CONTENTS

1.0 Analysis Overview

2.0 Assignment Details

2.1 Improving the Options Assignment

2.2 Transition Paragraph

2.3 Measuring the Level of Each Criterion

2.4 Normalizing the Level of Each Criterion

2.5 Weighting the Level of Each Criterion

2.6 Drawing the Conclusion

2.7 Caveats and Limitations

1.0 ANALYSIS OVERVIEW

The Analysis assignment is the fifth assignment. Before you begin the Analysis assignment, you must have submitted and received instructor feedback on the previous Options assignment.

The goal of this assignment is to measure or estimate each criterion's level for each of your options and then, through a process of normalization and weighting, identify which option is optimal.

2.0 ASSIGNMENT DETAILS

This text describes in very prescribed ways how you must complete this assignment. After each prescribed item below, you will see in parentheses the typical number of paragraphs (P) needed (e.g., "1-2P" means "1 to 2 paragraphs are typically needed). The outline also indicates when a figure (F) or table (T) is typically needed. Details about how to create and format figures and tables is in the "Figures and Tables" section of the "Resources" chapter.

The Analysis assignment must include:

1. An updated and improved version of the Options assignment.

2. A transition paragraph that helps readers understand the next step of the analysis. (1P)

3. A comparison and discussion of how well the options score in terms of the first criterion, including a description of how you objectively measured or subjectively estimated the first criterion's level for each option. Discuss any measurement or estimation issues that arose and how you addressed those. Include a table (i.e., Table 3) that shows vertically the criteria and horizontally each criterion's weight, each criterion's worst and best possible values, and the unweighted measured level or estimated score for each option. This section will be relatively longer if you have more options versus criteria. (2-4P and 1T)

4. A comparison and discussion of how well the options score in terms of the second criterion, including a description of how you objectively measured or subjectively estimated the second criterion's level for each option. Discuss any measurement or estimation issues that arose and how you addressed those. This section will be relatively longer if you have more options versus criteria. (2-4P)

5. A comparison and discussion of how well the options score in terms of the third criterion, including a description of how you objectively measured or subjectively estimated the third criterion's level for each option. Discuss any measurement or estimation issues that arose and how you addressed those. This section will be relatively longer if you have more options versus criteria. (2-4P)

6. Optional. A comparison and discussion of how well the options score in terms of the fourth criterion, including a description of how you objectively measured or subjectively estimated the fourth criterion's level for each option. Discuss any measurement or estimation issues that arose and how you addressed those. This section will be relatively longer if you have more options versus criteria. (2-4P)

7. Optional. A comparison and discussion of how well the options score in terms of the fifth criterion, including a description of how you objectively measured or subjectively estimated the fifth criterion's level for each option. Discuss any measurement or estimation issues that arose and how you addressed those. This section will be relatively longer if you have more options versus criteria. (2-4P)

8. A description of how and why you need to normalize the values from the previous table (i.e., Table 3). Include a new table (i.e., Table 4) that shows those normalized values using a scale of zero (0) to ten (10) where a higher value are preferred. (1P and 1T)

9. A description of how and why you need to weight the normalized values from the previous table (i.e., Table 4). Include a new table (i.e., Table 5) that shows those weighted normalized values. (1P and 1T)

10. A description of the results from the previous table (i.e., Table 5) that explains that each weighted normalized value reflects the relative ranking of each option on a scale of zero (0) to ten (10) where a higher value indicates a better option. Conclude your analysis by explaining that the option with the highest value is the best option. (2P)

11. Identify and explain important caveats and limitations of the prescribed analysis. (1P)

To submit your assignment, follow the assignment submission instructors provided to you by your instructor in the course syllabus or on the course site of your institution's learning management system.

2.1 Improving the Options Assignment

An important part of this assignment is that you review the instructor feedback on and make improvements to your previous assignment. Keep in mind that, even if you received a favorable grade or positive instructor feedback, you should not interpret that to mean that your instructor believes you do not need to make any improvements. You do! Self-review and peer-review strategies are described in that section of the "Resources" chapter.

