Chapter 14: Communicating Results: Capstone

14.1 From Answers to a Decision

It's the end of your first semester at Ridgeline. You've answered most of the questions Dana and Marcus asked on your first day. Promo days bring in more customers. The mobile coupon raised spending. Trained baristas get better ratings. Waiting costs satisfaction. Your answers are scattered across a dozen output sheets, though, and the owners have a planning meeting next week.

Marcus sends you a short message: "Dana and I need to decide four things. Should we keep promo days? Should we roll out the mobile coupon to all loyalty members? Should we require barista training? And where should we put money to raise satisfaction? One page, please. We'll read the first paragraph carefully and skim the rest."

This chapter is about that last step. An analysis that nobody can read and act on has no value to a business. You'll pull together the methods from the whole book into a decision guide, walk through the full workflow one more time, and then learn to write, chart and check a findings memo. The chapter ends with your capstone project: an analysis of your own, from question to memo.

14.2 Choosing the Right Method: A Decision Guide

In Chapter 1. Statistics, Data, and AI in Business, you saw a map of the tests ahead. You've now used every one of them. Here's the map again, in the form you'll actually use it: start from the question and the variables, and read across to the method.

Two questions get you most of the way:

1. What kind of question is it? Describe, estimate, compare groups, look for a relationship, or predict?
2. What types of variables are involved? Is the outcome numeric or categorical? Is the explanatory variable a grouping (two groups, several groups) or a number? Are there several explanatory variables?

The question	Outcome	Explanatory variable(s)	Method	Check in Excel	Chapter
What does the data look like?	any	none	summaries, histogram, box plot, PivotTable	AVERAGE, MEDIAN, STDEV.S, QUARTILE.INC	Chapter 4. Describing Data
How likely is an outcome?	count or measurement	none	binomial or normal model	BINOM.DIST, NORM.DIST	Chapter 5. Probability and Distributions
How much does a sample statistic vary?	numeric or Yes/No	none	sampling distribution, simulation	RANDARRAY, STDEV.S of simulated means	Chapter 6. Sampling and the Central Limit Theorem
What's the population value, roughly?	numeric or Yes/No	none	confidence interval for a mean or proportion	CONFIDENCE.T, T.INV.2T	Chapter 7. Confidence Intervals
Is the mean different from a target?	numeric	none	one-sample t-test	T.DIST.2T, T.DIST.RT	Chapter 8. Hypothesis Testing
Do two separate groups differ?	numeric	two independent groups	Welch two-sample t-test	T.TEST(…,2,3)	Chapter 9. Comparing Two Groups
Did the same units change?	numeric	two matched measurements	paired t-test	T.TEST(…,2,1)	Chapter 9. Comparing Two Groups
Do two groups differ in a percentage?	Yes/No	two groups	two-proportion z-test	z by formula, NORM.S.DIST	Chapter 9. Comparing Two Groups
Do several groups differ?	numeric	three or more groups	one-way ANOVA, then Tukey HSD	ToolPak Anova: Single Factor	Chapter 10. Comparing Many Groups: ANOVA
Are two categorical variables related?	categorical	categorical	chi-square test of independence	CHISQ.TEST	Chapter 11. Relationships in Categorical Data
Do counts match expected shares?	categorical	none	chi-square goodness-of-fit test	CHISQ.TEST	Chapter 11. Relationships in Categorical Data
Are two numeric variables related?	numeric	one numeric	correlation and simple regression	CORREL, SLOPE, LINEST	Chapter 12. Correlation and Simple Regression
What predicts an outcome, holding other things constant?	numeric	several, numeric or categorical	multiple regression with dummy variables	LINEST, ToolPak Regression	Chapter 13. Multiple Regression

A few habits make the guide work better:

• Identify the row first. Is one row a customer, a store-day or an employee? "Do promo days have more transactions?" is a two-group question about store-days. "Do stores differ?" might be a question about 12 stores, not 4,380 rows.
• Ask whether the groups are matched. The same store on promo and non-promo days is a paired design. Different customers in the coupon and control groups are independent samples.
• Ask whether you need to hold something constant. If a comparison could be confounded, as training was by tenure or region by wait, a regression with the confounder included is often the better method.
• Talk it through with your AI. Describe the question and variables and ask which method fits and why. Then check its suggestion against this table. If they disagree, find out why before you run anything.

