hypothesis testing
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Hypothesis TestingTRANSCRIPT
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Hypothesis Testing
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The logic of statistical hypothesis testing follows the logic of judicial decision making.
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A jury is asked to decide whether a defendant is guilty or not guilty.
![Page 4: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/4.jpg)
A jury is asked to decide whether a defendant is guilty or not guilty. It is a dicho-tomous decision, guilty or not guilty.
![Page 5: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/5.jpg)
A jury is asked to decide whether a defendant is guilty or not guilty. It is a dicho-tomous decision, guilty or not guilty. There is no in-between or partial decision.
???
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A jury is asked to decide whether a defendant is guilty or not guilty. It is a dicho-tomous decision, guilty or not guilty. There is no in-between or partial decision.The jury does not begin its decision-making process in a neutral position.
![Page 7: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/7.jpg)
A jury is asked to decide whether a defendant is guilty or not guilty. It is a dicho-tomous decision, guilty or not guilty. There is no in-between or partial decision.The jury does not begin its decision-making process in a neutral position.
The default position is “not guilty.”
![Page 8: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/8.jpg)
A jury is asked to decide whether a defendant is guilty or not guilty. It is a dicho-tomous decision, guilty or not guilty. There is no in-between or partial decision.The jury does not begin its decision-making process in a neutral position.
The default position is “not guilty.”
The prosecution must mount enough evidence to convince the jury to move from its default position of not guilty to a verdict of guilty.
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The jury will make a decision which may or may not coincide with reality.
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When the jury decides “not guilty” and the defendant is, in reality, not guilty,
It is true because the not guilty (negative) decision aligns with the not guilty (negative) reality.
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When the jury decides “not guilty” and the defendant is, in reality, not guilty, they have made a correct decision called a “true negative decision.”
It is true because the not guilty (negative) decision aligns with the not guilty (negative) reality.
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When the jury decides “not guilty” and the defendant is, in reality, not guilty, they have made a correct decision called a “true negative decision.”
It is true because the not guilty (negative) decision aligns with the not guilty (negative) reality.
not guilty
and I reallywasn’t guilty!
true negative
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When the jury decides “guilty” and the defendant is, in reality, guilty,
It is true because the guilty (positive) decision aligns with the guilty (positive) reality.
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When the jury decides “guilty” and the defendant is, in reality, guilty, they have made a correct decision called a “true positive” decision.
It is true because the guilty (positive) decision aligns with the guilty (positive) reality.
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When the jury decides “guilty” and the defendant is, in reality, guilty, they have made a correct decision called a “true positive” decision.
It is true because the guilty (positive) decision aligns with the guilty (positive) reality.
guilty
and I reallyWAS guilty!
true positive
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When the jury decides “not guilty” and the defendant is, in reality, guilty,
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When the jury decides “not guilty” and the defendant is, in reality, guilty, they have made an incorrect decision called a “false negative error” which is also called a Type II or beta error.
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When the jury decides “not guilty” and the defendant is, in reality, guilty, they have made an incorrect decision called a “false negative error” which is also called a Type II or beta error. It is false because the “not guilty” (negative) decision does not align with the guilty (positive) reality.
not guilty
and I reallyWAS guilty!
false negative
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When a jury decides “guilty” and the defendant is, in reality, not guilty,
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When a jury decides “guilty” and the defendant is, in reality, not guilty, they have made an incorrect decision called a “false positive error”
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When a jury decides “guilty” and the defendant is, in reality, not guilty, they have made an incorrect decision called a “false positive error” which is also called a Type I or alpha error.
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When a jury decides “guilty” and the defendant is, in reality, not guilty, they have made an incorrect decision called a “false positive error” which is also called a Type I or alpha error. It is false because the “guilty” (positive) decision is not aligned with the not guilty (negative) reality.
guilty
but I reallyWASN’T guilty!
false positive
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Although we prefer correct decisions, if we cannot be correct, we prefer the false negative error over the false positive error.
In other words you’d rather render a “NOT GUILTY” verdict when there is GUILT.
Than a “GUILTY” verdict where there is NO GUILT.
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Although we prefer correct decisions, if we cannot be correct, we prefer the false negative error over the false positive error.
In other words you’d rather render a “NOT GUILTY” verdict when there is GUILT.
Than a “GUILTY” verdict where there is NO GUILT.
not guilty
and I reallyWAS guilty!
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Although we prefer correct decisions, if we cannot be correct, we prefer the false negative error over the false positive error.
In other words you’d rather render a “NOT GUILTY” verdict when there is GUILT.
Than a “GUILTY” verdict where there is NO GUILT.
not guilty
and I reallyWAS guilty!
guilty
but I reallyWASN’T guilty!
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In judicial decisions we would rather let a guilty defendant go free . . .
than convict and imprison an innocent defendant.
Our default position of “not guilty” supports this
preference and protects against the least favorable condition.
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In judicial decisions we would rather let a guilty defendant go free . . .
than convict and imprison an innocent defendant.