One of the most significant ways to improve your work is to add concrete details (e.g., in footnotes) that build your credibility as an analyst. Suggestions for doing this can be found in the "Credibility, Evidence, and Footnotes" section of the "Resources" chapter. That section describes how to incorporate concrete details and improve the layout and attractiveness of your figures, tables, and writing.

Again, keep in mind that your instructor may not make any specific recommendations for improvement, but that does not mean that your word choice and punctuation are perfect or that your argument, analysis, and evidence do not still need improvement. Similarly, do not assume that your instructor has identified everything in your submission that needs to be corrected. The comments, feedback, and grade that your instructor provides are merely representative of the kinds of improvements that you need to make.

I have one more point. Your instructor likely has only a certain amount of time to review your submission and give you feedback. It is almost always true, no matter how excellent your submission is, that your instructor can find meaningful ways to help you improve your work. That means that, each time you submit your work for feedback, it should be your best work so that your instructor can help you improve. If you turn in something that is less than your best, the feedback you get from your instructor will be wasted because it will only be suggestions that you could have identified if you had just taken more time.

2.2 Transition Paragraph

You will need to craft and add language that appropriately helps your readers follow your transition from the Options section to the Analysis section. One way to do this is to create section headings. If you have not already, go back to your Objective assignment and identify the start of your "Context" section and insert at the start (i.e., just after your methods paragraph) a section heading titled "Context". Section headings should be left-justified on the page and should be distinguished from the rest of the text (e.g., using extra spacing, using bold or underlined text, and/or making the font sizes larger). Similarly, create a section heading for this section (i.e., "Analysis") and for the previous sections (i.e., "Criteria" and "Options").

While a few thoughtfully chosen section headings can help readers better follow your analysis, I want you to provide a transition paragraph that adds even more clarity. Here is the basic text that I want you to use:

Having identified a set of criteria and a set of options, the final step in MCDA is to evaluate how well each option scores in terms of each of the criteria. The author examines each of the____________________ [insert the number of evaluation criteria you have in your analysis] criteria one by one, providing details about how each criterion was measured or estimated and comparing the ____________________ [insert the number of options you have in your analysis] options in terms of each criterion. The author then normalizes and weights all of the measured or estimated values using a scale of zero (0) to ten (10) where higher values are preferred. To identify which option is best, the author then sums the weighted normalized scores for each option. Finally, the author identifies and describes several important caveats and limitations of the analysis.

Keep in mind that the words in brackets (i.e., "[" and "]") are simply messages to you should not be copied and pasted into your work. Similarly, you will have to insert into the blank spaces (e.g., "__________") the details that are particular to your individual analysis.

2.3 Measuring the Level of Each Criterion

The first step in the Analysis section is, according to the transition paragraph above, to evaluate how well the options score in terms of each of the criteria and to provide details about how you measured each of the criteria for each of your options. Keep in mind that you will organize the Analysis section by the criteria. You will look at how each of your options measure up in terms of your first criteria and then you will move on to look at your next criterion.

Your criteria have a natural order. You should start the Analysis section with the criterion that is weighted the highest. Looking at that criterion, you want show how you measured that criterion's level for each of your options. Keep in mind that you already described in the Criteria section how you plan to measure the level of each of the criteria. So, the reader should already have a good idea how you will measure the level of your first and all of the other criteria. What you need to do in the Analysis section is show how--not tell (again) how--you measured the level of each of the criteria for each of your options. Again, do this starting with the criterion that is weighted the most.

You do not want to burden your main text with a lot of mathematical calculations. Instead, put the calculations in your footnotes along with an explanation. In your main text, you want to describe generally what you did to measure the level of the criterion for each option.

Direct Measure. If you measured a criterion directly, describe how you did that, keeping in mind that you have (or should have) already described your general plan for measuring each criterion in your Criteria section. In this section, you want to give the specific numbers or measures, explain any unexpected challenges you encountered, explain how you dealt with those unexpected challenges, and provide a rationale.

