Writing Cases & Business Reports

Preparing Written Cases and Business Reports

The cases that you will be tackling in this course require you to communicate your statistical results. You may be discussing your results in class with me and/or your other classmates. You may be giving a formal classroom presentation. Often, you will be asked to prepare a written report of your findings. Writing effectively will be important in your professional career. Both oral and written communication skills are highly valued in the workplace. There are many ways to organize a business memo, but formal structure is probably less important than clear, concise communication. Preparing the written summary of your results will probably be just as difficult as doing the computations. Students say it takes about as long to write the results as it does to finish the statistical work. You might want to plan accordingly.

Writing Style

Once you are done with the computer work, you must interpret these findings for someone, perhaps a manager or your boss. A good report should be written so that anyone can understand it. Many professionals (accountants, lawyers, statisticians,...) hide their lights under bushels: no one appreciates their professional opinions because they simply can't write well. Sometimes it seems they use technical language to intimidate and overwhelm the recipient.

Unless you are writing to someone you know is well-versed in statistical techniques, avoid using statistical and mathematical jargon in your report. For instance, if you were the vice president of marketing who never had a statistics course, which of the following two summaries would you find most valuable?

  • The regression model is given by: SALES = 13,000 + 5*ADVERTISING,
    which means that the y-intercept is $13,000 and the slope is $5.
  • According to the model: (a) if the firm does no advertising, sales will be $13,000, and
    (b) each additional dollar spent on advertising will bring in five additional dollars in sales.

It may be hard at first to write in a nontechnical way because you will be using jargon in your course. So will I. So will your textbook. You will get used to using specific statistical terms like "least squares" and "p-values," but don't presume that your reader understands them. You will have to find a way to translate statistical concepts, methodologies, and outcomes for the uninitiated. Just by virtue of spending time in your statistics class, you may well forget that certain statistical concepts don't exist in most people's vocabularies. Here are some useful guidelines.

  • Do you have any words in the report that you did not commonly use before you walked into this class? If you used a word or phrase on a regular basis before signing up for statistics, it is probably acceptable to use in your write-up.
  • Would your next door neighbor understand the essence of your report?
  • What would the editor of your local newspaper think about publishing your report in tomorrow's newspaper?
  • Use the active voice where you can. "I ate my dinner" is livelier than "the dinner was eaten by me."
Introductory Material

It sometimes helps to provide background information about the problem at hand. This might include a statement of the problem or situation and the data available to answer this question. Since your report involves statistical analyses, you might also provide initial descriptive statistics (e.g., means and/or standard deviations) of some of the more important variables, unless that information would simply distract from the point you're trying to make. By providing this type of background information, you can put the problem in perspective and also ease the way into the upcoming material.

Good Grammar, etc.

Needless to say, good grammar, correct spelling and appropriate punctuation are all important components of an effective report. You probably can't convince a reader that your statistical results are valid if your writing is poor. Sloppy, misspelled and otherwise disorganized reports send the message that you don't think the report is very important anyway. Brush up on your writing skills. You will discover that it's both fun and valuable to write effectively. Word processors may help; a spelling checker is useful, too.

The Junked-Up Appendix Problem

Consider putting supporting statistical documentation, such as graphs, tables, and other statistical output at the end of your written report. Within the report, refer to these appendices for guidance. On the other hand, if one particular table or graph really contains the essence of the point you're making, you probably want to put it right in with the text, where your reader can see it quickly. The key question to ask here is: if I put it in with the text, will it distract the reader more than if the readerhas to turn to an appendix? A critical graph probably belongs in with the text. A table that provides relatively minor support to your argument probably belongs in an appendix.

Don't append to the main body of the report every single statistical printout you produced. Include the important ones. It's sometimes hard to decide exactly what is important and what is not, but if you can't, your readers certainly can't either. If you can't tell which ones are important, you're not done with your analysis yet. Once you have determined it, the following rule-of-thumb may help: don't append a statistical exhibit if you don't refer to it in the report, and, of course, don't refer to an exhibit that's not there.

Length

I generally place one-or two-page limits on the reports from students, but write as succinctly as you can, in any case. Remember you are trying to present the essence of your statistical findings, not a comprehensive validation of every step of your work. A manager is unlikely to wade through pages and pages of information. It's easy to overwhelm a reader who wants nothing more than a summary of the major findings, but why do so?

You must identify, then, the fine line between too much detail and not enough detail. You don't want to make your report so short that it's deceptive, but you don't want to bore or intimidate your intended reader with unnecessary details, either. Only you, as the reporter of the data, can decide on this issue of what to include.

