question archive Chapter Nine Quantitative Papers Presenting Results f you have ever been on a guided tour of a museum, a theater, or some other tourist attraction, you know that the guide can make or break your experience
Chapter Nine Quantitative Papers Presenting Results f you have ever been on a guided tour of a museum, a theater, or some other tourist attraction, you know that the guide can make or break your experience
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Chapter Nine Quantitative Papers Presenting Results f you have ever been on a guided tour of a museum, a theater, or some other tourist attraction, you know that the guide can make or break your experience. The excessively detail-oriented guide will put you to sleep, the ill-equipped comic guide will anger or embarrass you, and the overly casual guide will leave you puzzled and frustrated. But a guide who manages to walk you through the attraction, highlighting the most important and inter- esting features and weaving a coherent story that links together the parts of the attraction, is the guide who will give you the best possible tour. In the same way, the results section of your research paper is the attraction that readers have come to see. Your task as guide is to walk them through your analysis in a coherent, deft, and efficient manner. This chapter will alert you to some of the issues involved in achieving this level of sophistication in writing about quantitative data. The Goal The goal of the results section is to clearly, forcefully, and modestly com- municate to your readers what the data reveal. Notice that this goal fol- lows from the goals of your literature review (to establish what needs to be studied, why it is important, and which results are predicted) and the goals 61 62 Writing Quantitative Papers of your data and methods section (to describe the data set and how it was analyzed). Meanwhile, communicating what the data analysis reveals sets you up for the goal of your discussion and conclusion sections (to sum up the larger theoretical points raised and addressed by your analysis). Writing about quantitative results is unlike the writing that we are usu- ally taught in school. As opposed to writing an essay with thesis statements and supporting points, you here find yourself alerting the reader to things that you now consider obvious and that you have sought to make obvious in your tables and figures. Yet you now must point these things out to the readers. Additionally, you must allow for readers to verify your claims while at the same time not beating them over the head with endless details that they could get themselves by reading your tables and figures. 50 there is a delicate balancing of your efforts to point out the important points while at the same time respect your readers’ ability to consider the facts for them- selves. This is difficult to do well, and like many things, it only improves with practice. An Extended Example: Redundancy and Voice Let’s follow an example derived from a student paper researching American men’s incomes. In Table 9.1, we find the descriptive statistics for incomes of older and younger men. The author wants to comment on the difference between the two groups of men. Table 9.1 Income for American Men 25th 75th Mean Median Percentile Percentile n Young Men (18—40) 36,531 30,000 19,700 43,000 10,767 Income Older Men (41—65) 48,082 37,000 24,000 55,000 10,887 Income Here is the author’s first draft describing the data: My analysis shows that the mean earnings for the younger men is $36,531, and for older men it is $48,082. This is a difference of $11,551. There were 10,767 younger men and 10,887 older men in the subsamples.