Our default position of “not guilty” supports this
preference and protects against the least favorable condition.
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In judicial decisions we would rather let a guilty defendant go free . . .
than convict and imprison an innocent defendant.
Our default position of “not guilty” supports this
preference and protects against the least favorable condition.
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Review the following slide and answer the questions that follow:
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Review the following slide and answer the questions that follow:
What type of decision is made when a guilty (+) verdict is rendered and the person is guilty (+)?
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Review the following slide and answer the questions that follow:
What type of decision is made when a guilty (+) verdict is rendered and the person is guilty (+)?
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Review the following slide and answer the questions that follow:
What type of decision is made when a not guilty (-) verdict is rendered and the person is not guilty (-)?
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Review the following slide and answer the questions that follow:
What type of decision is made when a not guilty (-) verdict is rendered and the person is not guilty (-)?
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Review the following slide and answer the questions that follow:
What type of decision is made when a guilty (+) verdict is rendered and the person is not guilty (-)?
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Review the following slide and answer the questions that follow:
What type of decision is made when a guilty (+) verdict is rendered and the person is not guilty (-)?
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Review the following slide and answer the questions that follow:
What type of decision is made when a not guilty (-)verdict is rendered and the person is guilty (+) ?
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Review the following slide and answer the questions that follow:
What type of decision is made when a not guilty (-)verdict is rendered and the person is guilty (+) ?
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Each conviction protects against Type I error at a different stringency according to the gravity of the punishment to be imposed.
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The haunting reality is that we really never know the reality of the guilt or innocence of defendants.
We make our best decisions knowing that there is a probability that we have made an error.
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The haunting reality is that we really never know the reality of the guilt or innocence of defendants.
We make our best decisions knowing that there is a probability that we have made an error.
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Judicial Decisions
Statistical hypothesis testing and decision-making are directly analogous to judicial decision making.
Statistical Decisions
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Let’s consider an example:
A statistician is asked to decide whether a difference exists between two groups of people in terms of some attribute (e.g., excitability). It is a dichotomous decision (meaning only two options), different or not different. There is no in-between or partial decision.
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Let’s consider an example:
A statistician is asked to decide whether a difference exists between two groups of people in terms of some attribute (e.g., excitability). It is a dichotomous decision (meaning only two options), different or not different. There is no in-between or partial decision.
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Let’s consider an example:
A statistician is asked to decide whether a difference exists between two groups of people in terms of some attribute (e.g., excitability).
It is a dichotomous decision (meaning only two options), different or not different. There is no in-between or partial decision. ?x
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The statistician does not begin her decision-making in a neutral position. The default position is “not different.” This is also called the “null hypothesis.”
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The statistician does not begin her decision-making in a neutral position. The default position is “not different.” This is also called the “null hypothesis.”
![Page 47: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/47.jpg)
The statistician does not begin her decision-making in a neutral position. The default position is “not different.” This is also called the “null hypothesis.”
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The research findings must present sufficient evidence to convince the statistician to move from her default position of no difference to a conclusion that the groups are different in terms of the attribute.
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The statistician will make a decision which may or may not coincide with reality.
The apparent differences may be due to chance or may be real.
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The statistician will make a decision which may or may not coincide with reality.
The apparent differences may be due to chance or may be real.
OR Something that is really happening
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When the statistician decides “not different” (fails to reject the null hypothesis, maintains the default position) and the groups are, in reality, not different, she has made a correct decision called a “true negative decision.”
true negative
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It is true because the “no difference” (negative) decision aligns with “no difference” reality.
not guilty
and I reallyWASN’T guilty!
true negative
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When the statistician decides that there is a difference (rejects the null hypothesis, moves off of the default position) and the groups are, in reality, different, she has made a correct decision called a true positive decision.
true positive
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It is true because the “different” (positive) decision aligns with the “different” (positive) reality.
guilty
and I reallyWAS guilty!
true positive
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When the statistician decides “not different” (fails to reject the null hypothesis, maintains the default position) and the group are, in reality different, she has made a false negative error.
false negative
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It is false because the decision of no difference (negative) does not align with difference (positive) reality.
false negative
not guilty
Ha ha! and I really
WAS guilty!
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Although we prefer correct decisions, if we cannot be correct, we then prefer false negative error over the alternative error.
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When a statistician decides that there is a difference (positive) between the groups and rejects the null hypothesis of no difference and, in reality, there is no difference, she has made a false positive error (also called Type I error or alpha error.)
false positive
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It is false because the “difference” (positive) decision does not align with the “no difference” (negative) reality.
guilty
but I reallyWASN’T guilty!
false positive
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Our hypothesis testing conventions protect against false positive, Type I error by holding a default position of the null hypothesis.
αBeware of
Type I Error
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We set a standard of evidence that is required before rejecting the default null hypothesis.
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The standard of evidence is based on the probability density of the sampling distribution.
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Using probability density we can estimate the probability of Type I error.
If the mean of the sample is here, then we
have a .0001 or .01% chance that we made a
Type I error.