Proxy Measure. If you measured a criterion using a proxy, you will approach this in the same way as if you measured the criterion directly. Give the specific numbers for how you measured the level of the criterion for each of your options. If you encountered unexpected challenges, explain what they were, how you dealt with them, and why your response was reasonable and justified.

Composite Measure. As noted in the Criteria chapter, you may not be able to identify a single proxy measure for some criteria. Recall that a composite measure uses a formula to combine data from two or more proxy measures. If you elected to use a composite measure, you should have already explained the general process in your Criteria section.

Here, in the Analysis section, you want to show the details of those calculations. Composite measures often have detailed calculations. Typically you should not put detailed calculations in your main text. Instead, use the main text to describe the calculations generally using full sentences. Then, put the specific calculations in footnotes.

To measure the level of a composite criterion, you want to gather the needed data and then perform the calculations to normalize and weight (i.e., combine) the data. This is not as complicated as it might look. For example, suppose that you want to use "location" as a criterion to assess which job opportunity is best for a particular decision maker. The benefits of a particular job location obviously will depend on the subjective preferences of the decision maker. Suppose this decision maker tells you, "The best job location would be one that has low housing costs and lots of sunny weather." In this example, you have two factors that determine the measure of the criterion "location".

After defining the composite factors, you need to define a reasonable way to combine them into a single statistic or number. How might you do that? In this case, you might weight each factor equally (i.e., 50% and 50%):

• ( fifty percent x some measure of housing cost ) + ( fifty percent x some measure of sunny weather )

You have to be careful in how you select the measure of housing costs and sunny weather. For instance, housing costs can be measured in hundreds of thousands of dollars (e.g., $227,178) and sunny weather is usually measured in days per year of sunshine (e.g., 89 days).

• ( 0.50 x 227,178 ) + ( 0.50 x 89 ) = 113,633

• $113,589 + 45 = 113,633

However, this approach has a problem. If you just multiple 50% times the housing cost (0.50 x $227,178) and add that to 50% times the number of days per year the city has sunshine (0.50 x 89), then you get a statistic that mostly just reflects the housing price (i.e., 113,589 + 45 = 113,633). The effect of the sunshine (45) is swamped by the effect of home price (113,589) simply because they use different scales (i.e., days versus dollars).

To fix this problem, you need some way to make it so that both measures (i.e., of home values and days of sunshine) have the same scale. You need to make it so that the minimum and maximum possible values (i.e., range) for measuring housing costs are the minimum and maximum values for measuring the number of sunny days. This is called normalization. You need to normalize the measures. That means that you make the measures have the same minimum and maximum values (i.e., the same range).

To normalize a value, you need to force all the potential values into a specific range (e.g., from zero to positive ten). For example, to normalize the median housing costs for any particular city on a scale of zero to ten, you need to identify the best possible and worst possible (but still reasonable) median prices (i.e., the lower and upper bounds of median home prices across cities, respectively). Next, you need to subtract the worst possible value from the value the specific city that you want to normalize and then divide all of that by the best possible value minus the worst possible value. That should yield a value between zero and one (1), so you then need to multiply all of the that by the difference between the highest value on your chosen scale (e.g., 10) and the lowest value on your scale (e.g., zero).

Here is the calculation to normalize a value with a range of zero (0) to ten (10):

• [ ( SPECIFIC - WORST ) / ( BEST - WORST ) ] x ( HIGH - LOW )

Where:

SPECIFIC = the value to normalize

WORST = the worst possible value

BEST = the best possible value

HIGH = the highest value on the scale (e.g., 10)

LOW = the lowest value on the scale (e.g., 0)

To get my composite value for a particular city location, you need to normalize two values, one for the city's median home price and another value for the city's number of sunny days. To do this, you need information about median home values across a bunch of U.S. cities so you can identify a reasonable upper and lower bound for that parameter. Similarly, you need information about the number of sunshiny days in a bunch of U.S. cities as well.