Quantitative Papers: Presenting Results 63 Redundancy There’s not a nice way to say it. That’s boring! This example illustrates the first thing not to do. Writing about the analysis does not mean that you repeat line for line what is in the tables. The reader can easily see in the table what the author has written in this example. Typically, one does not write about the sample size (N) in the results section. Only rarely is it important for understanding the results. If sample sizes are small (fewer than 100 as a rule of thumb), it may be important to mention to the reader that the statistics being used are more vulnerable to the in?uence of individual cases (outliers) because the sample is small. In this example, however, this is not the case, and the comment about the sample sizes is redundant and wasteful. Meanwhile, the author obviously wants to draw attention to differences between the groups. 50 it may be better to simply point out that there is a difference of X dollars between the two groups’ average incomes without pointing out the raw values from which this difference was computed. Readers can verify your math if they want to, but at the same time, the author can efficiently point out a difference that he or she thinks is impor- tant. Another way to do this would be to point to the percentage difference between the two groups, identifying the fact that the older group makes about 30 percent more than the younger group. The student’s first draft, shown earlier, is equivalent to the museum guide’s pointing to the Mona Lisa and saying, “Notice that she has long dark hair, has fair skin, and is smiling.” The guide’s statement is so boring, obvious, and redundant that it might even be insulting to the museum visi- tor. Consider how much better it would be for the guide to say, “It is not her dark hair and fair skin that draw attention but rather her mysterious smile.” Here the guide points out some potentially overlooked characteristics and helps the listeners move quickly to consider the most important. Let’s consider a revision of that earlier focus on Table 9.1 to try to achieve the same confident mix of observation, description, and a bit of interpretation. Table 9.1 demonstrates that mean income is dramatically lower for younger men than for older men. Older men have incomes about 30 percent higher than young men’s. This is consistent with Oppenheimer’s (19 82) argument regarding the “life—cycle squeeze” wherein younger men obtain lower annual earnings at the start of their careers. Meanwhile, the mean is higher than the median for both variables among both groups of men, suggesting that signi?cant outliers are in?ating mean earnings and incomes. Even in the upper end of the income 64 Writing Quantitative Papers brackets the differences are pronounced. The upper quartile of older men make more than $55,000, but for younger men, the upper quartile begins at $43,000. Notice that with this revision, the author still points to the important issues but helps readers begin to interpret the numbers by (1) making com- parisons between younger and older men, using simple words such as lower, higher, or but; (2) using descriptive words such as dramatically, in?ating, and pronounced; and (3) avoiding a dull rewriting of all the numbers but highlighting only a few speci?c numbers. The author begins to offer some explanation for why they appear as they do, without getting bogged down in the theoretical explanations for these ?ndings, but also makes an insight- ful observation about how these ?ndings are consistent with what other authors have anticipated. This revision provides readers the freedom to read the table for themselves and to consider what the author wants them to begin to conclude. Voice: Visible or Invisible Authors, Analyses, and Audiences This revised paragraph raises the issue of voice. That is, how visible should the author and the author’s analysis be in the presentation of the results? The first draft shown earlier begins with “My analysis” bringing the author on to the stage by saying “my.” The author also highlights that the analysis is showing something, as opposed to the data’s revealing something. These are issues of taste and editorial license, but they are important because, at times, the author and the analysis can get in the way of the results and findings. Notice in the longer example of analysis of Table 9.1 that the revision has moved the author and the analysis off the stage by sidestepping owner- ship of the analysis (“my”). In this revised example, the table of analyzed data is the source of authority and information rather than “my analysis.” Let’s consider a further example. Using Table 9.2, the author wants to show that the educational level of men has an important effect on their incomes. Here is a first draft of some text about Table 9.2: From Table 9.2 you can conclude that educational level is extremely important for increasing the income of all men, regardless of age. Computer analysis of the data also reveals that the effects of college graduation grow over a person’s life. While among young men there is a $23,000 difference between college graduates and less-educated men, this gap grows to $32,000 for older men.