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Or in other words, we have a .01% chance of rejecting the null hypothesis that the group scores come from two different populations (claiming guilty) and being wrong when both groups were really part of the same population (not guilty)
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When the probability of Type I error is at a low enough level, we reject the default, null hypothesis. Like in our previous example.
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The conventional level of tolerable Type I error is .05.
95%
.05 or 5% chance that we selected a sample from this population and claimed it was a sample from another
population = false positive
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This means that out of 100 similar decisions based on these data …
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06 07 08 09 10 11 12 13 14 15
07 08 09 10 11 12 13 14
08 09 10 11 12 13
09 10 11 12
10 11
10 155
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… we will be wrong (make a Type I error) less than 5 times.
05 06 07 08 09 10 11 12 13 14 15 16
06 07 08 09 10 11 12 13 14 15
07 08 09 10 11 12 13 14
08 09 10 11 12 13
09 10 11 12
10 11
10 155
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One advantage that statisticians have over juries is that we can estimate the probability of Type I error while they cannot.
I can estimate the probability
of being right or wrong
Not sure of the probability of being right or
wrong
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(Or, at least it is easier for us to do so than for them. There is some recent research in rape cases that has estimated how frequently juries make Type I errors in such cases.)
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Even so, we do not get to make the similar decision 100 times.
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We tend to make the decision once. The haunting reality is that we never know in this one decision whether it is one of the probably occurring Type I errors.
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In other words, we take a sample of 30 persons and get a score of 7.
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06 07 08 09 10 11 12 13 15
07 08 09 10 11 12 13 14
08 09 10 11 12 13
09 10 11 12
10 11
10 155
14
14
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In other words, we take a sample of 30 persons and get a score of 7. And then another sample and get a score of 12, and another with a score of 11, and so on and so on until the distribution below emerges.
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06 07 08 09 10 11 12 13 15
07 08 09 10 11 12 13 14
08 09 10 11 12 13
09 10 11 12
10 11
10 155
14
14
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But since, in real life, we usually only take one sample of 30 for our research purposes,
05 06 07 08 09 10 11 12 13 14 15 16
06 07 08 09 10 11 12 13 14 15
07 08 09 10 11 12 13 14
08 09 10 11 12 13
09 10 11 12
10 11
10 155
14
14
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But since, in real life, we usually only take one sample of 30 for our research purposes,
05 06 07 08 09 10 11 12 13 14 15 16
06 07 08 09 10 11 12 13 14 15
07 08 09 10 11 12 13 14
08 09 10 11 12 13
09 10 11 12
10 11
10 155
14
14
10
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But since, in real life, we usually only take one sample of 30 for our research purposes, we don’t know if the sample was selected from the far left of the distribution below
05 06 07 08 09 10 11 12 13 14 15 16
06 07 08 09 10 11 12 13 14 15
07 08 09 10 11 12 13 14
08 09 10 11 12 13
09 10 11 12
10 11
10 155
14
14
06
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But since, in real life, we usually only take one sample of 30 for our research purposes, we don’t know if the sample was selected from the far left of the distribution below or the far right
05 06 07 08 09 10 11 12 13 14 15 16
06 07 08 09 10 11 12 13 14 15
07 08 09 10 11 12 13 14
08 09 10 11 12 13
09 10 11 12
10 11
10 155
14
14
16
![Page 79: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/79.jpg)
But since, in real life, we usually only take one sample of 30 for our research purposes, we don’t know if the sample was selected from the far left of the distribution below or the far right or the middle.
05 06 07 08 09 10 11 12 13 14 15 16
06 07 08 09 10 11 12 13 14 15
07 08 09 10 11 12 13 14
08 09 10 11 12 13
09 10 11 12
10 11
10 155
14
14
11
![Page 80: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/80.jpg)
But since, in real life, we usually only take one sample of 30 for our research purposes, we don’t know if the sample was selected from the far left of the distribution below or the far right or the middle. So, we examine the probability that the sample did or did not come from the far left or the far right.
05 06 07 08 09 10 11 12 13 14 15 16
06 07 08 09 10 11 12 13 14 15
07 08 09 10 11 12 13 14
08 09 10 11 12 13
09 10 11 12
10 11
10 155
14
14
![Page 81: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/81.jpg)
But since, in real life, we usually only take one sample of 30 for our research purposes, we don’t know if the sample was selected from the far left of the distribution below or the far right or the middle. So, we examine the probability that the sample did or did not come from the far left or the far right.
05 06 07 08 09 10 11 12 13 14 15 16
06 07 08 09 10 11 12 13 14 15
07 08 09 10 11 12 13 14
08 09 10 11 12 13
09 10 11 12
10 11
10 155
14
14
Hmm. . . What are
the chances
the sample came from
the far right or left
of the Distri-
bution?
![Page 82: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/82.jpg)
So let’s say we want to know if the students who go to a college party are more excited to be there than little girls at a birthday party.
![Page 83: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/83.jpg)
Here are the sampling distributions of the excitability of young girls at a birthday party.