At the Zillow website, you can see there is monthly time series data (1996 to 2021) for their estimated value for single family homes (35th to 65th percentile) in more than 25,000 U.S. cities. With so many cities, you may decide that it is reasonable to exclude the most expensive 250 cities and the least expensive 250 cities as likely outliers. Of the remaining cities, you will find that in January 2021 Pinecrest, Florida has the highest valued homes at $1,214,996 (i.e., worst possible value) and Lansford, Pennsylvania has the lowest valued homes at $35,871 (i.e., best possible value).

At the U.S. National Oceanic and Atmospheric Administration (NOAA) website, you can see that there is climate data showing the average number of clear days per year for 270 U.S. cities. The city with the most clear days (i.e., best possible value) is Yuma, Arizona with 242 days. The city with the fewest clear days (i.e., worst possible bound value) is Cold Bay, Alaska with only 10 days.

Assume that you want to create normalize composite location values with a scale of zero (worst) to 10 (best) for three cities:

• Lexington, Kentucky has home values of $227,178 and an average of 89 sunny days per year

• Phoenix, Arizona has home values of $318,799 and an average of 211 sunny days per year

• Austin, Texas has home values of $470,429 and an average of 115 sunny days per year

First, you need to calculate a normalize value for the home value and then a normalize value for sunny days. After you calculate these two normalized values, you then need to use them to calculate a composite location value for each of the three cities.

For Lexington, Kentucky calculate the normalize home value as:

• [ ( SPECIFIC - WORST ) / ( BEST - WORST ) ] x ( HIGH - LOW )

Where:

SPECIFIC = the value to normalize

WORST = the worst possible value

BEST = the best possible value

HIGH = the highest value on the scale (e.g., 10)

LOW = the lowest value on the scale (e.g., 0)

• [ ( 227,178 - 1,214,996 ) / (35,871 - 1,214,996 ) ] x ( 10 - 0 ) = 8.3776

For Phoenix, Arizona, I calculate the normalize home value as:

• [ ( SPECIFIC - WORST ) / ( BEST - WORST ) ] x ( HIGH - LOW )

• [ ( 318,799 - 1,214,996 ) / (35,871 - 1,214,996 ) ] x ( 10 - 0 ) = 7.6005

For Austin, Texas, I calculate the normalized home value:

• [ ( SPECIFIC - WORST ) / ( BEST - WORST ) ] x ( HIGH - LOW )

• [ ( 470,429 - 1,214,996 ) / (35,871 - 1,214,996 ) ] x ( 10 - 0 ) = 6.3146

Second, you need to calculate for these same three cities the normalized values for the sunny days.

For Lexington, Kentucky I calculate the normalize sunny day value:

• [ ( SPECIFIC - WORST ) / ( BEST - WORST ) ] x ( HIGH - LOW )

• [ ( 89 - 10 ) / (242 - 10 ) ] x ( 10 - 0 ) = 3.4052

For Phoenix, Arizona, I calculate the normalize sunny day value:

• [ ( SPECIFIC - WORST ) / ( BEST - WORST ) ] x ( HIGH - LOW )

• [ ( 211 - 10 ) / (242 - 10 ) ] x ( 10 - 0 ) = 8.6638

For Austin, Texas, I calculate the normalized sunny day value:

• [ ( SPECIFIC - WORST ) / ( BEST - WORST ) ] x ( HIGH - LOW )

• [ ( 115 - 10 ) / (242 - 10 ) ] x ( 10 - 0 ) = 5.4259

The final step is to join together the normalize values by weighting each one with the chosen weigh and then adding them together. In the earlier example, we just assumed that the decision maker (who was considering employment options in different cities) valued home value and sunny weather equally, so fifty percent (50%) for each factor.