Quantitative Papers: Presenting Results 63 Redundancy There‘s not a nice way to say it. That’s boring! This example illustrates the ?rst thing not to do. Writing about the analysis does not mean that you repeat line for line what is in the tables. The reader can easily see in the table what the author has written in this example. Typically, one does not write about the sample size (N) in the results section. Only rarely is it important for understanding the results. If sample sizes are small (fewer than 100 as a rule of thumb), it may be important to mention to the reader that the statistics being used are more vulnerable to the in?uence of individual cases (outliers) because the sample is small. In this example, however, this is not the case, and the comment about the sample sizes is redundant and wasteful. Meanwhile, the author obviously wants to draw attention to differences between the groups. 50 it may be better to simply point out that there is a difference of X dollars between the two groups’ average incomes without pointing out the raw values from which this difference was computed. Readers can verify your math if they want to, but at the same time, the author can efficiently point out a difference that he or she thinks is impor» tant. Another way to do this would be to point to the percentage difference between the two groups, identifying the fact that the older group makes about 30 percent more than the younger group. The student’s first draft, shown earlier, is equivalent to the museum guide’s pointing to the Mona Lisa and saying, "Notice that she has long dark hair, has fair skin, and is smiling.” The guide’s statement is so boring, obvious, and redundant that it might even be insulting to the museum visi- tor. Consider how much better it would be for the guide to say, “It is not her dark hair and fair skin that draw attention but rather her mysterious smile.” Here the guide points out some potentially overlooked characteristics and helps the listeners move quickly to consider the most important. Let’s consider a revision of that earlier focus on Table 9.1 to try to achieve the same confident mix of observation, description, and a bit of interpretation. Table 91 demonstrates that mean income is dramatically lower for younger men than for older men. Older men have incomes about 30 percent higher than young men's. This is consistent with Oppenheimer’s (1982) argument regarding the “life-cycle squeeze” wherein younger men obtain lower annual earnings at the start of their careers. Meanwhile, the mean is higher than the median for both variables among both groups of men, suggesting that signi?cant outliers are in?ating mean earnings and incomes, Even in the upper end of the income 64 Writing Quantitative Papers brackets the differences are pronounced. The upper quartile of older men make more than $55,000, but for younger men, the upper quartile begins at $43,000. Notice that with this revision, the author still points to the important issues but helps readers begin to interpret the numbers by (1) making com- parisons between younger and older men, using simple words such as lower, higher, or but; (2) using descriptive words such as dramatically, in?ating, and pronounced; and (3) avoiding a dull rewriting of all the numbers but highlighting only a few speci?c numbers. The author begins to offer some explanation for why they appear as they do, without getting bogged down in the theoretical explanations for these findings, but also makes an insight- ful observation about how these ?ndings are consistent with what other authors have anticipated. This revision provides readers the freedom to read the table for themselves and to consider what the author wants them to begin to conclude. Voice: Visible or Invisible Authors, Analyses, and Audiences This revised paragraph raises the issue of voice. That is, how visible should the author and the author’s analysis be in the presentation of the results? The first draft shown earlier begins with “My analysis” bringing the author on to the stage by saying “my.” The author also highlights that the analysis is showing something, as opposed to the data’s revealing something. These are issues of taste and editorial license, but they are important because, at times, the author and the analysis can get in the way of the results and ?ndings. Notice in the longer example of analysis of Table 9.1 that the revision has moved the author and the analysis off the stage by sidestepping owner- ship of the analysis (“my"). In this revised example, the table of analyzed data is the source of authority and information rather than “my analysis.” Let’s consider a further exarnple. Using Table 92, the author wants to show that the educational level of men has an important effect on their incomes. Here is a first draft of some text about Table 9.2: From Table 9.2 you can conclude that educational level is extremely important for increasing the income of all men, regardless of age. Computer analysis of the data also reveals that the effects of college graduation grow over a person’s life, While among young men there is a $23,000 difference between college graduates and less-educated men, this gap grows to $32,000 for older men,