![Page 84: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/84.jpg)
Let’s say we don’t have the same kind of distribution for college student excitability at a party.
?
![Page 85: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/85.jpg)
We want to know if there is a statistical difference between the girls at the birthday party and the excitability of college students at a Friday night party.
![Page 86: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/86.jpg)
We randomly select a group of college students at a party and measure their levels of excitability.
![Page 87: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/87.jpg)
Our random selection is “13”.
13
![Page 88: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/88.jpg)
Our random selection is “13”. Since this number does not lie in the extreme ends we would reject the null hypothesis or render a judgment of “not guilty”.
13
![Page 89: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/89.jpg)
Our random selection is “13”. Since this number does not lie in the extreme ends we would reject the null hypothesis or render a judgment of “not guilty”. College Students and little girls show no difference.
13
![Page 90: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/90.jpg)
However, what if we randomly selected a college student sample with an average excitability value of “05”.
05
![Page 91: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/91.jpg)
However, what if we randomly selected a college student sample with an average excitability value of “05”. Wow! This is a rare occurrence.
05
![Page 92: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/92.jpg)
Because the chance of that happening is so rare we would reject the null hypothesis.
05
![Page 93: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/93.jpg)
Because the chance of that happening is so rare we would reject the null hypothesis. We would say “guilty!”
05
![Page 94: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/94.jpg)
Because the chance of that happening is so rare we would reject the null hypothesis. We would say “guilty!” But if in reality there is no difference,
05
![Page 95: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/95.jpg)
Because the chance of that happening is so rare we would reject the null hypothesis. We would say “guilty!” But if in reality there is no difference, then we have made a type I error.
05
![Page 96: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/96.jpg)
Because the chance of that happening is so rare we would reject the null hypothesis. We would say “guilty!” But if in reality there is no difference, then we have made a type I error.
05
Researchers are willing to take that chance.
![Page 97: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/97.jpg)
In conclusion, hypothesis testing, is a way of determining the probability of our default position (not guilty or no difference) being correct or incorrect.
![Page 98: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/98.jpg)
In conclusion, hypothesis testing, is a way of determining the probability of our default position (not guilty or no difference) being correct or incorrect.
We determine the likelihood of being right or wrong based on the results.
![Page 99: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/99.jpg)
In conclusion, hypothesis testing, is a way of determining the probability of our default position (not guilty or no difference) being correct or incorrect.
We determine the likelihood of being right or wrong based on the results. Then we decide if we are willing to maintain our default position (no difference) or go out on a limb and change our default position (yes there is a difference).
![Page 100: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/100.jpg)
What follows are exercises to help you check your understanding.
![Page 101: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/101.jpg)
Go as far as you feel you need to until you have a good feel for what you know.
![Page 102: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/102.jpg)
First Set of Questions
![Page 103: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/103.jpg)
1. Which expression below from the world of judicial decision-making best describes the “Null-hypothesis”?
![Page 104: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/104.jpg)
1. Which expression below from the world of judicial decision-making best describes the “Null-hypothesis”?A. “Guilty as charged”B. “Not guilty until proven innocent”C. “Pleading no contest”
![Page 105: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/105.jpg)
1. Which expression below from the world of judicial decision-making best describes the “Null-hypothesis”?A. “Guilty as charged”B. “Not guilty until proven innocent”C. “Pleading no contest”
![Page 106: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/106.jpg)
1. Which expression below from the world of judicial decision-making best describes the “Null-hypothesis”?A. “Guilty as charged”B. “Not guilty until proven innocent”C. “Pleading no contest”
2. What is another way to say “Null-hypothesis”?
![Page 107: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/107.jpg)
1. Which expression below from the world of judicial decision-making best describes the “Null-hypothesis”?A. “Guilty as charged”B. “Not guilty until proven innocent”C. “Pleading no contest”
2. What is another way to say “Null-hypothesis”?A. Not clearB. Not differentC. Not important
![Page 108: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/108.jpg)
1. Which expression below from the world of judicial decision-making best describes the “Null-hypothesis”?A. “Guilty as charged”B. “Not guilty until proven innocent”C. “Pleading no contest”
2. What is another way to say “Null-hypothesis”?A. Not clearB. Not differentC. Not important
![Page 109: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/109.jpg)
With hypothesis testing we are attempting to set up a default position of not guilty. We stay in that position unless we have enough evidence to overturn it.
![Page 110: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/110.jpg)
With hypothesis testing we are attempting to set up a default position of not guilty. We stay in that position unless we have enough evidence to overturn it. Let’s say our null-hypothesis is the following:
![Page 111: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/111.jpg)
With hypothesis testing we are attempting to set up a default position of not guilty. We stay in that position unless we have enough evidence to overturn it. Let’s say our null-hypothesis is the following:
There is no difference in IQ between children who are exposed to classical music between the ages of 0 and 3 and those who were not.