For Lexington, we can calculate the composite location value as:

• ( fifty percent x normalized measure of housing cost ) + ( fifty percent x normalized measure of sunny weather )

• ( 0.50 x 8.3776) + (0.50 x 3.4052 ) = 5.8914

For Phoenix, Arizona, we can calculate the composite location value as:

• ( fifty percent x normalized measure of housing cost ) + ( fifty percent x normalized measure of sunny weather )

• ( 0.50 x 7.6005 ) + (0.50 x 8.6638 ) = 8.1322

For Austin, Texas, we can calculate the composite location value as:

• ( fifty percent x normalized measure of housing cost ) + ( fifty percent x normalized measure of sunny weather )

• ( 0.50 x 6.3146 ) + (0.50 x 4.5259 ) = 5.4202

Since the normalized measurement scale was zero to ten with ten being the highest and most preferred, we can interpret the above composite values to mean that Phoenix, Arizona (8.1322) scores the highest in terms of its location followed by Lexington, Kentucky (5.8914) and then Austin, Texas (5.4202).

Expert Measure. If you used an expert to measure the level of one of your criteria, you want to describe in your main text how you did that and then include an appendix that gives the details. The Criteria chapter of this text described the process. Recall that you want to define what are the characteristics that make a person an expert, find a person who has those characteristics, and then present that person with (1) brief written descriptions of the criterion that you want to measure, (2) brief written descriptions of each of your options, and (3) the scale that you want the expert to use (e.g., zero is bad and 10 is great). Then, ask the expert to read the description of the criterion and then rate the level of each option using the specified rating scale.

Create separate appendices for each criterion that you measured using an expert. Use letters to identify each appendix and give each appendix a title and a short description, much like you do for a figure or table. For example, you might have an appendix title:

Appendix A. The Process for Measuring the Level of Risk Associated with Three Options. To measure the level of risk, the author identified John Doe who had the defined expert credentials ("Expert Credentials"), presented him with a written description of the risk criterion ("Risk Criterion Description"), asked him to read the description of each option (e.g., "Description of Sell Business Option"), and then asked him to score each option on a scale of zero (bad) to ten (great). No additional information was provided to the expert.

Expert Credentials. [insert brief description of the credentials that a person must have to meet your definition of an expert for the purposes of assessing the level of this criterion and indicate the name and credentials of the person who you have identified as your expert.]

Risk Criterion Description. [Insert a brief description of how you have defined the risk criterion--or whatever criterion you are using instead.]

Description of the Sell Business Option. [Insert a brief description of your first option.]

Description of the ________________ Option. [Insert brief description of your next option. Have separate sections like this for all of your options.]

Appendices go at the very end of your paper. An appendix is like a footnote in that it contains details that not every reader will need or want to read, but unlike a footnote the information goes at the end of the paper. You use an appendix rather than a footnote when the amount of information is too much to fit nicely in a footnote at the bottom of a page.

After you have measured the level of each of the criteria for each of the options, you want to include a table (i.e., Table 3). Once you finish describing the levels for your first criterion for each of your options, you can put an in-text reference to Table 3. The table shows the level of all of the criteria for all of the options, but you can (and should) reference Table 3 after you finish describing your measures for your first criterion.

When you design Table 3, you should show vertically the criteria and horizontally each criterion's weight, each criterion's worst and best possible values, and each criterion's unweighted measured level or estimated score for each option. For example, suppose you are analyzing which used vehicle is best for your friend to purchase after graduating from college. Suppose you have identified five evaluation criteria that you will use to determine which used vehicle is best: (1) the cost of the vehicle, (2) how 'fun' the vehicle is to use, (3) the power that the vehicle has, (4) the expected maintenance costs, and (5) the fuel efficiency of the vehicle. Suppose you have identified three vehicle options: (1) a 2018 Jeep Wrangler sport utility vehicle, (2) a 2017 Honda Civic sedan, and (3) a 2018 RAM 1500 pickup truck. Here's what the table (i.e., Table 3) might look like showing the measured level of each of the criteria for each of the options:

After you show how you measured the levels of each criterion, you should as part of your discussion of Table 3 compare the actual levels from Table 3 with the levels that you hypothesized in the Options section (i.e., in Table 2). You could say that the hypothesized levels are in line with or conform well with the actual measured levels. You can then call attention to one or two instances where you hypothesized incorrectly and provide a brief explanation for why you think a difference occurred.