Quantitative Papers: Presenting Results 63 Redundancy There’s not a nice way to say it. That’s boring! This example illustrates the first thing not to do. Writing about the analysis does not mean that you repeat line for line what is in the tables. The reader can easily see in the table what the author has written in this example. Typically, one does not write about the sample size (N) in the results section. Only rarely is it important for understanding the results. If sample sizes are small (fewer than 100 as a rule of thumb), it may be important to mention to the reader that the statistics being used are more vulnerable to the in?uence of individual cases (outliers) because the sample is small. In this example, however, this is not the case, and the comment about the sample sizes is redundant and wasteful. Meanwhile, the author obviously wants to draw attention to differences between the groups. 50 it may be better to simply point out that there is a difference of X dollars between the two groups’ average incomes without pointing out the raw values from which this difference was computed. Readers can verify your math if they want to, but at the same time, the author can efficiently point out a difference that he or she thinks is impor- tant. Another way to do this would be to point to the percentage difference between the two groups, identifying the fact that the older group makes about 30 percent more than the younger group. The student’s first draft, shown earlier, is equivalent to the museum guide’s pointing to the Mona Lisa and saying, “Notice that she has long dark hair, has fair skin, and is smiling.” The guide’s statement is so boring, obvious, and redundant that it might even be insulting to the museum visi- tor. Consider how much better it would be for the guide to say, “It is not her dark hair and fair skin that draw attention but rather her mysterious smile.” Here the guide points out some potentially overlooked characteristics and helps the listeners move quickly to consider the most important. Let’s consider a revision of that earlier focus on Table 9.1 to try to achieve the same confident mix of observation, description, and a bit of interpretation. Table 9.1 demonstrates that mean income is dramatically lower for younger men than for older men. Older men have incomes about 30 percent higher than young men’s. This is consistent with Oppenheimer’s (1982) argument regarding the “life—cycle squeeze” wherein younger men obtain lower annual earnings at the start of their careers. Meanwhile, the mean is higher than the median for both variables among both groups of men, suggesting that signi?cant outliers are in?ating mean earnings and incomes. Even in the upper end of the income 64 Writing Quantitative Papers brackets the differences are pronounced. The upper quartile of older men make more than $55,000, but for younger men, the upper quartile begins at $43,000. Notice that with this revision, the author still points to the important issues but helps readers begin to interpret the numbers by (1) making com- parisons between younger and older men, using simple words such as lower, higher, or but; (2) using descriptive words such as dramatically, inflating, and pronounced; and (3) avoiding a dull rewriting of all the numbers but highlighting only a few speci?c numbers. The author begins to offer some explanation for why they appear as they do, without getting bogged down in the theoretical explanations for these ?ndings, but also makes an insight- ful observation about how these ?ndings are consistent with what other authors have anticipated. This revision provides readers the freedom to read the table for themselves and to consider what the author wants them to begin to conclude. Voice: Visible or Invisible Authors, Analyses, and Audiences This revised paragraph raises the issue of voice. That is, how visible should the author and the author’s analysis be in the presentation of the results? The first draft shown earlier begins with “My analysis” bringing the author on to the stage by saying “my,” The author also highlights that the analysis is showing something, as opposed to the data’s revealing something. These are issues of taste and editorial license, but they are important because, at times, the author and the analysis can get in the way of the results and findings. Notice in the longer example of analysis of Table 9.1 that the revision has moved the author and the analysis off the stage by sidestepping owner- ship of the analysis (“my”). In this revised example, the table of analyzed data is the source of authority and information rather than “my analysis.” Let’s consider a further example. Using Table 9.2, the author wants to show that the educational level of men has an important effect on their incomes. Here is a first draft of some text about Table 9.2: From Table 9.2 you can conclude that educational level is extremely important for increasing the income of all men, regardless of age. Computer analysis of the data also reveals that the effects of college graduation grow over a person’s life. While among young men there is a $23,000 difference between college graduates and less-educated men, this gap grows to $32,000 for older men.