14.3 The Workflow, End to End

Every analysis in this book followed the same loop. Here it is as a checklist you can use on any project:

1. State the business question in one sentence that names the decision it informs. "Should we roll out the coupon?" is a decision. "Look at the coupon data" isn't.
2. Identify what one row is, and the variables you need. Classify each one: categorical (nominal or ordinal) or numeric (discrete or continuous).
3. Prepare the data in Excel. Make it a Table, fix text and number storage, handle missing values and duplicates, and add helper columns (dummies, lookups, a weekend flag).
4. Explore before testing. Compute summaries and make a chart. Look for outliers, skew and anything that looks wrong.
5. Choose the method with the decision guide, and make sure you understand what it asks and assumes.
6. Describe the data to AI. In 2. Ask your AI, write what a row is, what the columns mean, the question, what you've learned, and what you want back. Click Copy prompt.
7. Read the script before you run it. Check that it uses the right data frame, the right variables in the right roles, the right test, and the right options (paired or not, baseline category, prediction or confidence interval).
8. Run it in R for Excel and send each output card to a New sheet.
9. Verify. Reproduce the key number with an Excel function or the ToolPak. Two tools, one answer.
10. Check the assumptions. Look at residuals or group spreads, and think about how the data were collected.
11. Interpret in business language, with the size of the effect and its uncertainty.
12. Communicate in a memo, a chart and a report sheet, with limitations stated.

Steps 1–5 and 9–12 are yours alone. The AI helps most with steps 6–8, and it can help you write in step 12. It can't decide what matters to the business.

14.4 Writing for a Decision Maker

Statistical writing for a class usually builds up to the answer: here's the data, here's the method, here are the results, and finally here's the conclusion. Writing for a manager works the other way round. Busy people read the top of a memo and decide whether to read on. Put the answer there.

14.4.1 The structure of a findings memo

1. Bottom line. The recommendation, in two to four sentences. A reader who stops here should know what you think they should do.
2. Evidence. For each decision, the key finding in plain words: what you compared, how big the difference was, and how sure you are. Use the units the reader cares about: dollars, transactions, rating points.
3. Uncertainty. A range for each key number, and how much weight it can bear. Was it an experiment or observational data? How large was the sample?
4. Recommendation. What to do, including what to do next to reduce the uncertainty that matters.
5. Limitations. What the analysis didn't cover and what could make it wrong. Say it plainly and briefly.

A memo isn't a methods section. Name the method in a few words ("a randomized test," "comparing each store's promo days with its other days," "a regression that holds region constant"), and keep the full output in an appendix or the workbook for anyone who wants it. Never paste raw output into the body.

14.4.2 A worked example

Here's a memo answering Marcus's four questions. Every number in it comes from an analysis earlier in the book. Read it once for content, and a second time for how it's built.

To: Dana Whitfield and Marcus Bell
From: Analytics
Re: Promo days, the mobile coupon, barista training, and satisfaction

Bottom line. Keep promo days, roll out the mobile coupon to loyalty members, and make barista training standard for new hires. To raise satisfaction, put the money into shorter waits at the Metro stores: wait time explains most of Metro's satisfaction gap, and it's something we can fix.

Promo days pay for themselves in revenue. Comparing each store's promo days with its own regular days in 2025, promo days averaged about 34 more transactions (about 10% more) and $138 more revenue per store per day, even though the average ticket was about $0.28 lower. Every one of our 12 stores showed a lift. At our current schedule of about 54 promo days per store, that's roughly $89,000 a year in extra revenue across the chain. A regression that holds weekends, weather and store features constant gives a similar lift, about 33 transactions. This is revenue, not profit: we haven't counted the extra product and labor cost of the busier days.

