Columbus wants to discover a route to India Columbus Discovers America Every body he sees are called Indian – Hypothesis Later learns they are not Indian – Hypothesis falsified
  • 8. The NULL Hypothesis The exact opposite of the perceived effect or change Eg: Gastric Juices DOES NOT cause Hunger Smoking DOES NOT Increase the risk of Developing Lung Cancer
  • 9. The Alternate Hypothesis The Exact opposite of the NULL Hypothesis Called alternate because the falsification is the primary logic of hypothesis testing Gastric Juices DOES NOT cause Hunger Smoking DOES NOT Increase the risk of Developing Lung Cancer Easier to Falsify things than prove facts?????
  • 10. Disproving Null Vs Proving the Alternate Null Alternate
  • 11. THE NEXT QUESTION WHEN DO WE REJECT THE NULL HYPOTHESIS ANSWER : WHEN THE CHANCES OF IT BEING TRUE ARE VERY SLIM ( NON SIGNIFICANT) PROBABILITY TESTING
  • 12. Probability (prob·a·bil·i·ty) Similar to Chance: Derived from the Noun Probable What is a probability : The chance of a event occurring at any given time The likelihood of an event having a particular outcome Eg: Flipping a coin All probability is between 0 and 1
  • 13. Flip a coin Likelihood of getting only 1 head in 1 flip = 0.5 2 flips = 0.34 4flips = 0.24 10 = 0.01 100=0.00001 Likelihood of getting atleast 1 head in 1 flip = 0.5 2 flips = 0.66 4flips = 0.76 10 = 0.99 100=0.999999
  • 14. Probability as related to hypothesis testing The p value The likelihood that the data collected is equal to or more extreme than the null hypothesis (logic: The Null hypothesis is the extreme value of an experiment) Alternatively: The probability that the expected outcome occurred purely by chance
  • 15. Significance - Definition The significance level of a test is the probability that the test statistic will reject the null hypothesis when the [hypothesis] is true .
  • 16. IN REAL TERMS Get Test statistic (outcome of research ) Null hypothesis – test statistic if > chance : accept test and reject null If ≤ chance : reject test Generally the significance is kept at 0.05 or 1 chance in 100 or 0.001( 1 in 1000)
  • 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. A type 1 error is considered much more serious than a type 2 error 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 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)