Quantitative Papers: Presenting Results 65 Table 9.2 Income by Age and Education for American Men Mean Median n Young Men (18—40) Less Than College 30,040 26,000 7,786 College Graduate 53,483 42,000 2,981 Older Men (4-1—65) Less Than College 37,507 32,000 7,246 College Graduate 69,129 51,421 3,641 This text raises two more issues of voice and the visibility of author and reader. The author says, “You can conclude.” The familiar you ?nds no place in formal academic writing. This is because the meaning of you is ambigu- ous. Is the author implying that the reader needed his or her permission to make this conclusion? Is this a veiled invitation to make this conclusion? A command to do so? Is this conclusion optional, such that some could make such a conclusion and others could not? Hence the ambiguity. Here is a related case: In looking at the average income of men within different educational catego- ries, we can say education has an important impact on. When the writer says, “we can say,” there is an assumption that the reader will want to say it too. The reader is once again visible but now is being asked to join the writer in saying something. The following approach would work better: The observation that income varies so widely with education supports other researchers’ claims that education is one of the most important in?uences on incomes. This revised text puts the responsibility on the author to assert the mean- ing of the data. The text does not ask the reader to say it too but allows the reader to accept or reject the interpretation offered. Consider again the earlier version of the text focused on Table 9.2, focusing on the second sentence: Computer analysis of the data also reveals that the effects of college graduation grow over a person’s life. This text also brings the computer to the stage. Generally, this is unwise. The reader does not really care whether the author computed these statistics 66 Writing Quantitative Papers on a computer, an adding machine, an abacus, or the back of an envelope. Similarly, references to computer software are generally not required (e.g., “analysis of the data with SPSS”), although you may occasionally see pub- lished research where the authors believed that the software’s unique abilities needed to be highlighted. However, in general, it is best to let the computer be invisible. Because most computer programs cannot handle names of variables such as “men’s earnings,” they use truncated names like “MENSINC.” Do not use these computer-generated code names in tables and/or in writing about tables. Readers should not have to learn a new vocabulary to read the results section. Even if the computer prints out attractive tables with MENSINC as the heading of a row or column, change this back to its real meaning, and discuss it as such in the text. Consider this side point: For researchers and students who have struggled with completion of their analysis, it is tempting to communicate to readers how hard they worked to produce this analysis. For example, an author might want to say, “Painstaking and time-consuming efforts to compute the differences in earnings demonstrate that indeed . . . ” Unfortunately, the readers of academic writing are not interested in the difficulties of research. Indeed, the author’s task is to make the results seem so self-evident and self- revealing that the reader will believe that these results effortlessly presented themselves. This observation stands in contrast to the kinds of information that a tour guide would provide: We actually find it interesting that the painter completed the portrait under difficult conditions. So who should be visible and invisible in writing about results? For sure, the computer and the readers should be invisible. The data or the analysis can be visible, although the author should beware of putting excessive focus on the analytic process and keep attention on the results. And the author? This remains a point of disagreement among academic writers. In the revi- sion for Table 9.1 suggested, the author remains offstage and simply makes statements about the results, letting them be the source of authority and information. Some writers stand on the stage with their analysis, introducing each phase of the analysis almost like magicians who say, “Next, I pull a rabbit out of a hat.” For example, the author could introduce Table 9.1 by saying, “I first compute the mean and median earnings for both groups of men. Table 9.1 demonstrates that . . . ” Thus, the author takes a more central role in the presentation of results and writes in the present tense. However, notice that the table is still the source of authority and information. In large part, the choice of whether the author appears in the text, usually as “I,” is an editorial choice that will meet with approval by some readers and disapproval by others.
Quantitative Papers: Presenting Results 67 Tense Yet? In all of the weak and strong examples provided so far, the author writes in the present tense. For example, “Table 9.1 demonstrates” and “computer analysis reveals.” This may feel somewhat awkward to the author since the results actually have been created over time through a laborious process of data construction and analysis. As a result, many first-time researchers are inclined to write in the past tense something like this: Evaluation of the data revealed that the gap in earnings between the two groups of men was very large. Authors of articles published in many social science journals write in the present tense when discussing quantitative analyses. This is true even when they are writing about aggregated data covering several decades! The rationale is that if the analysis revealed something last week or last year, it reveals the same thing today. So it’s not that Table 9.1 said something just on the day that the statistical analysis was completed; the results continue to say the same thing. The reader can