2.4 Normalizing the Level of Each Criterion

After you have shown how you measured the level of each of the criteria for each of the options, the next step is to normalize the measured values (i.e., the values in Table 3). Normalization is a way of modifying sets of numbers that each have different ranges so that each set has a common range while still preserving the relative differences within each set. In Table 3, you can see that the horsepower ranges from a low of 100 to a high of 400 while the efficiency (miles per gallon) ranges from a low of 15 to a high of 40. If we normalized these values, the ranges for both horsepower and efficiency would be the same (e.g., from zero to ten).

Before we go further, let me make sure you see why it is important to normalize the measurements. You can see that it is not appropriate simply to add up the values in each column and use the totals to compare each option. The problem with that approach is that each criterion is measured using a different scale. It does not make sense to add together the vehicle's cost, its "fun" factor, its number of horsepower, its current mileage, and its fuel efficiency in miles per gallon as a way of ranking different vehicles.

So, how do you normalize a set of values? If you studied how to create a composite measure above, you already have a good idea how this works. The formula has four variables:

NORMALIZED VALUE = [ ( SPECIFIC - WORST ) / ( BEST - WORST ) ] x ( HIGH - LOW )

Where:

SPECIFIC = the value to normalize

WORST = the worst possible value

BEST = the best possible value

HIGH = the highest value on the scale (e.g., 10)

LOW = the lowest value on the scale (e.g., 0)

For this section of the Analysis assignment, you need to explain what normalization is, why it is needed, show how it is done, and present the normalized values in a table (i.e., Table 4). Here is what Table 3 looks like after all of the values have been normalized:

You can see in Table 3 above that the "worst" and "best" possible values have been changed to a common scale (i.e., they have a common range from zero to 10). You can also see that for each criterion the values for each option fall within this same "worst" to "best" range of zero to ten.

Let me show you an example of how to normalize a set of values.

Look at Table 3 at the values for "Cost" for each vehicle. They are $26,566 (Jeep), $14,300 (Honda), and $22,012 (RAM). You also see from Table 3 the worst and best possible values, namely $30,000 and $10,000, respectively. To normalize this set of values, we need to identify the four variables for the formula. We will need to calculate the normalized value three times, once to get the value for the Jeep, another time for the Honda, and a third time for the RAM.

We can calculate a normalized value for "cost" for the Jeep first:

NORMALIZED VALUE = [ ( SPECIFIC - WORST ) / ( BEST - WORST ) ] x ( HIGH - LOW )

Where:

SPECIFIC = the value to normalize = $26,566

WORST = the worst possible value = $30,000

BEST = the best possible value = $10,000

HIGH = the highest value on the scale = 10

LOW = the lowest value on the scale = 0

Now, substitute the values in for each of the variables in the formula and simplify:

NORMALIZED VALUE = [ ( 26,566 - 30,000 ) / ( 10,000 - 30,000 ) ] x ( 10 - 0 ) = 1.72

We can calculate the normalized value for "cost" for the Honda similarly:

NORMALIZED VALUE = [ ( 14,300 - 30,000 ) / ( 10,000 - 30,000 ) ] x ( 10 - 0 ) = 7.85

Finally, we can calculate the normalized value for "cost" for the RAM:

NORMALIZED VALUE = [ ( 22,012 - 30,000 ) / ( 10,000 - 30,000 ) ] x ( 10 - 0 ) = 3.99

You can see that each time we calculate a normalized value, the value falls by design between the low and high values on the scale that we set (i.e., from zero to ten). Just so you see how it works, suppose that the cost of another option was the "worst" possible cost (i.e., $30,000). What would the normalized value be?

NORMALIZED VALUE = [ ( 30,000 - 30,000 ) / ( 10,000 - 30,000 ) ] x ( 10 - 0 ) = 0.00

The numerator would be zero since 30,000 minus 30,000 is zero, meaning the normalized value would be zero. That is what we would expect. And, similarly, if the vehicle cost was the "best" possible (i.e., just $10,000), then we would expect the normalized value to be the best possible (i.e., 10 on a 10 point scale).