![Page 112: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/112.jpg)
With hypothesis testing we are attempting to set up a default position of not guilty. We stay in that position unless we have enough evidence to overturn it. Let’s say our null-hypothesis is the following:
There is no difference in IQ between children who are exposed to classical music between the ages of 0 and 3 and those who were not.
This is our default position. We are not neutral, we are claiming at the outset that there is no difference.
![Page 113: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/113.jpg)
But then along comes some evidence that over turns that position. So we reject the null hypothesis and claim there is a probable difference.
![Page 114: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/114.jpg)
But then along comes some evidence that over turns that position. So we reject the null hypothesis and claim there is a probable difference.
Notice how we don’t say “there is a difference”. We say there is a probable or statistical difference. This just means that with statistics we are never 100% certain. We just say that the probability that we are wrong is a certain percent. Usually that percent needs to be pretty low.
![Page 115: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/115.jpg)
If we have estimated that there is a 60% chance that we are wrong, that is a risk not worth taking. If you were told that you had a 60% chance of losing a lot of money and a 40% chance of making a lot of money, would you take that chance?
Probably not. But if you were told that you had only a 5% chance of losing a lot of money and a 95% of earning a lot, that might be a chance you would be willing to take. The same holds true with hypothesis testing.
![Page 116: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/116.jpg)
If we have estimated that there is a 60% chance that we are wrong, that is a risk not worth taking. If you were told that you had a 60% chance of losing a lot of money and a 40% chance of making a lot of money, would you take that chance?
Probably not. But if you were told that you had only a 5% chance of losing a lot of money and a 95% of earning a lot, that might be a chance you would be willing to take. The same holds true with hypothesis testing.
![Page 117: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/117.jpg)
Based on that instruction, consider your answer to these questions again and explain the correct answer in your own words.
![Page 118: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/118.jpg)
Based on that instruction, consider your answer to these questions again and explain the correct answer in your own words.
1. Which expression below from the world of judicial decision-making best describes the “Null-hypothesis”?A. “Guilty as charged”B. “Not guilty until proven innocent”C. “Pleading no contest”
2. What is another way to say “Null-hypothesis”?A. Not clearB. Not differentC. Not important
![Page 119: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/119.jpg)
Second Set of Questions – see if you can answer these questions, if not go to the instruction that follows and you’ll be given an opportunity to respond to the questions armed with the instruction.
![Page 120: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/120.jpg)
3. When the jury decides “not guilty” and the defendant really is “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
![Page 121: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/121.jpg)
3. When the jury decides “not guilty” and the defendant really is “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
![Page 122: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/122.jpg)
3. When the jury decides “not guilty” and the defendant really is “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
![Page 123: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/123.jpg)
3. When the jury decides “not guilty” and the defendant really is “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
![Page 124: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/124.jpg)
3. When the jury decides “not guilty” and the defendant really is “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
4. When the jury decides “guilty” and the defendant actually was “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
![Page 125: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/125.jpg)
4. When the jury decides “guilty” and the defendant actually was “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
3. When the jury decides “not guilty” and the defendant really is “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
![Page 126: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/126.jpg)
4. When the jury decides “guilty” and the defendant actually was “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
3. When the jury decides “not guilty” and the defendant really is “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
![Page 127: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/127.jpg)
3. When the jury decides “not guilty” and the defendant really is “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
4. When the jury decides “guilty” and the defendant actually was “not guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
![Page 128: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/128.jpg)
5. When the jury decides “not guilty” and the defendant actually was “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
![Page 129: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/129.jpg)
5. When the jury decides “not guilty” and the defendant actually was “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
![Page 130: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/130.jpg)
5. When the jury decides “not guilty” and the defendant actually was “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
![Page 131: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/131.jpg)
5. When the jury decides “not guilty” and the defendant actually was “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
![Page 132: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/132.jpg)
5. When the jury decides “not guilty” and the defendant actually was “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
6. When the jury decides “guilty” and the defendant really is “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
![Page 133: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/133.jpg)
5. When the jury decides “not guilty” and the defendant actually was “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
6. When the jury decides “guilty” and the defendant really is “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
![Page 134: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/134.jpg)
5. When the jury decides “not guilty” and the defendant actually was “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
6. When the jury decides “guilty” and the defendant really is “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
![Page 135: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/135.jpg)
5. When the jury decides “not guilty” and the defendant actually was “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were wrong to do so.
B. REJECT the null hypothesis and it turns out - - - you were wrong to do so.
6. When the jury decides “guilty” and the defendant really is “guilty”, in statistics that is the same as saying:
A. ACCEPT the null hypothesis and it turns out - - - you were right to do so.
B. REJECT the null hypothesis and it turns out - - - you were right to do so.
![Page 136: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/136.jpg)
Accepting the null-hypothesis is essentially like saying “not guilty” or that we accept the default position of innocence or no difference.Rejecting the null-hypothesis is essentially like saying “guilty” or that we reject the default position of innocence or there is enough evidence to suggest there is a difference.
![Page 137: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/137.jpg)
Here is a visual:
![Page 138: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/138.jpg)
Here is a visual:
Null-hypothesis ACCEPTED!
