Logical Reasoning: Statistics

After combing through numerous tests looking for ways to improve my logical reasoning score, I isolated a concept throughout the preptests that I was having trouble with. I will not really be discussing any particular question type, more just the concept behind statistics, and the way the LSAT uses it. I'm going to break it down into two types of statistics: formal statistics and informal statistics. Formal statistics will deal with percentages, numbers within totals, and totals. I will also discuss average under formal statistics. Informal statistics are questions that involve polls, studies, surveys, and stuff like that.

FORMAL STATISTICS:
The test writers love confusing students using percentages and totals because they can be confusing concepts for people like me, who was never very good at math. "Formal statistics" questions have three elements to keep in mind when reading: overall total, numbers within the total, and percentage. You cannot make inferences without at least two elements.

Words indicating %: percent, proportion, fraction, likelihood, probability (note that the last two are speaking in "terms of probability" meaning the chance that an event will occur. "More likely" and "Less likely" are telling you that the chances are greater than 50% or less than 50% respectively.)

Words indicating #: amount, quantity, sum, total.

Note: there are other indicator words, but these are the ones most commonly used.

Here are some common tricks test writers use on students:
1) Increasing percentages leads to increasing numbers (this is not necessarily true because the overall size of the group under discussion could be smaller)
2)Decreasing percentages lead to decreasing numbers (this is not necessarily true because the size of the group under discussion could be larger)
3) Increasing numbers within (not total) leads to increasing percentages (again, the TOTAL could be larger)
4) Decreasing numbers (not total) leads to decreasing percentage. (this does not have to be true because the total number could be smaller.)

Here are some inferences you can make:
1) If the percentage decreases but the number within increases, then the overall must have increased

% decrease + # increase -> overall increased

Example: if I drink 30% less coke (in my overall diet of drinks) than I did three years ago, but now i'm drinking 20 more cokes a day than I was three years ago, then it just has to be true that I am drinking a lot more over all than I used to be.

2) If the percentage increases, but the number within decreases, then it must be true that the over all total has decreased

% increase + # decrease -> overall decreased

Example: lets look back at the coke example. If three years ago, I drank 2 cokes and 8 glasses of water. That is only 20 percent. Now I only drink one coke, but it makes up 30 percent of my liquid diet. Then it must be true that I am drinking less than I used to.

Most of the time LSAT uses formal statistics like this, they talk about it in terms of change I.E. percentage and number differences between two periods of time. Example: between 2000 and 2006 there was a 30% increase in violent crime or In 1990 the number of crashes was less than it was in 2000. Etc...

It is important to remember that despite the changes within the total, there are only three logical options for what change the total could take: it gets smaller, it stays the same size, or it becomes larger.

Tips and tricks:
1) To weaken or strengthen an argument using numbers and percentages, look carefully for information about the total amount.
2) for MBT: if the stimulus only talks %, avoid answer choices about #. If the stimulus only talks #s, avoid answer choices that talk %s.

AVERAGE:
When you get a change in average, whether it be higher or lower, it gives rise to a few possibilities.
When you have a rise in the average, the possibilities are:
1) there are more higher numbers than there used to be
2) there are fewer lower numbers than there used to be
3) both
When you have a dip in average, some possibilities are:
1) there are more lower numbers than there used to be
2) there are fewer higher numbers than there used to be
3) both

Example: PT 46 Q 22
"Over the last 10 years, ... Admin note: please review the Forum rules "Do not post LSAT questions"
https://7sage.com/lsat_explanations/lsat-46-section-3-question-22/

Our possibilities are: more older people, fewer younger people, or both. Our conclusion is that there are more older people, so to strengthen it we have to rule out the possibility that the average change was not because there were fewer younger people. To weaken it you could say that there are fewer younger people.

Inversely, it works the same. If I tell you that the average LSAT score has changed from 157 to 150 over a period of 10 years, that could be because there are more people scoring in the 120s or that there are less people scoring in the 170s, or both. Tailor your answer choice to the conclusion. Don't get caught in whether the total number of people increases or decreases unless they tell you they are members of the group that will affect the average (120s group). These are sometimes disguised causation problems, if the conclusion says that the change of average happened for a certain reason (more older people), the answer choice could strengthen that by blocking out the other alternative.

INFORMAL STATISTICS
Informal statistics are things like polls, surveys, or experiments, or studies. You can recognize these questions when the stimulus says something like:
"In a recent study"
"50% received vaccine X and 50% received a placebo" (Really anytime they talk about experimental and control groups)
"Randomly selected"
"A nationwide poll"
"Consulted"
" _____ were surveyed"
Etc. The LSAT will almost always (maybe always I haven't taken every test) indicate when you are in informal statistics territory. While many questions that fall under the category of informal statistics have answer choices that refer to the causation mechanism in the stimulus, there are a lot of questions that revolve around your understanding of how an experiment should be tested. Here are some questions you should ask yourself.

