P11 Interactive Seminar Activity 1_Suggested Answer

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A104 Biology

P11 Hypothesis, Evidence, Decision I

Interactive Seminar

(Activity 1 – Answer)

Activity owner: You Sean Chung

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Murder Case

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Discussion 1

Before the man is being brought to court, which of the following constitutional right do you think the man

deserve?

The man is to be

first

assumed guilty

. His

defence lawyer should

gather every evidence to

prove his innocence.

The man is to be

first

assumed innocent

. The

prosecutor should gather

every evidence to prove

otherwise.

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Discussion 1

•_{Discuss this within your team and give the reason for the}

choice you have chosen.

•_{Why should the choice you have chosen be the status quo}

assumption made on the man before any further investigation is carried out?

[Note: Status quo assumption means the assumption on the existing default state of the man.]

The man is to be

first

assumed guilty

. His

defence lawyer should

gather every evidence to

prove his innocence.

The man is to be

first

assumed innocent

. The

prosecutor should gather

every evidence to prove

otherwise.

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Discussion 1 (Suggested Answer)

For all status quo assumption, we should always assume the neutral setting as the existing state.

For example:

-We should first assume someone as honest instead of assuming that he/she is a liar.

-We should first assume that a new method (or a new drug) introduced has no significant difference as compared to the existing method (or drug).

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Discussion 1 (Suggested Answer)

After which, it is our duty to collect data and evidence to disprove our assumption.

From the previous examples:

-We will first assume the person to be honest, our next step is to collect data or evidence to show the dishonesty of the person.

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For the murder case, the man has to be first assumed

innocent. It is the duty of the prosecutor to gather evidence sufficient enough to charge the suspect in the court.

Reason for this assumption:

Think about the seriousness of the situation if the suspect is to be assumed guilty first. In this case, if the defence lawyer is incompetent and had done very little for the suspect,

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Discussion 2

• _{For this murder case, there are two possible realities.} • _{The court will decide whether the man is innocent or}

guilty based 100% on the available evidence.

Murder Case

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Discussion 2

• _{In principle, an innocent man will be set free and a guilty}

man will be convicted.

• _{However, is it possible that mistake can happen where}

an innocent man is convicted while a guilty man is set free? Discuss the possibility of such situation and what could be the reason that lead to this mistake.

Murder Case

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Discussion 2 (Suggested Answer)

All decisions to be made are based 100% on the available information and evidence. There should be no biased.

However, in reality, the problem faced by human is that we may not be able to gather ALL the evidence. In fact, most of the time, it is almost impossible to get ALL the evidence.

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For a court case, the judge has to pass the judgement based 100% on available evidence. However, we have to understand that due to the limitation of human ability, there is still a

possibility of missing evidence that is not found.

Though the chance is low, there is possibility that an innocent man is convicted. Likewise, there is also possibility that a guilty man is let go.

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Discussion 3

• _{In discussion 2, we understand that there is a possibility}

of mistake where an innocent man is convicted or a murderer is set free. This gives rise to 4 possible

outcomes as shown above.

Murder Case

The man is innocent. The man is a murderer.

The man is set free

The man is convicted

The man is set free

The man is convicted

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Discussion 3

Let’s arrange the outcome in a table form as shown below for ease of discussion.

Two of these four possible outcomes are in fact an error. Which of these two errors is a more serious error in this case? Discuss.

Reality Court’s decision Correct/Error

The man is innocent The man is set free Correct decision The man is innocent The man is convicted Type I error

The man is a murderer The man is set free Type II error

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Discussion 3 (Suggested Answer)

Which Error is more serious? Type I or Type II error?

In this case, Type I error is more serious. This is because if Type I error is committed, an innocent man will be

wrongfully convicted and may be sentenced to death (In Singapore).

Reality Court’s decision Correct/Error

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Discussion 3 (Suggested Answer)

Which error is more serious? Type I or Type II?

There is no fix rule to decide which error is more serious. It depends a lot on the situation.

Though, most of the time, we will try to avoid committing Type I error, there are also situations where Type II error is more

serious where we will try to avoid.

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Discussion 3 (Suggested Answer)

The 4 possible outcomes of diagnostic check up are:

For Type I error, a healthy man is wrongly diagnosed with a terminal disease. Though this may be psychologically devastating for the

man, the situation may not be as bad. A person who is diagnosed with a terminal disease will normally have to go through a second round of diagnostic test. The chances of getting both wrong

diagnosis will be low.