recall that the data were collected during a certain time (this information is revealed in the data and methods section), and the date on the paper indicates when the author is making the current claim. The benefit of writing in the present tense is that it makes the quantita- tive results more compelling. However, some social science journals and some professors prefer that you write the paper in the past tense. It should be noted that social science research based on participant observation or face-to-face interviews may best be communicated by writ- ing in the past tense. If the research process is integral for understanding the results, then this particularly makes sense. For example, if the researcher wants readers to know that the setting in which the data were collected may have in?uenced the findings, then it makes sense to say so. Almost 75 percent of the workers indicated that they were not being paid enough for their work, although when the boss entered the room they quickly changed the subject and hid their questionnaires. 01‘ I pressed the managers for more detail when they evaded my questions about the earnings of workers down on the shop ?oor. In these instances, the data and the acquisition of the data require that the author write in the past tense. However, quantitative data are generally treated (perhaps naively so) as timeless and context independent, and thus academic writers most often talk about them in the present tense. 68 Writing Quantitative Papers Directing Attention to Tables and Graphs Consider again being on a tour of a museum during which the guide repeat- edly drones, “Look at this painting—it is called . . . ” At some point you would begin to wish that the guide would quit saying, “Look here, look there,” and instead simply point and start talking about the different paintings: Compared to the Mona Lisa in the other room, the portrait of her sister here looks quite different. In the same way, it is challenging to point out tables and ?gures without being heavy-handed. Here are a few examples from some students’ writing about tables and ?gures: Looking at Table X for men’s earnings and focusing on the mean and median and comparing . . . it shows that the mean and the median are . . . Table X illustrates that . . . The data show that . . . (Table X). Consider Table X, which shows that . . . The ?rst example contains an implicit command to join the author in looking, and the next two just assume that readers will want to verify what the author is asserting, with the author merely pointing out the location where this veri?cation can be found. The last one commands readers to look for themselves. One or two of these commands may not be bother- some to readers, but many of them will make readers feel like they are being bossed around. The goal is to focus on the ?ndings by either stating what a certain table or ?gure reveals or by using the parenthetical maps (e.g., Table X, Figure X) to point people in the right direction for con?rmation of the claim. Earth-Shaking, Surprising, Considerable, and Negligible Results “The chances of becoming homeless increase an astonishing 25 percent for people who suffer from . . . ” “By controlling for . . . , the gender gap in pay plummeted to only . . . ” “The impact of . . . on . . . is highly signi?cant.”
Quantitative Papers: Presenting Results 69 “The average total income (using the mean) was much higher than the median.” “There is a real discrepancy between the average income of highly and less- educated men.” The results section of the paper is the ?rst place where the author can begin to provide some interpretation about how surprising or expected the results are. After many weeks of painstaking work, the temptation is to claim that the results are remarkable or awe inspiring when in fact they are much more modest. On the other hand, many authors are excessively humble and fail to assert the importance of their ?ndings. This is where colleagues and reviewers are helpful for determining how big or little, important or trivial, memorable or forgettable, signi?cant or not are the results of the research. Phrases such as much higher and real are open for argument. Signi?cant may mean statistically significant or substantively significant (whether or not we tested its statistical significance). Beware the apparently neutral phrase much higher. There is definitely a place for being persuasive and honest about findings, and if the difference is huge, noteworthy, or much bigger, then say so. But make sure that you keep in mind the cynical reader whose first reaction might always be, “Oh yeah? Why do you say that?” If you can defend against such an aggressive reading of your work, then you are right to give emphasis to your findings. In one of the preceding examples, the author has indicated that the differ- ence between the two groups is “real” (an apparently reasonable and testable assertion of statistical significance). Words such as big, real, and important have their place in a results section, but be prepared to defend them. Consider how they either might be misunderstood or might raise red ?ags for the reader. Final Thoughts Writing about quantitative data is one of the least common experiences for most social science majors. It is hard to do well, especially the first couple times you do it. You have numbers and tables that might be boring to some people but that tell an important sociological story. Overcoming the dull- ness of numbers and tables to appropriately reveal the compelling story behind them is the challenge. The final figures and tables represent hours of hard work, so it is difficult to remain understated and casual enough to keep yourself, your computer, and your painful research experiences off center stage so the data can tell the story. Yet the data do not really tell the story on their own. You are the tour guide who must help the reader see the whole story in the data.