![Page 139: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/139.jpg)
Here is a visual:
Null-hypothesis ACCEPTED!
I was found NOT
GUILTY!
![Page 140: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/140.jpg)
Here is a visual:
Null-hypothesis ACCEPTED!
I was found NOT
GUILTY!
Na, na, . . . nanana! There is NOT enough statistical evidence to convict or reject the null-hypothesis!
![Page 141: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/141.jpg)
Here is a visual:
Null-hypothesis ACCEPTED!
I was found NOT
GUILTY!
Na, na, . . . nanana! There is NOT enough statistical evidence to convict or reject the null-hypothesis!
Not Guilty = Accept the Null
![Page 142: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/142.jpg)
Here is a visual:
Null-hypothesis REJECTED!
![Page 143: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/143.jpg)
Here is a visual:
Null-hypothesis REJECTED!
I was found
GUILTY!
![Page 144: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/144.jpg)
Here is a visual:
Null-hypothesis REJECTED!
I was found
GUILTY!
Wa, Wa! There IS enough statistical evidence to convict or reject the null-Hypothesis!
![Page 145: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/145.jpg)
Here is a visual:
Null-hypothesis REJECTED!
I was found
GUILTY!
Wa, Wa! There IS enough statistical evidence to convict or reject the null-Hypothesis!
Guilty = Reject the Null
![Page 146: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/146.jpg)
Third Set of Questions - see if you can answer these questions, if not go to the instruction that follows and you’ll be given an opportunity to respond to the questions armed with the instruction.
![Page 147: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/147.jpg)
7. When the jury decides “guilty” (reject the null) and the defendant actually was “not guilty” (shouldn’t have rejected the null), what type of error has been committed?
A. Type I errorB. Type II error
![Page 148: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/148.jpg)
7. When the jury decides “guilty” (reject the null) and the defendant actually was “not guilty” (shouldn’t have rejected the null), what type of error has been committed?
A. Type I errorB. Type II error
8. When the jury decides “not guilty” (accept the null) and the defendant actually was “guilty” (reject the null), what type of error has been committed?
A. Type I errorB. Type II error
![Page 149: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/149.jpg)
9. Which type of error is preferable?A. Type I errorB. Type II error
![Page 150: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/150.jpg)
9. Which type of error is preferable?A. Type I errorB. Type II error
10. Question: What is the haunting reality? Answer: We actually never know for sure if we have committed a type I or II error. All we are doing is determining the probability that we . . .have committed an error. are correct in our hypothesis.
![Page 151: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/151.jpg)
9. Which type of error is preferable?A. Type I errorB. Type II error
10. Question: What is the haunting reality? Answer: We actually never know for sure if we have committed a type I or II error. All we are doing is determining the probability that we . . .have committed an error. are correct in our hypothesis.
![Page 152: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/152.jpg)
9. Which type of error is preferable?A. Type I errorB. Type II error
10. Question: What is the haunting reality? Answer: We actually never know for sure if we have committed a type I or II error. All we are doing is determining the probability that we . . .
A. have committed an error. B. are correct in our hypothesis.
![Page 153: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/153.jpg)
Let’s consider each type of error
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1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence,3. Determine if the evidence merits accepting or rejecting
the null-hypothesis,4. You accept the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is a difference between men and women sports-car color preference and you should have rejected the null.
6. This is a type I error
![Page 155: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/155.jpg)
1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence3. Determine if the evidence merits accepting or rejecting
the null-hypothesis,4. You accept the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is a difference between men and women sports-car color preference and you should have rejected the null.
6. This is a type I error
![Page 156: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/156.jpg)
1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence3. Determine if the evidence merits accepting or rejecting
the null-hypothesis4. You accept the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is a difference between men and women sports-car color preference and you should have rejected the null.
6. This is a type I error
![Page 157: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/157.jpg)
1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence3. Determine if the evidence merits accepting or rejecting
the null-hypothesis4. You accept the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is a difference between men and women sports-car color preference and you should have rejected the null.
6. This is a type I error
![Page 158: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/158.jpg)
1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence3. Determine if the evidence merits accepting or rejecting
the null-hypothesis4. You accept the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is a difference between men and women sports-car color preference and you should have rejected the null.
6. This is a type I error
![Page 159: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/159.jpg)
1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence3. Determine if the evidence merits accepting or rejecting
the null-hypothesis4. You accept the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is a difference between men and women sports-car color preference and you should have rejected the null.
