#5 - When girls are educated in single-sex secondary schools

[Administrator]

Complete Question Explanation

Parallel Flaw-SN. The correct answer choice is (B)

The stimulus of this problem contains a classic Mistaken Reversal error, where the author incorrectly attempts to use the necessary condition of a given relationship to conclude that the sufficient condition must be true. Here is the first sentence premise:

• Sufficient Necessary
  
  Educated single-sex school Do better academically

The author then goes on to conclude that, since Alice did better academically than her peers, she was probably educated at a single-sex school. In other words, because the necessary condition has been met, the sufficient must also have occurred.

This is the hallmark of a Mistaken Reversal, where satisfying the condition at the end of the arrow (necessary) is thought to also satisfy the condition at the beginning of the arrow (sufficient). The reason that is flawed is that there could be other reasons besides being educated in a single-sex school that explain Alice's strong academic performance, and therefore we can't know for sure what type of school she previously attended.

(Note the the conditionality here is what I'd call "light" conditional reasoning, as it's qualified ever so slightly with words like "tend to" and "probably;" the principle of an incorrect reversal still holds however, and for ease of diagramming below you'll see me focus on the reversal idea rather than those hedging words)

Answer choice (A): This answer choice is simply a restatement, where the conditional premise is repeated in the conclusion. The first line states that:

• Sufficient Necessary
  
  Individual math tutoring Good grades on finals

We're then told that Celia received individual tutoring, so it makes since to conclude that she will probably get good grades. That is valid reasoning, so (A) is out.

Note too that this answer choice deals with the same subject as the stimulus (academics and grads), making it even more unlikely to be correct.

Answer choice (B): This is the correct answer choice. It contains the same reversal error as the stimulus. First sentence:

• Sufficient Necessary
  
  Babies taught to swim More ear infections

The author then goes on to conclude that, since Janice has more ear infections than anyone else in the swimming club, she was probably taught to swim as a baby. Note the immediate reversal that has occurred! Of course, as with the stimulus, there could be other reasons besides being taught to swim as a baby as to why she has more ear infections than the other swim club members, so this is a duplicate of the stimulus's flaw.

Answer choice (C): Here we have neither a reversal nor a restatement, but rather the introduction of a new, third term. The author in (C) starts with a conditional form, but then moves from that (study music early appreciate variety) to conclude something about the talent of future musicians. This new term immediately removes this choice from consideration.

Answer choice (D): This answer choice contains flawed reasoning, but the flaw is not quite the same as the one in the stimulus. Instead, this is known as a Mistaken Negation, where the absence of the sufficient condition is used to incorrectly conclude the absence of the necessary. Here's the first sentence:

• Sufficient Necessary
  
  Practice piano 30 minutes/day Pass piano exams

Then we're given this fact:

Practice piano 30 minutes/daySally

And finally this conclusion:

• Pass piano examsSally

As you can see, this is not the same as the reversal we encountered in the stimulus and in answer choice (B). Instead, the author attempts to apply the original conditional statement despite the fact that the trigger—the initial sufficient condition—never occurs, hence the name Mistaken Negation (the sufficient is gone/negated, and the author mistakenly proceeds anyway). The flaw in this error is that without the sufficient, the necessary is free to occur on not occur: Sally can still pass her exams, even if she practices less than a half hour/day. That amount of practice is enough to guarantee that she will probably pass, but it isn't required to pass.

This flaw and the Mistaken Reversal error are by far the two most errors you will encounter in conditional reasoning on the LSAT.

Answer choice (E): This answer choice has a couple of issues. First, and primarily, it confuses causality with conditionality. We don't know from the stimulus that single-sex schools are the REASON girls tend to do better academically, only that there is a reliable correlation. So saying the first piece causes the second fails to match what we're given in the stimulus. Second, there is no reversal here. We know a reversal must be present, and when one is not the answer is instantly eliminated. Finally, the subject matter of academic achievement makes me nervous: highly unlikely you'd see the same subject as the stimulus repeated in the right answer.

[Johnclem]

Hello powerscore,

I got this question right , however I am a bit confused as to what the flaw maybe. Initially I saw it as mismatch of sufficient and necessary . But the conclusion states " probably " which allows for the possibility of the sufficient condition to occur after the necessary has been met.
What am I doing wrong ?


Thanks
John

[Adam Tyson]

When conditional language gets modified with the language of probability, things can get a little weird. Here we have an argument that tells us a condition is sufficient to make another condition likely ("tends to" is a statement of probability, meaning more probable than not). In that sense it's not conditional at all, because there is nothing "necessary", just likely. We're getting into the world of "formal logic" here, and there are some great articles in our blog and other discussions in this forum that can go into much more detail about how to approach formal logic.

For now, though, we can borrow from what we know of conditional language to see the problem here - the author has said the likely outcome occurred, so the sufficient condition probably also occurred. Sounds a lot like a mistaken reversal, except for that pesky language of probability, right?