NORMALIZED VALUE = [ ( 10,000 - 30,000 ) / ( 10,000 - 30,000 ) ] x ( 10 - 0 ) = 10.00

In the above equation, you can see that the numerator and denominator are both the same (i.e., 10,000 minus 30,000), making the value equal to one. Then, one times 10 minus zero is 10, just as expected.

In your submission, you do not want or need to show the reader every single calculation. Instead, I suggest that you explain in the main text generally how you normalized the values, then in a footnote show one or at most two examples, and then simply tell the reader that you performed the same normalization calculations to get the other values.

2.5 Weighting the Level of Each Criterion

The next step in your analysis is to take the normalized values from Table 4 and weight them using the criteria weights. This is an important step because it takes into account that, as you will recall, decision makers rarely place the same or equal importance of all of the evaluation criteria. Some criteria are typically more important to the decision makes and other criteria are typically less important. The criteria weights reflect the relative importance that the decision maker places on each of the criteria.

Suppose you didn't weight the normalized values from Table 4. What would that mean? Well, if you just added the normalized values for each option in Table 4 and compared the totals, it would mean that, in effect, each of the criteria has been weighted equally. The maximum possible value for each of the five criteria is 10 so the maximum possible value would be 50 and the lowest possible value would be zero. When you added up the unweighted normalized totals, you would get 24.28 (Jeep), 29.04 (Honda), and 23.88 (RAM), suggesting that the Honda is best, then the RAM, and the Jeeps is third.

If we use the weights, we must multiply each of the normalized values by the weight expressed as a decimal percent (i.e., "40" is "0.40"). So, for the "Cost" criterion, we would multiply the Jeep score (1.72) times the weight (0.40) and get the weighted Jeep score (0.69). We would multiply the Honda score (7.85) times the weight (0.40) and get the weighted Honda score (3.14). And, we would multiply the RAM score (3.99) times the weight (0.40) and get the RAM weighted score (1.60).

You can see from Table 5 the other weighted scores and, most importantly, the total weighted score for each option on the last row. The total weighted score is the sum of the individual weighted scores. The maximum value possible for the total score is 10 and the lowest possible total score is zero. Note that the ranking with the weighted criteria is different than when we calculate the ranking using no weights (i.e., equal weights).

2.6 Drawing the Conclusion

You want to be sure to highlight the results of Table 5. This is the table that reveals the conclusion of your analysis. In Table 5, you can see that when we use the weights the best option (i.e., the option that scores the highest) is the Honda. It has a total score of 5.54 out of a possible 10. The next best option is the RAM with a total score of 5.22 out of a possible 10. The third best option is the Jeep with total weighted score of 4.93 out of a possible 10. In your Objective section, you identified a specific question that asked what is best. Table 5 provides you with your logical and methodical answer to that original question.

In this case, looking at Table 5, I would say that the best used vehicle for this decision maker to buy is the 2017 Honda Civic with 25,000 miles, 158 horsepower. This vehicle costs the least ($14,300) and has the best fuel economy (36 miles per gallon). Even though this vehicle scored the lowest in terms of its "fun" factor, the other criteria more than compensated for this weakness, ultimately make the Honda the best option.

I might also point out that the scores for all three vehicles were fairly close together, suggesting that the other two vehicles might still be good choices. While I did not conduct a sensitivity analysis, the close total scores for the three vehicles suggest that slight changes in the weighting might alter the calculations enough to change the overall rankings.

2.7 Caveats and Limitations

You should conclude your Analysis section with a paragraph acknowledging important caveats and limitations of your analysis. You should describe how resource constraints (e.g., time and financial) affected the quality of the analysis. Remember, you did not get paid to do this analysis, and you had only one semester to complete it. What weaknesses does your analysis have as a result of these resource constraints and what, if anything, would you do differently if you had more money and time for your analysis? Where in your analysis would you invest more time and money if you could? What claims in your analysis have the weakest evidence as a result of your resource constraints? Also, you should provide a general caveat that making recommendations depends on a careful understanding of the decision maker's or decision making group's interests and preferences. Explain that you (the analyst) take responsibility for any errors in characterizing these interests and preferences.