The mobile coupon works, and we know it caused the increase. In our randomized test of 1,000 loyalty members, customers who received the coupon spent $3.81 more over the next 30 days than those who didn't (95% confidence interval: $2.01 to $5.61) and visited more often. Because customers were assigned to the coupon at random, the difference is due to the coupon, not to who chose to use it. If each redeemed coupon costs us $2.00, the cost is about $0.68 per customer we send it to, against about $3.81 in extra spending. Again, that's revenue, so the margin on the extra spending is what has to cover the $0.68.

Training is associated with better ratings, even after accounting for experience. Trained staff are rated about 0.34 points higher on the 1–5 customer rating (95% CI: 0.23 to 0.45) than untrained staff with the same tenure and role. Experience matters too, but it doesn't explain the training gap. This comes from our staff records, not an experiment, so some of the gap could reflect who chooses to take the training. Requiring it for new hires, and comparing their ratings over the next six months, would settle that.

Shorter waits are the best lever on satisfaction. Each extra minute of waiting goes with a satisfaction rating about 0.33 points lower on our 10-point scale, even comparing customers in the same region. Metro customers wait 5.8 minutes on average, against 3.7 minutes at our other stores, and that difference accounts for most of Metro's lower satisfaction. Cutting Metro waits by 2 minutes would be expected to raise Metro ratings by roughly 0.7 points. A smaller Metro gap, about 0.3 points, remains even at equal waits and is worth a separate look.

Recommendations.

1. Keep the current promo-day schedule. Before adding more, estimate the profit margin on promo-day sales.
2. Roll out the mobile coupon to all loyalty members, and keep a small random control group so we can keep measuring its effect.
3. Require barista training for new hires, and track their ratings against recent hires who weren't trained.
4. Fund wait-time reductions at Metro stores first (staffing at peak hours, equipment, mobile ordering). Re-survey Metro customers after the change.

Limitations. All figures are from 2025 data at our 12 stores. The promo, training and satisfaction findings come from observational data, so they show associations after accounting for the factors we measured, not proof of cause. Only the coupon finding comes from an experiment. Revenue figures don't include costs. The survey reached 600 customers, and we're assuming they represent our customers in general.

Notice what this memo does:

• The first paragraph answers all four questions. Dana could stop there.
• Each finding leads with its business meaning in bold, and the number follows.
• The language matches the evidence. "We know it caused" appears only for the randomized coupon test. The promo, training and wait findings say "goes with," "associated with" or "would be expected to."
• Uncertainty is stated in plain words, with a 95% range for the key numbers. It never says "p < 0.001." The owners don't need p-values. They need to know whether the effect is real and how big it might be.
• Every recommendation includes a way to learn more: a control group, a tracked rollout, a re-survey.
• The limitations are honest and short.

14.5 Reporting Uncertainty in Plain Words

Most managers don't think in p-values and confidence levels. Translate them:

Instead of	Write
"p < 0.001"	"This difference is far too large to be explained by chance."
"p = 0.21, not significant"	"We can't tell whether there's any difference; the data are consistent with none."
"95% CI [$2.01, $5.61]"	"about $3.81 more, and very likely somewhere between $2 and $5.60"
"R² = 0.39"	"Wait time accounts for about 40% of the differences in ratings."
"β = −0.33, holding region constant"	"Each extra minute of waiting goes with a rating about a third of a point lower, comparing customers in the same region."
"95% prediction interval [383, 510]"	"Plan for about 450; almost any such day will fall between 380 and 510."

Two cautions. First, "not significant" doesn't mean "no effect." It means the data can't rule out no effect, which is a weaker statement. Second, don't round away the uncertainty to sound confident. "Training raises ratings by 0.34" sounds more certain than the data allow. "Trained staff are rated about a third of a point higher" is just as clear and more honest.

14.6 Honest Charts in Excel

A chart persuades faster than any sentence, which is exactly why it has to be honest. Two rules cover most of the problems.

14.6.1 Rule 1: bar charts start at zero

The length of a bar is how a reader judges its size. If the axis starts above zero, the bars' lengths no longer match their values, and small differences look huge.