Even if your report is a lengthy, major course project, I suggest that you make the very first page an "executive summary." An executive summary should be written for someone who has never had a statistics class, and doesn't care to have statistics explained. It should include only the important results and implications derived from the data. It should also include any necessary caveats or limitations of your findings. For instance, you might not trust your results because of a small sample size, or some confidence interval might suggest inaccuracy of a point estimate. Try to limit this executive summary to one page, single-spaced. It's hard to do!

To start you off, I've attached sample reports below.You'll find that the task of preparing your own reports will become increasingly straightforward with practice. Good luck!

A Pretty Lousy Business Report

TO:

Tom Jones, Director of Personnel

FROM:

Jana Smith, Statistician

DATE:

5/19

SUBJECT:

Analysis of Personnel Data

Per your request, I have analyzed the data on sick days and the company's new wellness program. The results are summarized below.

The regression model suggests that there is a statistically significant relationship between the two variables. The correlation between dollars contributed to the wellness program and absenteeism is a positive 0.63. The standard error is 0.073. The r-squared statistic on the simple regression model is 56%, which is pretty good for cross-sectional data. Moreover, the F-statistic measuring the statistical significance of the model as a whole is 54.90, indicating a good model.

When analyzing the relationship by gender, there is no statistically significant impact here. The p-value on the categorical variable called GENDER (see EXHIBIT II) is .46. This means that absenteeism does not seem to be correlated with the gender of the employee. On the other hand, it just might be a multicollinearity problem with the two independent variables.

I'd be happy to assist in any further analysis of this data at your request.

A Pretty Good Business Report

TO:

Tom Jones, Director of Personnel

FROM:

Jana Smith, Statistician

DATE:

5/19

SUBJECT:

Analysis of Personnel Data

As you asked, I have analyzed the data on sick days and the company's new wellness program. Here are my results.

Data

The personnel department provided a sample of 125 randomly chosen employee files. From those files, we obtained:

  • the company's payment for the employee's participation in our wellness program,
  • the employee's absentee record (measured in number of absent days) over the past two years, and
  • the gender of the employee.

72% of the sample group was female.

Results

  • On average, our employees missed 15 days of work in the first year. The typical fluctuation around the average of 15 days was seven days.
  • In the second year, after starting the wellness program, the average number of absent days declined to 10 days, and the typical fluctuation also decreased to 2 days. We committed about $50 per employee to the wellness program last year.
  • A statistical model (see EXHIBIT below) of the relationship between dollars committed to wellness, absenteeism, and gender indicates that the wellness program has a statistically significant relationship to absenteeism. The model suggests that:
    • each additional dollar committed to our wellness program was associated with a two hour decline in absenteeism, and,
    • there is no statistically significant relationship between gender and absenteeism.

    The model would generally be considered a statistically strong one, since 56% of the variation in absenteeism is explained by the model. Although this leaves 44% of the variation unexplained, it is difficult to do much better with the type of data available for this analysis.

    Recommendation

    Because of the decline in absenteeism after the institution of the wellness program, I recommend that the program be continued.

    Limitations

    Consider redoing this study in another year with a larger sample size. It is not clear whether one year is enough to observe the full benefits of the wellness program. Also, there are some troubling aspects of the statistical results that might be alleviated with a larger sample size. For instance, many of the standard errors in the model (that is, measures of the accuracy of the estimates) are quite large in my opinion.

    I'd be happy to answer any further questions that you might have about my analysis or report.

___________________________________________

EXHIBIT II

	The regression equation is        	
	ABSENT = 12.2 - 0.26 DOLLARS + 0.07 GENDER        	
   
	Predictor     Coef  Stdev  t-ratio       p    	
	Constant      12.2   3.37   3.62      0.00    	
	DOLLARS      -O.26   0.04   6.50      0.00    	
	GENDER        0.07   0.25   0.28      0.80        	
   
	s = 7.9     R-sq = 56.2%  R-sq(adj) = 55.5%        	
   
	Analysis of Variance        	
	SOURCE      DF     SS    MS     F         p    	
	Regression   2   9770  4885    78.3   0.000    	
	Error      122   7614  62.4                    	
	Total      124  17384

___________________________________________

adapted from Practicing Data Analysis, by Bryan and Smith

ALSO SEE A CASE REPORT FOR BOWERMAN CASE : exercises 2.87 and 6.41
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