This is a type I error
![Page 160: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/160.jpg)
1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence3. Determine if the evidence merits accepting or rejecting
the null-hypothesis4. You reject the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is NO difference between men and women sports-car color preference and you should have accepted the null
This is a type II error
![Page 161: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/161.jpg)
1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence3. Determine if the evidence merits accepting or rejecting
the null-hypothesis4. You reject the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is NO difference between men and women sports-car color preference and you should have accepted the null
This is a type II error
![Page 162: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/162.jpg)
1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence3. Determine if the evidence merits accepting or rejecting
the null-hypothesis4. You reject the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is NO difference between men and women sports-car color preference and you should have accepted the null
This is a type II error
![Page 163: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/163.jpg)
1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence3. Determine if the evidence merits accepting or rejecting
the null-hypothesis4. You reject the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is NO difference between men and women sports-car color preference and you should have accepted the null
This is a type II error
![Page 164: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/164.jpg)
1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence3. Determine if the evidence merits accepting or rejecting
the null-hypothesis4. You reject the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is NO difference between men and women sports-car color preference and you should have accepted the null
This is a type II error
![Page 165: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/165.jpg)
1. State your null-hypothesis; There is no significant difference between females and males in terms of their preference of certain sports-car colors
2. Collect your evidence3. Determine if the evidence merits accepting or rejecting
the null-hypothesis4. You reject the null5. In reality (and you could never know this for sure) you
were wrong. In actuality there is NO difference between men and women sports-car color preference and you should have accepted the null
This is a type II error
![Page 166: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/166.jpg)
You’ll never know if you committed a type I or II error.
You can only estimate the probability that you did!
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That’s because with statistics we deal in
probability, not certainty.
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Based on the instruction you just received, respond to these questions again. Explain your reasoning for selecting the options you did.
![Page 169: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/169.jpg)
7. When the jury decides “guilty” (reject the null) and the defendant actually was “not guilty” (shouldn’t have rejected the null), what type of error has been committed?
A. Type I errorB. Type II error
![Page 170: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/170.jpg)
7. When the jury decides “guilty” (reject the null) and the defendant actually was “not guilty” (shouldn’t have rejected the null), what type of error has been committed?
A. Type I errorB. Type II error
![Page 171: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/171.jpg)
7. When the jury decides “guilty” (reject the null) and the defendant actually was “not guilty” (shouldn’t have rejected the null), what type of error has been committed?
A. Type I errorB. Type II error
8. When the jury decides “not guilty” (accept the null) and the defendant actually was “guilty” (reject the null), what type of error has been committed?
A. Type I errorB. Type II error
![Page 172: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/172.jpg)
7. When the jury decides “guilty” (reject the null) and the defendant actually was “not guilty” (shouldn’t have rejected the null), what type of error has been committed?
A. Type I errorB. Type II error
8. When the jury decides “not guilty” (accept the null) and the defendant actually was “guilty” (reject the null), what type of error has been committed?
A. Type I errorB. Type II error
![Page 173: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/173.jpg)
9. Which type of error is preferable?A. Type I errorB. Type II error
![Page 174: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/174.jpg)
9. Which type of error is preferable?A. Type I errorB. Type II error
![Page 175: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/175.jpg)
9. Which type of error is preferable?A. Type I errorB. Type II error
10. Question: What is the haunting reality? Answer: We actually never know for sure if we have committed a type I or II error. All we are doing is determining the probability that we . . .have committed an error. are correct in our hypothesis.
![Page 176: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/176.jpg)
9. Which type of error is preferable?A. Type I errorB. Type II error
10. Question: What is the haunting reality? Answer: We actually never know for sure if we have committed a type I or II error. All we are doing is determining the probability that we . . .have committed an error. are correct in our hypothesis.
![Page 177: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/177.jpg)
9. Which type of error is preferable?A. Type I errorB. Type II error
10. Question: What is the haunting reality? Answer: We actually never know for sure if we have committed a type I or II error. All we are doing is determining the probability that we . . .
A. have committed an error. B. are correct in our hypothesis.
Answers: 7-A, 8-B, 9-B, 10-A
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9. Which type of error is preferable?A. Type I errorB. Type II error
10. Question: What is the haunting reality? Answer: We actually never know for sure if we have committed a type I or II error. All we are doing is determining the probability that we . . .
A. have committed an error. B. are correct in our hypothesis.
Answers: 7-A, 8-B, 9-B, 10-A
![Page 179: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/179.jpg)
Fourth Set of Questions - see if you can answer these questions, if not go to the instruction that follows and you’ll be given an opportunity to respond to the questions armed with the instruction.
![Page 180: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/180.jpg)
11. Question: How do we decide how much evidence is required before we will reject the null hypothesis?
Answer: We estimate the probability of being ______ a certain percent of the time (e.g., .05 or 5% of the time).
a. rightb. wrong
![Page 181: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/181.jpg)
11. Question: How do we decide how much evidence is required before we will reject the null hypothesis?
Answer: We estimate the probability of being ______ a certain percent of the time (e.g., .05 or 5% of the time).
a. rightb. wrong
![Page 182: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/182.jpg)
11. Question: How do we decide how much evidence is required before we will reject the null hypothesis?
Answer: We estimate the probability of being ______ a certain percent of the time (e.g., .05 or 5% of the time).
a. rightb. wrong12. Question: What does a .05 rejection level mean?