Here's an example from Chapter 7. Confidence Intervals. Average spend per survey visit was $8.33 in Metro, $8.40 in Mountain and $8.72 in Suburban. Plot those as columns, and Excel may choose an axis that starts at $8.10. Suburban's bar then looks more than twice as tall as Metro's. Start the axis at zero, and the three bars look nearly the same, which is the truth: Suburban customers spend about 5% more.

To fix an axis in Excel: right-click the vertical axis, choose Format Axis, and under Axis Options > Bounds set Minimum to 0. If Excel shows Auto beside it, typing 0 overrides it.

The rule applies to bars and columns. A line chart or scatterplot doesn't need to start at zero, because readers judge position there, not length. Even so, label the axis clearly so no one mistakes a small change for a large one.

14.6.2 Rule 2: show the uncertainty

A bar shows a sample mean. Readers will treat the difference between bars as real unless you show them how uncertain each one is. Error bars built from confidence intervals do that.

The 95% confidence intervals for mean spend are Metro [$7.97, $8.69], Mountain [$8.03, $8.76] and Suburban [$8.36, $9.08]. To add them as error bars:

1. Set up a small table: region in A2:A4, mean in B2:B4, lower limit in C2:C4 and upper limit in D2:D4.
2. Add two helper columns. In E2, the distance up: =D2-B2. In F2, the distance down: =B2-C2. Fill both down. (Each is about $0.36.)
3. Select A1:B4 and choose Insert > Insert Column or Bar Chart > Clustered Column. Set the vertical axis minimum to 0.
4. Click the chart, then Chart Design > Add Chart Element > Error Bars > More Error Bar Options.
5. In the Format Error Bars pane, under Error Amount, choose Custom and click Specify Value.
6. For Positive Error Value, clear the box and select E2:E4. For Negative Error Value, clear the box and select F2:F4. Click OK.
7. Add a note under the chart: "Error bars show 95% confidence intervals. n = 217 Metro, 190 Mountain, 193 Suburban customers."

The overlapping error bars tell the reader at a glance that the regions' spending isn't very different. A caution in reading them: overlapping 95% intervals don't prove two means are equal, and slightly overlapping ones can still differ significantly. For a formal comparison, use the test. The error bars are for honest display.

14.6.3 Other habits of honest charts

• Label everything: a title that states the finding ("Longer waits, lower satisfaction"), axis titles with units, and the data source and sample size in a note.
• Use the same scale when charts will be compared side by side.
• Skip 3-D effects, shadows and pie charts with many slices. They make values harder to read.
• Show the whole period, not the window that happens to support your point.
• Let the chart type match the variables: columns for comparing groups, a scatterplot for two numeric variables, a line for change over time.

14.7 A Report Sheet in Excel

The memo is for reading. The workbook is for checking. A good analysis workbook ends with a report sheet that pulls the key results together in one place, linked to the sheets they came from.

A layout that works:

Area	What goes there
Top rows	Title, date, author, and one sentence on the data used ("Ridgeline 2025 daily sales, survey and staff records").
Bottom line	The memo's bottom line, in a merged cell with text wrapping.
Key results table	One row per finding: the question, the estimate, its 95% range, the method, and the sheet it came from.
Charts	One honest chart per key finding, sized to fit the page.
Verification	For each key number, the R value, the Excel check, and a cell that says whether they match.
Limitations	Three or four short bullets.

Two Excel habits make a report sheet trustworthy:

• Link, don't retype. If the coupon difference is in cell B17 of the sheet R for Excel created, enter ='Coupon test'!B17 in the report rather than typing 3.81. If the analysis is rerun, the report updates, and nobody can introduce a typo. Use =ROUND(…,2) or Home > Number Format to control how many decimals show.
• Build a match check. In the verification area, put the R result in one cell, the Excel check (for example =T.TEST(…)) in the next, and =IF(ABS(B5-C5)<0.001,"Match","CHECK") in a third. A "CHECK" in red (Home > Conditional Formatting > Highlight Cells Rules > Text that Contains) tells you something changed.

