A primer on Variance Analysis

Question

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Variance analysis is a sure shot test to verify that you have chosen the correct answer for “Evaluate the argument” question types. In this article, we will discuss the theory of Variance analysis, talk about how to apply the test through various examples, and solve multiple exercise questions.

What is Variance Analysis?  
By definition, the correct answer choice to evaluate an argument will either increase or decrease the validity of the argument. By performing the variance analysis, we can see whether an answer choice does that. In other words, test exploits the duality or the dual behavior of the correct answer choice.

Those of you who read my earlier article on the  negation test  (or are in general aware of the same) will see some parallels with the negation test. However, there is a stark difference between the two.

The negation test, when applied on the correct answer choices (or the assumption) breaks the argument down, whereas the variance analysis when performed on the correct answer choice goes both ways – validates the argument (makes the argument much more believable) and invalidates the same (i.e. makes the argument less believable).

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How to apply this test?

To apply this test to a particular answer choice, take that answer choice to one extreme. Let’s call this extreme 1. Notice the impact on the conclusion of the argument. Then take the answer choice to the other extreme, extreme 2, and notice the impact on the conclusion again. If extreme 1 validates the argument and extreme 2 invalidates the argument or vice versa, then this is the correct answer choice. If the argument is only validated or invalidated at one of the extremes and nothing happens to it at the other extreme then this is not the correct choice.

https://e-gmat.com/blogs/wp-content/uploads/2013/02/Variance-test.png

Note that extremes usually fall in two categories;
1. High/low
2. Yes/No
The examples and exercise questions below will help you practice both the extremes.

Let’s take an example:  
 
Joshua is one of the most thanked members on GMATClub. Hence, Joshua will most likely score above 700 on his GMAT.

Which of the following below would help you evaluate the argument above?
A. Whether all GMATClub members who score above 700 receive at least one thanks.
B. Whether, Rosy, another member who was one of the most thanked members on GMATClub, scored above 700.
C. Whether Joshua scored more than 700 in his most recent mock test?
D. Whether most GMATClub’s most thanked members score above 700.
E. Whether Joshua received the “most thanked” status by being active on just the quant forum or both quant and verbal forum.
F. Whether GMATClub members who are not rated “most thanked” are as likely to score above 700 as those who are?

Now let’s take each answer choice and evaluate it. But before we do that lets understand what the argument is saying. The argument states that Joshua has a greater than 50% (note: most likely = greater than 50%) chance of scoring above 700 because he is one of the “most thanked” members on GMATClub.

Choice A  : Whether all GMATClub members who score above 700 receive at least one thanks?
 Extreme 1 :  Yes, All GMATClub members who score above 700 receive at least one thanks

Does this validate the argument? No it does not. What extreme1 says is that if you are a GMATClub member who had scored above 700, then you must have received one thanks. This has no bearing on the conclusion which says that if you are the most thanked member, you have greater than 50% chance to score 700. Hence this extreme neither validates nor invalidates the argument. At this point, you may leave this choice and go to choice 2. However we will analyze extreme 2 for academic fun.

Extreme 2 :  No, All GMATClub members who score above 700 do not receive at least one thanks 
Using the same logic as above, it can be said that this extreme has no bearing on the conclusion. Hence let’s move on to choice B.

Choice B  : Whether, Rosy, another member who was one of the most thanked members on GMATClub, scored above 700.

Extreme 1 : Y es, Rosy, another member who was one of the most thanked members on GMATClub, scored above 700. 
Does that strengthen the conclusion – yes, because we have one more instance in which the conclusion is true. However, does this validate the conclusion – No. Therefore, this  choice is not the correct choice.

Choice C ]: Whether Joshua scored more than 700 in his most recent mock test?

Extreme 1 :  Yes, Joshua scored more than 700 in his most recent mock test.

This is another choice that strengthens the argument but does not either validate or invalidate the argument. Note, that this extreme would increase our belief in the conclusion that Joshua is likely to score above 700 in the real test but not because of the reasons stated in the argument, which is what we are evaluating right now. Hence, it does not validate the author’s argument.