Answer: If we were to take the same small sample 100 times from a population, we would be willing to _____________________ .05 or 5% of the time
a. . . . take the chance of being wrong . . . b. . . . reject the null hypothesis . . .
![Page 183: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/183.jpg)
11. Question: How do we decide how much evidence is required before we will reject the null hypothesis?
Answer: We estimate the probability of being ______ a certain percent of the time (e.g., .05 or 5% of the time).
a. rightb. wrong12. Question: What does a .05 rejection level mean?
Answer: If we were to take the same small sample 100 times from a population, we would be willing to _____________________ .05 or 5% of the time
a. . . . take the chance of being wrong . . . b. . . . reject the null hypothesis . . .
![Page 184: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/184.jpg)
In statistics we generally ask ourselves, “What is the probability that we have made a type I error?”
![Page 185: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/185.jpg)
In statistics we generally ask ourselves, “What is the probability that we have made a Type I Error?”
Type I errors are considered a bigger issue because if we are wrong, than we might waste a lot of money or impact people negatively (e.g., spend millions of dollars on a new drug that doesn’t work).
![Page 186: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/186.jpg)
In statistics we generally ask ourselves, “What is the probability that we have made a Type I Error?”
Type I errors are considered a bigger issue because if we are wrong, than we might waste a lot of money or impact people negatively (e.g., spend millions of dollars on a new drug that doesn’t work).
Type II errors are considered less of an issue because if we are wrong, than we may stop or continue researching.
![Page 187: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/187.jpg)
We have to have determine a cut-off point as to when we will reject the null-hypothesis. No matter what cut-off point we could have chosen, the decision would always have been somewhat arbitrary.
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We have to have determine a cut-off point as to when we will reject the null-hypothesis. No matter what cut-off point we could have chosen, the decision would always have been somewhat arbitrary.
Would we be satisfied with a 75% chance of committing a type I error? Probably not. That means out of 100 experiments we would live with being wrong about our conclusions 75 times.
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Would we be satisfied with a .01% chance of committing a type I error? Probably not. That means out of 10,000 experiments we would live with being wrong about our conclusions only once. If that were the case, then almost no null-hypothesis could ever be rejected.
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In the discipline of statistics .05 or 5% of a chance of committing a type I error has been deemed an acceptable arbitrary cut-off point. This means that out of 100 experiments we will live with being wrong five times.
Would we be satisfied with a .01% chance of committing a type I error? Probably not. That means out of 10,000 experiments we would live with being wrong about our conclusions only once. If that were the case, then almost no null-hypothesis could ever be rejected.
![Page 191: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/191.jpg)
Based on the instruction you just received, respond to these questions again. Explain your reasoning for selecting the options you did.
![Page 192: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/192.jpg)
11. Question: How do we decide how much evidence is required before we will reject the null hypothesis?
Answer: We estimate the probability of being ______ a certain percent of the time (e.g., .05 or 5% of the time).
a. rightb. wrong
![Page 193: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/193.jpg)
11. Question: How do we decide how much evidence is required before we will reject the null hypothesis?
Answer: We estimate the probability of being ______ a certain percent of the time (e.g., .05 or 5% of the time).
a. rightb. wrong
![Page 194: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/194.jpg)
11. Question: How do we decide how much evidence is required before we will reject the null hypothesis?
Answer: We estimate the probability of being ______ a certain percent of the time (e.g., .05 or 5% of the time).
a. rightb. wrong
![Page 195: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/195.jpg)
11. Question: How do we decide how much evidence is required before we will reject the null hypothesis?
Answer: We estimate the probability of being ______ a certain percent of the time (e.g., .05 or 5% of the time).
a. rightb. wrong12. Question: What does a .05 rejection level mean?
Answer: If we were to take the same small sample 100 times from a population, we would be willing to _____________________ .05 or 5% of the time
a. . . . take the chance of being wrong . . . b. . . . reject the null hypothesis . . .
![Page 196: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/196.jpg)
11. Question: How do we decide how much evidence is required before we will reject the null hypothesis?
Answer: We estimate the probability of being ______ a certain percent of the time (e.g., .05 or 5% of the time).
a. rightb. wrong12. Question: What does a .05 rejection level mean?
Answer: If we were to take the same small sample 100 times from a population, we would be willing to _____________________ .05 or 5% of the time
a. . . . take the chance of being wrong . . . b. . . . reject the null hypothesis . . . Answers: 11-B, 12-A
![Page 197: Hypothesis Testing](https://reader035.vdocuments.mx/reader035/viewer/2022070319/55847905d8b42aca538b5126/html5/thumbnails/197.jpg)
11. Question: How do we decide how much evidence is required before we will reject the null hypothesis?
Answer: We estimate the probability of being ______ a certain percent of the time (e.g., .05 or 5% of the time).
a. rightb. wrong12. Question: What does a .05 rejection level mean?
Answer: If we were to take the same small sample 100 times from a population, we would be willing to _____________________ .05 or 5% of the time
a. . . . take the chance of being wrong . . . b. . . . reject the null hypothesis . . . Answers: 11-B, 12-A