what am I studying?
comes from the context + premise
PT 51
"Seventy-five percent of dermatologist surveyed Admin note: please review the Forum rules "Do not post LSAT questions"
https://7sage.com/lsat_explanations/lsat-51-section-1-question-04/
So here we are studying dermatologist's preference of skin cream using Dermactin, and they are conducting a survey to figure out the results
PT 30
"In a recent study, a group of subjects had Admin note: please review the Forum rules "Do not post LSAT questions"
https://7sage.com/lsat_explanations/lsat-30-section-4-question-22/
PT 34
"A group of 1,000 students was randomly selected Admin note: please review the Forum rules "Do not post LSAT questions"
https://7sage.com/lsat_explanations/lsat-34-section-3-question-04/

It does not have to be a detailed summary of the experiment, but you should know a brief summary of what they are testing because it is helpful in answering the other questions.

Is the premise representative of the conclusion?
Representativeness is a concept the LSAT repeats frequently. What does it mean for the premise to be representative of the conclusion? Well it means the conclusion should not be too broad compared to the evidence presented. If your conclusion is that most Americans love McDonalds then the answer come from a survey, poll, or study, that is diverse, large and unbiased enough to represent the general sentiment of most Americans. For a long time whenever I thought of representativeness in studies and polls, I usually only thought about if the sample size was large enough. While this may be important, it is only part of what you should be focused on when you are reading a stimulus for representation.

Here are some other flaws you should look for:
1) Under coverage: when some members of a population are inadequately represented in a survey/study/experiment.
2) Non-response: individuals are unwilling or unable to participate in survey/study/experiment. Bias that results when respondents differ in meaningful ways from non-respondents.
3) Voluntary response: sample members are self selected (Example: call in radio show)
4) Leading questions: questions encourages a particular answer.
5) Social desirability: most people like to present themselves in a positive light

Lets look at some examples of representation in logical reasoning problems

PT 36 #24: Flaw
"George Orwell's book 1984 has exercised much influence Admin note: please review the Forum rules "Do not post LSAT questions"
https://7sage.com/lsat_explanations/lsat-36-section-1-question-24/

The correct answer picked up on the fact that we don't know the specific numbers of who picked what. Does 1984 influence a great number of readers? Not if 999 people picked the bible and only 1 person picked 1984.

PT 31 #3: Flaw
"Announcement for a television program: Are female physicians Admin note: please review the Forum rules "Do not post LSAT questions"
https://7sage.com/lsat_explanations/lsat-31-section-2-question-03/

PT 34 #13: Necessary assumption
"Essayist: one of the claims of laisses-faire economics...
Admin note: please review the Forum rules "Do not post LSAT questions"
https://7sage.com/lsat_explanations/lsat-34-section-2-question-13/

For the conclusion to hold, the fast-food restaurants must be representative of the industries in general.

Note: although representation is a big thing that test makers will test you on, there are a lot of wrong answer choices that try to trick you into thinking the flaw or assumption is about. Don't bother too much with it unless there is a glaring representation issue. Example: 40 fourth graders took lessons in reading, and all of them improved their reading skills. Thus, lessons in reading can help fourth graders improve their reading skills. The conclusion is weak enough for the 40 fourth graders to be sufficient evidence. Would more students help? yeah probably. But as it stands "it shows reading classes can help students on their reading skills." Here is 40 students where it did.

Is there a control aspect to the experiment?
Control parts of the study are crucial aspects of conducting experiments because they allow you to eliminate and isolate variables.
PT 31 #9: Strengthen
"During the three months before and three months after Admin note: please review the Forum rules "Do not post LSAT questions"
https://7sage.com/lsat_explanations/lsat-31-section-3-question-09/

What are we missing? To find out whether or not earthquakes had an effect on California student's dreams, we would need to control for what they dreamed of before the earthquake, and monitor the change.

Was there a difference in the results of a laboratory experiment vs the same experiment tested out in the real world?
One way a study/experiment can be flawed is if they only study it under laboratory conditions. Imagine you plant seeds in a testing center, and they grow amazing. Out in the world the seeds grow like shit. Well there are a lot of reasons why the seed did not grow as well in the real world. It could be because in the lab they got more water, or they weren't vulnerable to insects, etc...

How long was the study? Did it need to be longer?
There was a really tough parallel flaw question that hinged on you understanding of the timing concept in the study. It was something like they asked a bunch of young kids if viewing a cigarette pack made them want to smoke, and concluded that because the kids didn't want to smoke it at the age of 9, it had no impact on the desire to smoke. The obvious flaw is why are you asking kids this? They are not representative. But the more subtle flaw is that the experiment should have taken longer, maybe come back to them when they are a few years older and can buy cigs and ask them again.

Your job is to strengthen, weaken, point out flaws, or explain experiments. Remember to ask yourself these questions when you see informal statistics, it will allow you to be able to better pre-phrase the correct answer choice.

I hope this lesson has been helpful for anyone who took the time to read it. Statistics is such a big concept that i'm sure that there is stuff I missed out on. Please let me know if there is anything I should add on, or change, to make this better!