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.

1. Hypothesis testing
anandunnithan on research methods
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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?
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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. 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. 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%
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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. 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 %
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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. 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 %
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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. 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 %
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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. 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
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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?
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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
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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?
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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. 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?
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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?
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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?
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