Extreme 2 :  No, Joshua did not score more than 700 in his most recent mock test.

Similarly, the fact that Joshua did not perform as well on the mock does not invalidate the argument that Joshua has greater than 50% chance of scoring above 700.

Choice D  : Whether most GMATClub’s most thanked members score above 700?

Extreme 1 :  Yes, most GMATClub’s most thanked members score above 700?

This validates the argument. Notice, that the while claiming that Joshua is most likely to score above 700 because he is one of the most thanked members, the author assumes that most of the “most thanked” members score above 700. Extreme 1, validates that assumption thereby validating the argument.

Extreme 2 :  No, most GMATClub’s “most thanked” members do not score above 700? 
This invalidates the argument. Note how “Extreme 2” breaks the argument. If most “most thanked” members do not score above 700 then there is no reason to believe that Joshua will score above 700.

Due to this bipolar nature exhibited by this answer choice, we can easily say that  this is the correct answer choice. 
 
 Choice E  : Whether Joshua received the “most thanked” status by being active on just the quant forum or both quant and verbal forum?

Extreme 1 :  Yes, Joshua received the “most thanked” status by being active on just the quant forum?

Does this validate or invalidate the argument. It does neither. Note that the author does not state whether those “most thanked” members who score above 700 are active just on quant or verbal or on both forums. Since the author does not make any such claim, the answer to choice E does not validate or invalidate the argument.
 
 Choice F  : Whether GMATClub members who are not rated “most thanked” are as likely to score above 700 as those who are?

E-GMAT customers would instantly reject this answer choice because this talks about a segment of population that is not the focus of the argument. This answer choice talks about those members who are not rated as “most thanked”, something that has little bearing on the point that the argument is trying to make. Therefore, this choice is not correct.

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TAKEAWAYS FROM THE EXAMPLE ABOVE 
1.  A choice that just strengthens need not be the correct choice : A number of people have this notion that validation is the same as strengthening. As we saw with choice B such is not the case. While a choice that validates the argument will strengthen it, the converse need not be true. 
2.  The correct choice is built around the Assumption : This must now be intuitive. An argument is validated only if one or more of the assumptions that the author makes are validated in some form. E-GMAT customers would recall the Joshua example, from Evaluate Concept in e-GMAT CR Course, in which we derive 3 possible evaluate answer choices from a single assumption. This means that the Prethinking process for assumptions that we learned in the Prethinking Session is highly useful in helping you solve evaluate questions as well.
3.  The variance analysis is a close cousin of Negation test : The negation test when applied on the correct answer choice breaks the argument (invalidates the argument), while the correct answer choice either validates or invalidates. The fundamental principle governing both these tests is the same – an argument has assumptions, which when negated can invalidate the argument.

AbhiJ · Answer

Not sure about F. If not thanked members are as likely as thanked members then this proves that thanks has no significance in GMAT score. Vice versa proves that thanks has significance in GMAT score.

egmat · Answer

Let’s understand the argument to address your doubt.

Joshua is one of the most thanked members on GMAT Club. Hence, Joshua will most likely score above 700 on his GMAT.

Let’s understand the conclusion. The conclusion states that Joshua has greater than 50% (note: most likely =  greater than 50% ) chance of scoring above 700. For the sake of this discussion, to make things simple, let’s fix the conclusion at 60%. So our modified argument will be:

Joshua is one of the most thanked members on GMAT Club. Hence, there is 60% probability that Joshua will score about 700.

Note: The conclusion is about a  specific  likelihood.

Now let’s take choice F
• Whether GMAT Club members who are not rated “most thanked” are as likely to score above 700 as those who are?

Extreme 1 : Yes, GMAT Club members who are not rated “most thanked” are as likely to score above 700 as those who are? 
Does Extreme 1 validate/invalidate the hypothesis that there is a 60% probability that Joshua will score above 700? 
Not at all, since  we are not discussing any probability number  here. Furthermore, as stated earlier, the argument is about achieving a specific outcome. The  performance of a complimentary segment does not have a bearing on the conclusion .
Carefully note that the argument does not say and neither should you assume that being the “most thanked” member is the only way to get a score of 700.

