KA P/S Type 1 Error passage question

[JustinM88]

Can someone walk me through their thinking process of this one?
I understand that a Type 1 error is a "false positive" aka a "false alarm",
that Miller's Law (the null hypothesis) says 7 +/-2 items is what one can remember,
and that the average for the study was merely 4.73 items remembered.

Also, in this study, what could be an example of a Type II error (a false negative)?

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[3AA]

Can someone walk me through their thinking process of this one?
I understand that a Type 1 error is a "false positive" aka a "false alarm",
that Miller's Law (the null hypothesis) says 7 +/-2 items is what one can remember,
and that the average for the study was merely 4.73 items remembered.

Also, in this study, what could be an example of a Type II error (a false negative)?


For this question, I would utilize a process of elimination method. A type I error is a false positive, as you said, so in this case, it would be the subject saying a # that they thought they heard, but was actually never said. With this in mind, let's look at all the answer choices and see which would be most likely to interfere with the subject hearing the digits correctly. In A, the researcher reading digits too quickly could definitely cause a reader to not hear correctly and thus report a digit that wasn't actually said. In B, a researcher reading the digits too slowly would most likely help the subject better listen to and remember the digits. In C and D, the subject repeating the digits back too slowly or too quickly aren't really the best reason as to why they would come up with a digit that they didn't hear (for the Type 1 Error, it makes more sense to put the fault on the researcher rather than the subject, as something with them not being able to hear the right digit would result in them coming up with a digit that wasn't actually said). On the other hand, I think a Type II error would be the subject's fault, as them not listening to the digits correctly would lead to them providing a false negative (although again, the researcher interfering with the subject's ability to hear the digits could influence this as well) . Out of curiosity, do you know what the KA answer explanation was?

 

[JustinM88]

It's a beast of an explanation, so that's kind of why I posted up this question to see if anyone could walk me through it in a quicker manner haha

 

[NextStepTutor_1]

Hi @JustinM88 -

Excellent question! A type 2 error in the context of this passage would be if Miller's Law were to actually be false, but the researchers thought they confirmed it anyway.

The logic of this question is that reading the stimuli too fast would trip up the participants in a way that doesn't necessarily invalidate Miller's Law. The argument would basically be that their technique wouldn't be valid if the stimuli were read so fast that the participants couldn't even process them -- that wouldn't be a meaningful test of working memory.

In the spirit of a picture being worth a thousand words, this image—which I've seen widely circulated online among people who are into stats & diagnostic medicine—captures the difference between type 1 and type 2 errors very concisely, at least as applied to clinical diagnoses (this image isn't very careful about defining the null hypothesis, but it is very helpful for remembering the difference between a false positive and a false negative in a medical context!).

Hope this helps, & best of luck!

 

[3AA]

Sorry, but I'm a bit confused- if Miller's Law was false, but the researchers thought it was true, wouldn't that be a Type 1 error - the researchers falsely believed that Miller's Law was correct? Would a type 2 error be if Miller's Law was true, but the researchers found it to be false? Thanks for the help!

 

[NextStepTutor_1]

Hi @3AA,

The tricky part about this question is that type 1 & 2 errors are technically defined based on the null hypothesis, so we have to determine what that is. The context of the passage suggests (& the explanation confirms) that the null hypothesis of these researchers is that Miller's Law is true. A type 1 error is defined as an incorrect rejection of a true null hypothesis, which is what the question suggests might have happened -- that is, if they gave the participants stimuli too quickly to process, then they were not correct to conclude that their findings rejected Miller's Law. In other words, we have an incorrect rejection (based on a problematic protocol) of a true null hypothesis (Miller's law). (A weak point in this reasoning is that we don't technically have explicit confirmation of Miller's Law being true, but it's a reasonable assumption given that it's presented to us in our MCAT studying as a "law").

A type 2 error is defined as incorrectly supporting a false null hypothesis. This would be the case if Miller's Law were actually incorrect, but the researchers thought they confirmed it anyway.

Let me further spell out the pregnancy analogy encapsulated in the above picture -- that might help clarify things a little bit. In this context, the null hypothesis would be "no pregnancy" (after all, pregnancy is not the default state of human existence). In the type 1 error example, of a middle-aged man, we know that the null hypothesis is true (this guy is definitely not pregnant), but for some reason the doctor thinks he is, thereby incorrectly rejecting a true null hypothesis. In the type 2 error example, the null hypothesis is actually false -- the woman shown is pregnant -- but for some reason the doctor incorrectly maintains the false null hypothesis. Of course, this is sort of a humorous example, but hopefully it helps.

Another example of a type 2 error would be if we were to take the null hypothesis of the earth being flat (as a child might do) and come up with some evidence that we think supports that incorrect interpretation. The key point is that for a type 2 error, the null hypothesis (whether or not it is reasonable) is incorrect.

