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# Hypothesis Testing

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A conceptually simple logical approach to teach hypothesis testing. When decision is taken based on p value often reported by statistical packages, this kind of a presentation is useful.

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### Hypothesis Testing

1. 1. Hypothesis testing anandunnithan on research methods 1
2. 2. Case of Murder trial • Murder Accused is facing the trial in a court. The court looks at the evidence to judge whether the accused is innocent or Guilty • What is the Null Hypothesis here? • What is the Alternate Hypothesis? 2
3. 3. Case of Murder trial • Null Hypothesis – H0 : The accused is NOT GUILTY (Innocent) – H1 : The accused is GUILTY • How do we test this hypothesis? • Against evidence – What is the evidence available? – Often evidence is circumstantial and Not Conclusive • Eye witnesses • Fingerprint • Motives 3
4. 4. Circumstantial evidence • Null Hypothesis – H0 : The accused is NOT GUILTY (Innocent) – H1 : The accused is GUILTY • Evidence 1 – CC TV recorded the murder and the recording is available • The argument : If the accused were indeed innocent (H0 is true) what is the probability of having this evidence? – 0% • What is your decision ? – Not Guilty ? Guilty? – Accept or Reject Null Hypothesis • What is your confidence in this decision? – What is the probability that you are wrong? – What is the consequence of your wrong judgment? 4
5. 5. Circumstantial evidence • Null Hypothesis – H0 : The accused is NOT GUILTY (Innocent) – H1 : The accused is GUILTY • Evidence 2 – Fingerprint of accused is found on the murder weapon -a knife • The argument : If the accused were indeed innocent (H0 is true) what is the probability of having this evidence? –1% 5
6. 6. Circumstantial evidence • What is your decision ? – Not Guilty ? Guilty? – Accept or Reject Null Hypothesis • What is your confidence in this decision? – What is the probability that you are wrong? – What is the consequence of your wrong judgment? • An innocent person will get punished • A Guilty person will be acquitted • Which of these you want to reduce? • Can both be simultaneously reduced? 6
7. 7. Circumstantial evidence • Null Hypothesis – H0 : The accused is NOT GUILTY (Innocent) – H1 : The accused is GUILTY • Evidence 3 – Fingerprint of accused is found in the room where body was found • The argument : If the accused were indeed innocent (H0 is true) what is the probability of having this evidence? – 15 % 7
8. 8. Circumstantial evidence • What is your decision ? – Not Guilty ? Guilty? – Accept or Reject Null Hypothesis • What is your confidence in this decision? – What is the probability that you are wrong? – What is the consequence of your wrong judgment? • An innocent person will get punished • A Guilty person will be acquitted • Which of these you want to reduce? • Can both be simultaneously reduced? 8
9. 9. Circumstantial evidence • Null Hypothesis – H0 : The accused is NOT GUILTY (Innocent) – H1 : The accused is GUILTY • Evidence 4 – Eye witness found the accused sharing a drink with the victim 2 hours before the time of death • The argument : If the accused were indeed innocent (H0 is true) what is the probability of having this evidence? – 70 % 9
10. 10. Circumstantial evidence • What is your decision ? – Not Guilty ? Guilty? – Accept or Reject Null Hypothesis • What is your confidence in this decision? – What is the probability that you are wrong? – What is the consequence of your wrong judgment? • An innocent person will get punished • A Guilty person will be acquitted • Which of these you want to reduce? • Can both be simultaneously reduced? 10
11. 11. Circumstantial evidence • Null Hypothesis – H0 : The accused is NOT GUILTY (Innocent) – H1 : The accused is GUILTY • Evidence 5 – The accused had borrowed a large sum of money from the victim • The argument : If the accused were indeed innocent (H0 is true) what is the probability of having this evidence? – 90 % 11
12. 12. Circumstantial evidence • What is your decision ? – Not Guilty ? Guilty? – Accept or Reject Null Hypothesis • What is your confidence in this decision? – What is the probability that you are wrong? – What is the consequence of your wrong judgment? • An innocent person will get punished • A Guilty person will be acquitted • Which of these you want to reduce? • Can both be simultaneously reduced? 12
13. 13. Are effective teachers motivated by power? • Manifest Needs – Needs for affiliation, achievement , power and autonomy • What are the characteristics of effective teachers? • Need for power and effectiveness as teachers – A sample of 100 teachers – Measured Need for power – Measured Effectiveness – Both scaled variables 13
14. 14. Are effective teachers motivated by power? • Need for power and effectiveness • Correlation ‘r’ for sample of 100 = 0.62 • How do we make a generalization for all the teachers? • Can we say therefore that for the entire population, Need for power and effectiveness are correlated? • Teachers with a high need for power are more effective? 14
15. 15. Are effective teachers motivated by power? • Need for power and effectiveness • Correlation ‘r’ for sample of 100 = 0.62 • How do we make a generalization for all the teachers? • Hypothesis testing – To determine if sample results are applicable for population – A statement you make about relationships among population parameters – Tested using sample statistics – Based on distribution assumptions – Can be Non parametric 15
16. 16. Are effective teachers motivated by power? • Need for power and effectiveness • Correlation ‘r’ for sample of 100 = 0.62 • Null Hypothesis (neutral) – H0 : Rho =0 where Rho is the correlation coefficient for population – H1 : Rho ≠ 0 • If null hypothesis were true ie, if Rho is indeed zero, what is the probability of getting a sample with r=0.62? – 90% (0.9) • What is your conclusion? 16
17. 17. Are effective teachers motivated by power? • Correlation ‘r’ for sample of 100 = 0.62 • Null Hypothesis (neutral) – H0 : Rho =0 where Rho is the correlation coefficient for population – H1 : Rho ≠ 0 • If null hypothesis were true ie, if Rho is indeed zero, what is the probability of getting a sample with r=0.62? – 90% (0.9) • What is your conclusion? • Accept or Reject Null Hypothesis • What is the probability that you are wrong if you accept the null hypothesis? 17
18. 18. Are effective teachers motivated by power? • Need for power and effectiveness • Correlation ‘r’ for sample of 100 = 0.62 • Null Hypothesis (neutral) – H0 : Rho =0 where Rho is the correlation coefficient for population – H1 : Rho ≠ 0 • If null hypothesis were true ie, if Rho is indeed zero, what is the probability of getting a sample with r=0.62? – 40% (0.4) • What is your conclusion? 18
19. 19. Are teachers motivated by power? • Correlation ‘r’ for sample of 100 = 0.62 • Null Hypothesis (neutral) – H0 : Rho =0 where Rho is the correlation coefficient for population – H1 : Rho ≠ 0 • If null hypothesis were true ie, if Rho is indeed zero, what is the probability of getting a sample with r=0.62? – 8% (0.08) • What is your conclusion? • Accept or Reject Null Hypothesis • If you reject null what is your conclusion? • What is the probability that you are wrong if you accept the null hypothesis? • What is the probability that you are wrong if you reject the null hypothesis? 19
20. 20. Are teachers motivated by power? • Correlation ‘r’ for sample of 100 = 0.62 • Null Hypothesis (neutral) – H0 : Rho =0 where Rho is the correlation coefficient for population – H1 : Rho ≠ 0 • If null hypothesis were true ie, if Rho is indeed zero, what is the probability of getting a sample with r=0.62? – .07% (0.007) • What is your conclusion? • Accept or Reject Null Hypothesis • If you reject null what is your conclusion? • What is the probability that you are wrong if you accept the null hypothesis? • What is the probability that you are wrong if you reject the null hypothesis? 20