Extreme 2 : No, GMAT Club members who are not rated “most thanked” are as likely to score above 700 as those who are? 
Does Extreme 2 validate/invalidate the hypotheses that there is a 60% probability that Joshua will score above 700? 
The discussion of Extreme 1 applies here as well. This extreme does not validate or invalidate the conclusion since we are not talking about any probability number here.

Hope this helps clarify your doubt.

-Rajat

egmat · Answer

Here is an exercise question to apply the variance analysis to:

The Nile Delta of Egypt was invaded and ruled from 1650 BC to 1550 BC by a people called Hyksos. Their origin in uncertain but archaeologists hypothesize that they were Canaanites. In support of this hypothesis, the archaeologists point out that excavations of Avaris, the Hyksos capital in Egypt, have uncovered large number of artifacts virtually identical to artifacts produced in Ashkelon, a major city of Canaan at the time of the Hyksos invasion.

In order to evaluate the force of the archaeologists evidence, it would be most useful to determine which of the following?

A. Whether there were some artifacts found at Avaris that were unlike those produced in Ashkelon but that date to before 1700 BC.
B. Whether the Hyksos ruled any other part of Egypt besides the Nile Delta in the period from 1650 B.C. to 1550 B.C.
C. Whether Avaris was the nearest Hyksos city in Egypt to Canaan.
D. Whether Ashkelon after 1550 B.C. continued to produce artifacts similar to those found at Avaris.
E. Whether many of the artifacts found at Avaris that are similar to the artifacts produced in Ashkelon date to well before the Hyksos invasion

skamal7 · Answer

E-Gmat,

Is E the answer to the last question mentioned in the post?

egmat · Answer

Hi, Yes. The answer is E.

Thanks, Chiranjeev

bluemaverick · Answer

Hi Chiranjeev,

Could you please explain why ans 'E' is correct and others are not?

Thanks for posting the article. This is my 1st attempt at answering such questions, so feel free to point out mistakes in my logic & reasoning.

The argument states that Nile Delta was invaded/ruled 1650-1550 by Hyskos and that these people maybe Canaanites. Reason – excavations at Avaris (which was Hyksos city) showed artifacts similar to those produced in Ashkelon (which was Cannan city)

A.  Whether there were some artifacts found at Avaris that were unlike those produced in Ashkelon but that date to before 1700 BC. 
 Ext 1 – Yes , there were some artifacts found at Avaris that were unlike those produced in Ashkelon but that date to before 1700 BC. This weakens the argument, and it talks about period before 1700BC. The argument is for 1650-1550
 Ext-2 – No,  there were no artifacts found at Avaris that were unlike those produced in Ashkelon but that date to before 1700 BC. This again talks about time period outside the one discussed in the argument

B. Whether the Hyksos ruled any other part of Egypt besides the Nile Delta in the period from 1650 B.C. to 1550 B.C. 
 Ext 1 – Yes,  Hyksos ruled other part of Egypt besides the Nile Delta in the period from 1650 B.C. to 1550 B.C. This does not validates the argument, perhaps a strengthener, if at all
 Ext-2 – No , Hyksos did not rule other part of Egypt besides the Nile Delta in the period from 1650 B.C. to 1550 B.C. This could be a strengthener but does not validate or invalidates if they were Canaanites

C. Whether Avaris was the nearest Hyksos city in Egypt to Canaan. 
 Ext 1 – Yes , Avaris was the nearest Hyksos city in Egypt to Canaan. Just for the fact that it was the nearest city does not validate or invalidates that Hyksos were Canaanites
 Ext-2 – No , Avaris was the nearest Hyksos city in Egypt to Canaan. Same reasoning as above

D. Whether Ashkelon after 1550 B.C. continued to produce artifacts similar to those found at Avaris. 
 Ext 1 – Yes,  Ashkelon continued to produce….Not the correct choice as the argument is not concerned with Ashkelon producing artifacts after 1550
 Ext 2 - No , Ashkelon did not continue to produce….same reasoning, not concerned with whether Ashkelon produced after 1550 or not