There's also an issue here about whether we are talking about the right groups. The original claim was about a comparison between those that did and those that did not attend single-sex schools. Do we know whether anyone at Alice's university went to a single-sex school? Maybe they all did? Being at the top of the class tells me nothing. What if only one tenth of 1% of all students go to single-sex schools - wouldn't there be a good chance that nobody at any given university did that? Kind of ruins the claim that Alice probably did, right?

There are a few ways to attack this argument, to analyze it, and to decide what is parallel to it. Some would even approach this one causally, saying that attending a single-sex school causes higher grades, and that the conclusion here is that the effect happened so the cause probably did, too. Ultimately, which approach you take is less important than finding the parallels in the correct answer. Is there an element of reversal? Is probability included in both the premise and the conclusion?

One thing I would caution you about, and that's the concept that you raised in your question about the sufficient condition occurring later than the necessary. It's important to note that conditional language does NOT include, or imply, and chronological relationship. A sufficient condition can occur before the necessary, or after the necessary, or at the same time as the necessary. The issue is not chronology (as it may be in a causal argument, where the cause MUST precede the effect), but merely conditionality.

For example, I can make a conditional claim that "if I eat spicy food tonight then I will have indigestion in the morning", but can also make a similar claim that "if I have indigestion in the morning then I must have had spicy food the night before." The chronology is not what matters, but rather the logical relationship between the sufficient condition (the "if" statement) and the necessary condition (the "then" statement). If the sufficient condition occurs, it proves that the necessary must also occur, but the necessary condition may also happen on its own, regardless of whether or not the sufficient occurs.

Keep working on that idea, and dig into some of our material on formal logic for a better understanding of how those work, too. Good luck!

[Johnclem]

Thank you so much ! Just one more thing !
So if this were to be a flaw question rather than a parallal .. Would the correct answer than hinge on inappropriate comparison rather than a mistaken negation since this is not an actual conditional reasoning ?


John

[Jonathan Evans]

John, good question. To extrapolate upon Adam's excellent explanation, in a "flaw" question-type situation, I would start abstractly with the two most obvious flaws present here.

First, the comparison flaw involving the remainder of the student body at the university might lead one to prephrase:

"Mistaken comparison about one student's experience when the experiences of other classmates are unknown."

Second, the causal flaw might lead to the prephrase:

"Mistakenly assumes one explanation for current performance when other causes also plausible."

The occurrence of one flaw does not preclude the possibility of other flaws. As Adam brought up, one may attack the flawed causal reasoning present in this argument. For this argument, in a hypothetical flaw question situation, I find this causal avenue the most propitious but not necessarily the exclusive manner to approach it. I instruct students to zero-in on causal reasoning wherever it occurs in Logical Reasoning since a plethora of assumptions and problems are implicit therein.

[Toby]

Hello!

I mistook the reasoning in this stimulus to be conditional instead of causal reasoning. I saw the "when" in the first sentence and then diagrammed this sentence conditionally. On a similar note, I thought that the reasoning in all of the answer choices was conditional because they all begin with "when." I would really appreciate some tips on differentiating causal from conditional reasoning in questions where conditional indicator words appear. Thanks for help!

Toby

[Jon Denning]

Hi Toby - thanks for the message.

I actually agree with you here. To me the hallmark of causality is something actively making a result or outcome occur. I don't see that in this question.

Instead, I see what I'd call light conditional reasoning, where it's not as hardline absolute as you typically encounter ("if...then" style with no qualifying language) due to the presence of the word "tend," but there's still a definitive relationship in place where one term reliably tells you something about the other. And that's more than close enough!

So what I'm going to do here is amend the original explanation up top to correct references to causality to ones about conditionality, and that should do the trick! The upside to that is, aside from calling conditional reasoning causal, the explanation above still works nicely: the diagrams are all accurate, the reversal seen in the stimulus and correct answer are properly noted, and the wrong answers are outlined correctly in terms of how they fail to parallel the original. So at least there's that

Sorry for the confusion and good catch on your end! Changes coming shortly.

[Toby]

Thanks for the clarification, Jon!

[EL16]

Hi,

I see the discussion above, suggesting that this is actually conditional reasoning and not causal reasoning. Just to confirm, would this be considered a mistaken reversal?

I had diagrammed it in the following way:
Premise: Girls educated in single-sex school do better academically
Conclusion: Alice does better academically Alice educated in a single-sex school

And then for answer B I diagrammed it as:
Premise: Babies taught to swim more ear infections
Conclusion: Janice has more ear infections Janice taught to swim as a baby

Is this correct, and is the flaw here mistaken reversal?

Thanks!
Elana

[Jon Denning]

Elana - that's exactly right! This is a Mistaken Reversal error, both in the stimulus and in the correct answer.

Nicely done!