You can also write sentences that update themselves. ="Coupon customers spent "&TEXT('Coupon test'!B17,"$0.00")&" more over 30 days." produces "Coupon customers spent $3.81 more over 30 days." and keeps the number linked.

To print or share it as a PDF, select the report area and choose Page Layout > Print Area > Set Print Area, then on Page Layout set Width to 1 page. File > Export > Create PDF/XPS gives a one-page attachment.

14.8 Using AI to Draft and Critique

An AI assistant is a useful writing partner, as long as you remember who the author is. It can tighten prose, suggest structure, and catch claims that go beyond the evidence. It can also round a number wrongly, flip a sign, turn "associated with" into "causes," or invent a statistic that sounds right. You're responsible for every word and number in your memo.

Two uses work especially well.

14.8.1 Critique a draft

Write your own first draft, then ask the AI to attack it. Overclaiming causation is the most common problem in business analysis writing, and an AI is good at spotting the language of cause. Paste your draft after a prompt like this:

Read the critique as you'd read a colleague's comments. Accept the suggestions that make the memo more accurate. Reject the ones that make it vaguer, longer or wrong. An AI will sometimes over-correct, hedging even the coupon finding that a randomized test supports. Telling it which findings came from an experiment, as the prompt above does, helps.

14.8.2 Turn a results sheet into plain-language bullets

Copy a results sheet from Excel (for example, the Model B regression sheet from Chapter 13. Multiple Regression) and paste it into the AI with a prompt like this:

Asking the AI to list where each number came from makes your checking quick: go down the list and compare each one with the sheet. Then check the meaning. Did it describe Metro as "compared with Suburban"? Did it interpret the intercept, which you know is meaningless? Did "goes with" become "causes"?

14.9 Common Pitfalls: A Checklist

Run through this list before you send any analysis to a decision maker. Each item is a mistake that this book's data showed you how to catch.

• Correlation isn't causation. Is your evidence from a randomized experiment or observational data? Only the coupon test was randomized. For everything else, write "associated with" and say what else could explain the pattern.
• Watch for confounding, including reversals. Could a third variable explain the relationship? Seats looked worth 6.2 transactions each until region was added, and then 2.0. Region looked like the cause of low Metro satisfaction until wait time was added. When a lurking variable is strong enough, an apparent effect can shrink, vanish or even reverse direction, a pattern known as Simpson's paradox. Ask what differs between the groups besides the thing you're studying.
• Multiple testing. At a 0.05 significance level, about one test in 20 will look significant by chance even when nothing is going on. The survey's correlation matrix had 10 pairs; test enough pairs, and something will turn up. Decide on your main question before you look, use methods built for many comparisons (like Tukey HSD), and treat a surprise found by searching as a lead to check with new data.
• Statistical versus practical significance. With 4,380 store-days, temperature's correlation with transactions was "significant" at r = −0.06, explaining under 1% of the variation. Always report the size of an effect, in business units, not just its p-value.
• Extrapolation. Don't predict outside the range of your data. The wait model knows nothing about 15-minute waits.
• Non-random samples. Who's in your data, and who's missing? A survey of customers who chose to respond, or of one store's mobile users, may not represent all customers. Customers who gave up and left the line may never have been surveyed at all.
• The wrong unit. Check what one row is. Averaging store averages isn't the same as averaging store-days. Store features like seats vary across 12 stores, not 4,380 rows.
• Dependent observations. The same store on consecutive days isn't 365 independent observations. Methods that assume independence will overstate your precision.
• Unverified numbers. Report only numbers that came from an analysis that actually ran on your data, and that you checked a second way.

14.10 Your Capstone Project

The capstone puts the whole semester together. You'll pick a business question, answer it with the workflow from this book, and report your answer to a decision maker.