E. Whether many of the artifacts found at Avaris that are similar to the artifacts produced in Ashkelon date to well before the Hyksos invasion 
 Ext 1 – Yes,  many of the artifacts found at Avaris that are similar to the artifacts produced in Ashkelon date to well before the Hyksos invasion. This validates that Hyksos were producing artifacts similar to those found in Ashkleon way before the invasion and carried through during the invasion as well. 
 Ext 2 - No,  not many of the artifacts found at Avaris that are similar to the artifacts produced in Ashkelon date to well before the Hyksos invasion.  Not sure how this invalidates the argument  – my guess – the Hyksos produced artifacts perhaps during or after the invasion? Thus not presenting any relation to them being Canaanites?

MBAjunkie16 · Answer

Hi Chiranjeev,

Based on this article and the course, I tried applying the variance analysis on this GMATPrep question below and am stumped. Can you help?

Last August the XT chain of gasoline stations had a temporary sales promotion in effect. In the promotion, any customer who made a purchase of ten or more gallons of gasoline was entitled to a free car wash. For the month of August, XT experienced a ten percent increase in gasoline sales as compared to sales in August the previous year, so evidently the promotion was successful as a means of boosting sales.
In evaluating the argument, it would be most helpful to answer which of the following?
A. In the areas in which XT’s gasoline stations operate, how did total combined gasoline sales for all gasoline stations last August compare with sales for the previous August?
B. Was the money that XT earned from the increase in gasoline sales enough to offset the cost of providing free car washes during the promotion?
C. Were there any customers who bought ten or more gallons at an XT gasoline station during the promotion who would have or more gallons at an XT gasoline in lower quantities, but more frequently, if the promotion had not been in effect?
D. Did XT or any of its gasoline stations have to pay other businesses to provide the car washes that customers were offered in the promotion?
E. Are XT’s gasoline sales in August usually significantly higher than one twelfth of XT’s annual gasoline sales?

My selected answer was C because if more number of people who would normally purchase gasoline in amounts <10 Gal were now purchasing >10 Gal due to the promotion, then that could result in the promotion being successful. If I apply the variance test as follows
More people chose to purchase gasoline >10 Gal because of promotion who would otherwise have not - Validates conclusion -> promotion was successful.
People who purchased > 10 Gal gasoline did not intend to purchase gasoline in smaller amounts than 10 Gal than before ==> these are not new,converted customers due to the promotion - Invalidates conclusion ==> promotion not successful in bringing new customer who contributed to the increased sales.

Now, per the variance test this option holds true. But the OA is A.

Can you help me think about how to solve this question and help outline an approach? Thanks!

egmat · Answer

Hi, First of all, option C is grammatically incorrect. As is, the option statement does not make any sense to me. I even asked my colleagues to help me out and they were also clueless :!:

Now, even if I don't understand option C completely, I can still see that it is incorrect. When you analyse this option statement, you have ignored "were there any" part in the option. So, if you look at it: the option C wants to find out if there is at least one customer who would have something something. Now, does that provide any relevant information? The answer is a BIG NO. What do we gain by knowing that there is at least one sweet guy out there who would have done something. In a population, you will have find some people doing one thing or the other. It does not really impact the conclusion about the success of the program as a whole. You can appreciate that a single person cannot really affect the success of a program. Right? Now, just to tell you - this is a common trick used by GMAT in not only evaluate but also strengthen and weaken questions, where they will talk about a general trend in the argument and one of the option statement will says that "some" people did not follow the trend. This does not mean that general trend does not hold because "some" persons don't follow it. There are always going to be exceptions. For example: Consider this official question and let me know the correct answer: Businesses are suffering because of a lack of money available for development loans. To help businesses, the government plans to modify the income-tax structure in order to induce individual taxpayers to put a larger portion of their incomes into retirement savings accounts, because as more money is deposited in such accounts, more money becomes available to borrowers. Which of the following, if true, raises the most serious doubt regarding the effectiveness of the government’s plan to increase the amount of money available for development loans for businesses? (A) When levels of personal retirement savings increase, consumer borrowing always increases correspondingly. (B) The increased tax revenue the government would receive as a result of business expansion would not offset the loss in revenue from personal income taxes during the first year of the plan. (C) Even with tax incentives, some people will choose not to increase their levels of retirement savings. (D) Bankers generally will not continue to lend money to businesses whose prospective earnings are insufficient to meet their loan repayment schedules. (E) The modified tax structure would give all taxpayers, regardless of their incomes, the same tax savings for a given increase in their retirement savings. Thanks, Chiranjeev