Reality Diagnosis result Correct/Error

Man is healthy No disease detected Correct diagnosis Man is healthy Disease detected Type I error

Man has the disease No disease detected Type II error

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Discussion 3 (Suggested Answer)

The 4 possible outcomes of terminal disease diagnosis are:

For Type II error, a man who has the disease will have the diagnostic result showing nothing. As such, no medical action is taken. If the terminal disease is left untreated, it will get worse as days pass. This is going to be a very

serious.

Reality Diagnosis result Correct/Error

Man is healthy No disease detected Correct diagnosis Man is healthy Disease detected Type I error

Man has the disease No disease detected Type II error

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Discussion 4

There is no perfect system in the world where we can be 100% sure of the truth. Thus, each of the 4 possible outcomes has a probability of happening.

As a fair society, our duty is to reduce the probability of making the two error as much as possible. Discuss if it is possible to reduce the two probabilities,  and , to zero.

Possible outcome Correct/Error Probability

An innocent man is set free Correct decision 1 -  An innocent man is convicted Type I error 

A murderer is set free Type II error 

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Discussion 4 (Suggested Answer)

For the murder case:

There is always a probability of committing either Type I or Type II error.

The probability of committing Type I error is denoted as . The probability of committing Type II error is denoted as .

Possible outcome Correct/Error Probability

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Discussion 4 (Suggested Answer)

For the murder case:

To reduce the probability of committing the two errors, the

necessary step is to collect as much evidence and data as possible pertaining to the case.

However, in reality, it is almost unlikely that ALL the data and

evidence can be collected. Thus, it is almost unlikely to reduce the probability ,  or , to zero.

Possible outcome Correct/Error Probability

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Discussion 5

If you think there is no way to reduce  and  to zero, then how much tolerance would you allow yourself to make judgement with the probability of making an error?

[For example, if you are confident that you will have at most a 5% chance (ie  = 5%) of convicting an innocent man (ie committing Type I error), are you willing to convict him? Or would you want to lower the  before you are confident to convict the man. Discuss.]

Possible outcome Correct/Error Probability

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Discussion 5 (Suggested Answer)

Since it is almost unlikely to reduce the probability of committing the error to zero, we will have no choice but to accept a certain tolerance for error.

Suppose  = 5%, this means that if we convict the man, we

actually have a 5% chance of wrongfully convict an innocent man. The question is are we willing to take the chance and convict him?

Possible outcome Correct/Error Probability

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Discussion 5 (Suggested Answer)

For a murder case, a 5% chance of committing an error by

convicting an innocent man is simply too high. We are definitely not going to take the chance.

If  = 1%, our chance of committing an error by convicting the suspect is now lower. Now, does 1% chance of wrongfully convict an innocent man give you more confidence to convict him?

Possible outcome Correct/Error Probability

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Discussion 5 (Suggested Answer)

In fact, for murder case like this, we have no answer to how low

 should be before one can be confident enough to convict the man. This is because it is not easy to quantify  and the

consequences of wrongfully convict an innocent man is very serious. The man will face death sentence.

So, let’s leave this decision to the judge.

Possible outcome Correct/Error Probability

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Discussion 6

If on the other hand, this is just a case of a peeping tom on trial, is your tolerance for  different from the case of a murder?

[Note: A convicted peeping tom will only be jailed for a couple of months but a convicted murderer will face death sentence]

Possible outcome Correct/Error Probability

A peeping tom is set free Type II error 

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Discussion 6 (Suggested Answer)

Now, if the case is about a peeping tom on trial, our tolerance for

 may change a little.

The reason is that the punishment for a peeping tom is relatively lighter as compared to murderer. (Maybe a couple of weeks of jail term and fine).

Possible outcome Correct/Error Probability

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Discussion (Level 6)

As such, our tolerance for  will be higher than that for a murder case. We may be willing to convict the man even if our chance of wrongfully accuse him is 5% (ie  = 5%).

(Yes, I know that by willing to accept a 5% chance of making a mistake to convict an innocent man as a peeping tom is a bit unfair. We are just using these two cases as an example for illustrating the idea.)

Possible outcome Correct/Error Probability

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Summary: The thinking stages

Stage 1:

Before we start investigation, we will always make assumption on the status quo state.

Stage 2:

We will then proceed to collect evidence and data to disprove our assumption.

Stage 3:

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Summary: The thinking stages

Stage 4:

There are two realities and two possible decisions which lead to 4 outcomes.

Stage 5:

There are two type of errors from the 4 possible outcomes.

Reality Court’s decision Correct/Error

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Summary: The thinking stages

Stage 6:

There is a probability of us committing the error.

The probability to commit Type I error is . The probability to commit Type II error is .

Possible outcome Correct/Error Probability

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Summary: The thinking stages

Stage 7:

d. http://en.wikipedia.org/wiki/Wrongful_execution