14.10.1 The assignment

1. Choose a question. Use the Ridgeline data, or your own data set if your instructor approves it. It must be a question that a manager would care about and that the data can answer, and it must need at least one inferential method from Chapter 7. Confidence Intervals onward. Some Ridgeline questions this book hasn't answered:
   • Does the promo-day lift in transactions differ by region?
   • Do loyalty members spend more per visit than non-members, after accounting for age?
   • Is a store's average ticket related to its region or its drive-thru?
   • Does hourly wage go with higher customer ratings, holding role and tenure constant?
   • Is revenue per seat higher at stores with a drive-thru?
   • Do the coupon's effects on spending differ between customers who redeemed it early and late? (Check first whether the data can answer this. Part of the skill is recognizing when they can't.)
2. Prepare the data in Excel. Use Tables, helper columns and lookups as needed, and document every step on a "Notes" sheet.
3. Explore. Include descriptive statistics and at least one chart.
4. Analyze with AI and R for Excel. Save your data description, the AI conversation, and the script you ran. Mark anything in the script you changed, and why.
5. Verify each key result with an Excel function or the ToolPak, and check the method's assumptions.
6. Build a report sheet with linked results, at least one honest chart with error bars or another display of uncertainty, and a verification block.
7. Write a one-page memo to the person who would make the decision, following the structure in this chapter.
8. Use AI to critique your memo, and include a short note (three to five sentences) on which suggestions you accepted and rejected, and why.

Submit the workbook and the memo, with the AI conversations as an appendix.

14.10.2 Rubric

Criterion	Points	Full credit	Partial credit
Question and data	10	A specific question tied to a decision; the row, sample and variables (with types) are clearly identified.	The question is vague or doesn't connect to a decision, or variable types are misidentified.
Data preparation	15	Tidy Excel Tables, correct types, missing values and duplicates handled, helper columns built with correct formulas, steps documented.	Some preparation is missing or undocumented, or a formula error affects the data.
Method choice and understanding	15	The method fits the question and variable types; the memo or notes explain in plain words what it asks and assumes, and why it was chosen over alternatives.	The method fits but isn't explained, or a better-fitting method was overlooked.
AI use and script reading	10	A complete data description; the script is checked line by line for data, variables, test and options; any changes are explained.	The description is missing meaning or context, or the script was run without evidence of reading it.
Verification and assumptions	15	Every key number is reproduced in Excel and matches; assumptions are checked with an appropriate plot or summary.	Some numbers are unverified, or assumptions aren't checked.
Interpretation and uncertainty	15	Results are stated in business units with confidence intervals in plain words; causal language matches the study design; practical significance is discussed.	Results are reported mainly as p-values, uncertainty is missing, or causation is overclaimed.
Memo	10	Bottom line first; clear evidence, recommendation and limitations; one page; no jargon; every number traceable to the workbook.	The answer is buried, jargon or raw output appears, or numbers can't be traced.
Report sheet and chart	10	Linked results, a verification block, and an honest, fully labeled chart with uncertainty shown.	Results are retyped rather than linked, or the chart misleads (for example, a truncated bar axis) or lacks labels.
Total	100

Points off are deserved most for an unsupported claim of cause, a number that doesn't match the analysis, and a memo that doesn't answer the question. Points are earned most for honest, clear judgment, including saying plainly what the data can't tell you.

14.11 Summary

The last step of any analysis is helping someone decide. A decision guide that starts from the question and the types of variables leads you to the right method, and a twelve-step workflow takes you from question to verified result: Excel for preparation and checking, the AI for planning and writing the script, R for Excel for running it, and you for every judgment along the way.

A findings memo puts the bottom line first, then gives evidence in business units, uncertainty in plain words, recommendations that include a way to learn more, and honest limitations. Its language matches the evidence: only a randomized experiment, like Ridgeline's coupon test, supports "caused." Honest charts start bars at zero and show uncertainty with error bars, and a report sheet links every number to its source. AI can draft and critique, but you verify every number and remain the author. Before you send anything, run through the pitfalls: causation, confounding, multiple testing, practical significance, extrapolation, non-random samples, the wrong unit, dependence and unverified numbers. Then do it all yourself in the capstone.