egmat · Answer

Hi Bluemaverick, Thank you for your query. Here’s the original argument: The Nile Delta of Egypt was invaded and ruled from 1650 BC to 1550 BC by a people called Hyksos. Their origin in uncertain but archaeologists hypothesize that they were Canaanites. In support of this hypothesis, the archaeologists point out that excavations of Avaris, the Hyksos capital in Egypt, have uncovered large number of artifacts virtually identical to artifacts produced in Ashkelon, a major city of Canaan at the time of the Hyksos invasion. Let’s break down the information given in the passage: (1) Hyksos invaded and ruled the Nile Delta of Egypt from 1650 BC to 1550 BC (2) Avaris = Hyksos capital in Egypt Ashkelon= major city of Canaan (3) Excavations of Avaris have uncovered large number of artifacts that are almost identical to the artifacts produced in Ashkelon at the time of the Hyksos invasion (1650 BC-1550 BC) (4) Conclusion (Hypothesis by archaeologists regarding origin of Hyksos) ----Hyksos were probably Canaanites The assumption made by the archaeologists: Hyksos brought these artifacts to Avaris from Ashkelon when they invaded the Nile Delta of Egypt. Unless the above assumption is true, the archaeologists’ conclusion will not hold. Keeping this in mind, let’s analyse the answer choices. A. Whether there were some artifacts found at Avaris that were unlike those produced in Ashkelon but that date to before 1700 BC. This choice is out of scope on two accounts: a) It talks about some other artifacts and not the one with which the author is concerned b) The time period referred to is not the same as what the author is concerned with Since the answer choice is out of scope, the Variance Analysis will not yield any statement that will impact the conclusion of the argument. Ideally, the Variance Analysis should be done to only the contender answer choices. The logic behind this is very simple. In the exam, you will not have the time to test each answer choice on the Variance analysis. However, since you are in the initial stage of applying the Variance Analysis, one can appreciate your effort of testing each answer choice on this parameter. Ext 1 ( your analysis) – Yes, there were some artifacts found at Avaris that were unlike those produced in Ashkelon but that date to before 1700 BC. ---Agree This weakens the argument, and it talks about period before 1700BC. The argument is for 1650-1550. ----Disagree Our take on your analysis: The above statement is out of scope, as it doesn’t talk about the artifacts referred to by the archaeologists . Therefore, it will not have any impact on the conclusion. Hence, it does not weaken the conclusion. Ext-2 ( your analysis) – No, there were no artifacts found at Avaris that were unlike those produced in Ashkelon but that date to before 1700 BC. ----Agree This again talks about time period outside the one discussed in the argument --- Agree B. Whether the Hyksos ruled any other part of Egypt besides the Nile Delta in the period from 1650 B.C. to 1550 B.C. Ext 1 ( your analysis) – Yes, Hyksos ruled other part of Egypt besides the Nile Delta in the period from 1650 B.C. to 1550 B.C. ---Agree This does not validates the argument, ------ Agree perhaps a strengthener, if at all---- ---- Disagree Our take: This choice again talks about an area with which the author is not concerned. You are right, that an answer to this question does not validate the argument. Also, since the archaeologists mentioned in the argument are only concerned with The Nile Delta of Egypt, any information that deals with other parts of Egypt can neither strengthen nor weaken the argument. So it is NOT a strengthening statement. Ext-2 – ( your analysis) No, Hyksos did not rule other part of Egypt besides the Nile Delta in the period from 1650 B.C. to 1550 B.C. ---- Agree This could be a strengthener ---- Disagree …but does not validate or invalidates if they were Canaanites. ------ Agree Answer Choice B is out of scope since the region referred to is NOT the Nile Delta and, hence, the answer to this question will not impact the author's conclusion, which deals only with the Hyksos in