#21 - In an experiment, subjects were shown a series of

[Administrator]

Please post your questions below! Thank you!

[T.B.Justin]

I think the correct inference for this question is the combination of the numerical and formal logic idea of these sentences:

-..Appearing usually at the top but occasionally at the bottom.

-The guessed correctly less than half the time.

-If they had simply guessed that the next image would always appear at the top, they would have been correct most of the time.

With the big emphasis on the second sentence in my sequence. Since they guessed incorrectly most of the time, they must have occasionally guessed that the image would appear at the bottom of the screen.

[Lily123]

Can someone please explain why (A) is wrong? Is it because we're speculating about what they believed as opposed to that they REPORTED to believe?

[Adam Tyson]

Thanks for the question, Lily123! It's because we cannot know whether such a guessing pattern could have been based on a perceived pattern. Maybe someone could have guessed that way and done so due to a pattern they perceived? The facts of the stimulus cannot tell us what they would have believed if they had done something different. That would be pure speculation on our part! Instead, we can only prove something about the numbers.

[claudiagarin]

Hi, could someone explain why E is wrong? The argument seems to imply this would be correct.

Also, could anyone break down this question for me? I'm having a hard time really understanding how some incorrect guesses have to be at the bottom? Could someone explain? Thanks!

[Adam Tyson]

Hey there claudiagarin, the reason that E is incorrect is that we have no idea what guessing strategy would have been rational, even though we know in hindsight what strategy would have been more successful. Rationality just never comes into play in this stimulus.

The proof of the correct answer is based on Formal Logic, which is basically math. We know that the image usually appeared at the top, which means more than half of the time. We also know that most people were wrong more than half of the time. So let's use some simple numbers to analyze those facts.

Imagine there were just 10 images shown. More than half - 6 of them - were shown at the top. Most people were wrong more than half the time, so at least 6 wrong answers. Is there any way they could have been correct every time they guessed the bottom, and still gotten 6 wrong answers? If they never guessed bottom, and made 10 guesses of top, they would have been right 6 times, but we know that didn't happen. If they guessed bottom four times and were right every time, they also would have guessed top 6 times and also been right every time, getting a perfect score, which did not happen.

Play with those number a bit and you will see that they must have guessed bottom at least a couple times when the image appeared at the top. Otherwise, they would have been right more than half the time instead of wrong more than half the time.

[christinecwt]

Hi Team - can anyone explain why Answer Choice A and B are wrong? Thanks!

[Robert Carroll]

christinecwt,

Both of those answer choices rely on completely unknown information.

For answer choice (A): imagine people guessed the next image would appear at the top. Why can't they be doing that because they think there's a pattern? There's no answer to that question, so no possible basis for answer choice (A).

For answer choice (B): this is far out of the scope of the stimulus, which is based on a single experiment. Is guessing based on patterns really worse in general than guessing based on what previously happened? In fact...isn't guessing based on what previously happened guessing based on a pattern? Since this answer choice is already about situations far beyond the stimulus, this is enough to get rid of it, but in fact the answer doesn't even have to be true about the experiment in the stimulus! In the stimulus, people did suboptimally because they thought they saw patterns, and, since they weren't completely optimal, we know there was some imperfection in their beliefs about those supposed patterns. But...if they were just better at recognizing the real pattern that existed, wouldn't guessing based on a pattern be the best possible way to guess even in this experiment?

Because these two answers require information beyond what the stimulus presents, they're both incorrect.

Robert Carroll

[SwanQueen]

Greetings,

I'm not sure I understand the two explanations above for why (A) is wrong.

My reasoning for eliminating (A):

We know from the stimulus that "the subjects all reported that they based their guesses on patterns they believed they saw in the sequence"

However (A) says if they had always guessed top, then not based on "ANY pattern they believed they saw in the sequence"

It could be true that they believed they saw two different patterns: one that's on top every third time, and one that's on top every time. They opted to report the former.

Hence, (A) is not MBT since "any" is too strong. It could be true that they did see that pattern as well, but chose to go with another pattern they also believed to have seen.

What are your thoughts on the above rationale?

I would also appreciate if someone could elaborate on the two other explanations for why (A) is wrong, as I don't understand them.

Thank you in advance!

[Jeff Wren]

Hi Swanqueen,

The first thing to realize about Answer A is that it is describing something that did not happen in the experiment.

I mention this because your explanation that the subjects saw two patterns but chose one of the patterns is not required to explain and rule out this answer.

We know from the stimulus that:

1. Subjects guessed correctly less than half the time (meaning that they did not always guess the top screen, because if they had, then they would have been correct more than half the time)
2. Subjects reported that they based their answers on patterns that they believed they saw.

Answer A is making a hypothetical claim, that IF the subjects had always guessed that the next image would appear at the top of the screen, then their reason for doing so could not have been based on a pattern that they believed that they saw.

This isn't necessarily true.

If someone were to alway choose the top screen, there are two plausible explanations.

1. The person realized that the image had appeared at the top more than the bottom and decided to always choose the top to maximize his or her chance of success. (This is what this answer is basically assuming.)

2. The person believes there is a pattern, (say the person thinks that the image appears on the bottom exactly every 500th time) and still always chooses the top screen based on that pattern because when asked to choose, it was not the 500th time. If this were to happen even once, then Answer A would not necessarily be true.

Of course, there are also other reasons that someone could always choose the top screen that may be quite arbitrary, such as personal preference.

I realize that the answer mentions subjects (plural), but the reasoning above would still apply to all of the subjects.