Hope this helps clarify things! For what it's worth, this is known to be an area of confusion for many people who have successfully completed stats coursework...

 

[JustinM88]

Hi @3AA,

The tricky part about this question is that type 1 & 2 errors are technically defined based on the null hypothesis, so we have to determine what that is. The context of the passage suggests (& the explanation confirms) that the null hypothesis of these researchers is that Miller's Law is true. A type 1 error is defined as an incorrect rejection of a true null hypothesis, which is what the question suggests might have happened -- that is, if they gave the participants stimuli too quickly to process, then they were not correct to conclude that their findings rejected Miller's Law. In other words, we have an incorrect rejection (based on a problematic protocol) of a true null hypothesis (Miller's law). (A weak point in this reasoning is that we don't technically have explicit confirmation of Miller's Law being true, but it's a reasonable assumption given that it's presented to us in our MCAT studying as a "law").

A type 2 error is defined as incorrectly supporting a false null hypothesis. This would be the case if Miller's Law were actually incorrect, but the researchers thought they confirmed it anyway.

Let me further spell out the pregnancy analogy encapsulated in the above picture -- that might help clarify things a little bit. In this context, the null hypothesis would be "no pregnancy" (after all, pregnancy is not the default state of human existence). In the type 1 error example, of a middle-aged man, we know that the null hypothesis is true (this guy is definitely not pregnant), but for some reason the doctor thinks he is, thereby incorrectly rejecting a true null hypothesis. In the type 2 error example, the null hypothesis is actually false -- the woman shown is pregnant -- but for some reason the doctor incorrectly maintains the false null hypothesis. Of course, this is sort of a humorous example, but hopefully it helps.

Another example of a type 2 error would be if we were to take the null hypothesis of the earth being flat (as a child might do) and come up with some evidence that we think supports that incorrect interpretation. The key point is that for a type 2 error, the null hypothesis (whether or not it is reasonable) is incorrect.

Hope this helps clarify things! For what it's worth, this is known to be an area of confusion for many people who have successfully completed stats coursework...

Awesome description which has helped clarify everything for me.

I'm going to actually have to study those "incorrect rejection of a true null hypothesis" phrases aren't I haha ><

 

[JustinM88]

Hi @3AA,

The tricky part about this question is that type 1 & 2 errors are technically defined based on the null hypothesis, so we have to determine what that is. The context of the passage suggests (& the explanation confirms) that the null hypothesis of these researchers is that Miller's Law is true. A type 1 error is defined as an incorrect rejection of a true null hypothesis, which is what the question suggests might have happened -- that is, if they gave the participants stimuli too quickly to process, then they were not correct to conclude that their findings rejected Miller's Law. In other words, we have an incorrect rejection (based on a problematic protocol) of a true null hypothesis (Miller's law). (A weak point in this reasoning is that we don't technically have explicit confirmation of Miller's Law being true, but it's a reasonable assumption given that it's presented to us in our MCAT studying as a "law").

A type 2 error is defined as incorrectly supporting a false null hypothesis. This would be the case if Miller's Law were actually incorrect, but the researchers thought they confirmed it anyway.

Let me further spell out the pregnancy analogy encapsulated in the above picture -- that might help clarify things a little bit. In this context, the null hypothesis would be "no pregnancy" (after all, pregnancy is not the default state of human existence). In the type 1 error example, of a middle-aged man, we know that the null hypothesis is true (this guy is definitely not pregnant), but for some reason the doctor thinks he is, thereby incorrectly rejecting a true null hypothesis. In the type 2 error example, the null hypothesis is actually false -- the woman shown is pregnant -- but for some reason the doctor incorrectly maintains the false null hypothesis. Of course, this is sort of a humorous example, but hopefully it helps.

Another example of a type 2 error would be if we were to take the null hypothesis of the earth being flat (as a child might do) and come up with some evidence that we think supports that incorrect interpretation. The key point is that for a type 2 error, the null hypothesis (whether or not it is reasonable) is incorrect.

Hope this helps clarify things! For what it's worth, this is known to be an area of confusion for many people who have successfully completed stats coursework...

Awesome description which has helped clarify everything for me.

I'm going to actually have to study those "incorrect rejection of a true null hypothesis" phrases aren't I haha ><

I always like to whittle things down as simple as possible, so this is how my mind will process these scenarios next time:
"The null hypothesis is 7, and it is true.
The researcher's data says it should actually be 4.73.
*Null hypothesis rejected*
But wait, we discover that the researchers were reading the #'s too quickly.
*INCORRECT rejection of a true null hypothesis!*
Type 1 error.
Boom."

haha ^.^