the Nile Delta around 1650 BC- 1550 BC. C. Whether Avaris was the nearest Hyksos city in Egypt to Canaan. Ext 1 ( your analysis) – Yes, Avaris was the nearest Hyksos city in Egypt to Canaan. ------ Agree Just for the fact that it was the nearest city does not validate or invalidates that Hyksos were Canaanites. ------ Agree Ext-2 ( your analysis) – No, Avaris was the nearest Hyksos city in Egypt to Canaan. Same reasoning as above. ------ Agree D. Whether Ashkelon after 1550 B.C. continued to produce artifacts similar to those found at Avaris. Ext 1 ( your analysis) – Yes, Ashkelon continued to produce….Not the correct choice as the argument is not concerned with Ashkelon producing artifacts after 1550. --- Agree Ext 2 ( your analysis) - No, Ashkelon did not continue to produce….same reasoning, not concerned with whether Ashkelon produced after 1550 or not. ------ Agree E. Whether many of the artifacts found at Avaris that are similar to the artifacts produced in Ashkelon date to well before the Hyksos invasion Ext 1 (your analysis) – Yes, many of the artifacts found at Avaris that are similar to the artifacts produced in Ashkelon date to well before the Hyksos invasion.--- Agree This validates that Hyksos were producing artifacts similar to those found in Ashkleon way before the invasion and carried through during the invasion as well. ---- Disagree Our analysis: You have misinterpreted the implication of the above statement. The above statement casts a doubt on the fact that the Hyskos people were probably Canaanites. This is because if these artifacts date to well before the Hyskos invasion, then it means that probably the artifacts existed in The Nile Delta before it was invaded by the Hyskos and that the Hyskos did not bring these artifacts from Ashkelon. The job of the correct answer choice, when subjected to Variance analysis, is that one end of the answer will weaken the conclusion drawn and the other end will support the conclusion. In this case, a positive answer to the question posed in answer choice E, weakens the conclusion. SO if a negative or a NO to question posed in answer choice E weakens the conclusion, then it is the correct choice. Ext 2 (your analysis) - No, not many of the artifacts found at Avaris that are similar to the artifacts produced in Ashkelon date to well before the Hyksos invasion. .--- Agree Not sure how this invalidates the argument – my guess – the Hyksos produced artifacts perhaps during or after the invasion? ---- Disagree Ext 2 Our take – You have misinterpreted the implication of the statement we arrive at, by replying NO to question posed in answer choice E supports the answer choice. It does not invalidate the argument; instead it increases our belief in the fact that the Hyskos people probably brought in the artifacts from Ashkelon to the Nile Delta when they invaded the place. If this indeed had been the case, then the Hyskos people could have been Canaanites. Hope this helps

---Neeti.

MBAjunkie16 · Answer

My bad - I copied it from an online location since GMATPrep software doesn't allow you to copy paste and didn't realize its missing a few key words. Were there any customers who bought ten or more gallons at an XT gasoline station during the promotion who would have purchased 10 or more gallons at an XT gasoline in lower quantities, but more frequently, if the promotion had not been in effect? This is brilliant and my biggest takeaway. Thanks for explaining it so clearly. :-D

In this case, my answer is A. And the thought process behind it as follows: Two weakeners for the argument can be potentially a) Money saved due to the changed tax structure and consequent savings does not go towards disbursing development loans b) Despite govt encouragement, people don't save more in retirement savings accounts Based on this both A and C were potential answers. When applying the variance analysis on C, and taking into consideration that it says "some people" we can eliminate it. Please let me know if this the right way. Thanks!

egmat · Answer

Yes. Absolutely correct.

-Chiranjeev

Bunuel · Answer

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