Determine the skewness and kurtosis for the pounds sold


Web Analytics at Quality Alloys, Inc.

Company Background

Quality Alloys, Inc. (QA)1 is a relatively small (less than $75 million in annual sales) US- based distributor of different grades of a variety of alloys used in industrial manufacturing. Its products include, for example, refractory alloys, which have the property of maintaining strength at high temperatures and are used in furnaces and aircraft turbine engines.
QA's market niche is based on a number of factors:

1. It has expert knowledge regarding which suppliers manufacture the different grades of alloys and those who do so reliability.
2. It sells in small quantities.
3. It cuts material to user-specified sizes, with tolerances of less than .001 of an inch.
4. It ships items in stock the same or next day.

QA's customers are generally small companies that make parts out of the alloys they purchase. They generally can't buy directly from mills (the alloy producers) as their orders are not large enough. These customers do not inventory the alloys purchased from QA, and they typically purchase what they need for specific jobs they have in hand. One purchase may not be an accurate predictor of future purchases; that is, one purchase may not signal what will be purchased in the future, or when a future purchase will occur. The individuals making the purchasing decisions may be engineers, purchasing agents, or the business owners.
QA is well-respected in its market space. Its competitors are other intermediaries providing similar services.

QA markets its products through direct mail, advertising in trade magazines and, more recently, via paid listings on two industrial product web portals, GlobalSpec and ThomasNet. In mid-2008 QA decided to extend its marketing reach by establishing a company web presence. The goals of the company's website were to (a) drive new sales, (b) make product and contact information available, and (c) give or add legitimacy to its brand. Further, in addition to providing QA with another opportunity for reaching out to its traditional clients, management thought the website would enable QA to extend its reach to many more customers in the United States, Europe, and Asia. The Asian market was viewed as particularly important to QA given the shift towards manufacturing in the Pacific Rim.

Given the intricacies of QA's products, the website was not designed to allow users to enter orders over the web. However, in addition to providing descriptions of the products and services offered by QA, the website does allow potential customers to submit request for quotations; that is, a request to be contacted. These requests are given to inside sales staff for follow up. As is the case for other business-to-business (B2B) providers, there's no direct way to connect a visit with a sale as there is no "shopping cart" on the website.
QA commissioned a professionally produced brochure providing an overview of the company's products and services and sent it to potential customers in mid-December 2008. The list of potential customers and their addresses was purchased by QA. The total cost of the promotion is estimated to be approximately $25K.

There are a number of questions that would be useful for QA to have answered before investing in further promotional activities. Foremost of these are the following:
- How many people visit the website? How do they come to the website?
- Is the website generating interest, and does this interest yield actual sales?
- Do traditional promotions drive web traffic, and in turn drive incremental sales?
- How can visits to the website best be modeled?
- Where and how should QA advertise?

Business Value Assessed
While the usefulness of B2B websites in terms of advertising, sales promotion, public relations, and marketing is generally recognized, valuing B2B websites remains elusive. For business-to-consumer (B2C) websites, the valuation task is facilitated by the fact that purchases are typically made via the website. Data can be compiled on sales volume, the effect of promotions on sales, how website design changes impact sales, etc. For B2B websites without "shopping cart" functionality the task is considerably more challenging. A principal conclusion of a Forrester Report on B2B marketing is that "business-to-business (B2B) marketers collect mounds of data . . . but still struggle to find effective ways to measure and demonstrate success." Some 44% of the survey respondents cited "demonstrating ROI" as the top challenge in managing their website.2
More generally, there has been a longstanding debate on the value of organizational investments in information technology (IT). Some have argued that investments in IT are

closely linked to organizational effectiveness.3 Others, on the other hand, have gone so far as to argue that "IT doesn't matter."4

Web Analytics
QA's website developer utilized Google Analytics (https://www.google.com/analytics/), a free web analytics tool so that the site would track, and QA management would have access to, a wide variety of web metrics. Google Analytics is implemented by putting the appropriate code, provided by Google, on each web page. The data collected is sent to Google; users, like QA managers, access it by logging in to their Google Analytics account. Typical metrics include the number of visitors to a site, the amount of time they spent on the site, the number of pages viewed, etc.
Apart from Google Analytics, QA participated in Google's AdWords program.5 AdWords ads are the "sponsored links" that appear next to, and sometimes above, Google search results. That is, QA paid to have these ads (with links to the QA website) appear on the Google search result page when relevant search terms (specified by QA) were used.

Assignment The Deliverable

Your job, as a trusted advisor to QA management, is to examine the value of QA's website by tracking not just website metrics (e.g., visitors, pages/visit, time per visit, etc.), but the associated (non-web-based) financial measures of sales, profit and amount of merchandise sold. One focus of your efforts should be an analysis for senior management regarding the effectiveness of QA's promotional effort.

Your report should be submitted in two parts. The first part should be an executive summary, one to two pages in length. It should summarize results and provide recommendations to QA managers as to how they might best market their business with an aim towards improving sales. Your recommendations may rely on your knowledge and experience beyond the case, but your suggestions must be supported by the data and your analyses. (You may, and probably should, do additional analyses other than those required here. You should at least review all the data.) You can use the questions from the Company Background section of this document on page three as a guide for what your summary should cover. Finally, note that this is a "real-world" case; that is, depending on your analysis you may not have all the data you want. You may certainly include as part of your recommendations that additional data be collected.

The second part of your report should be responses to the questions posed in the Analysis section that follows. Be sure your responses are numbered, corresponding with their respective questions. There is no need for added verbiage, just your answers to the questions in order. It's preferable if this is submitted in Word or .pdf format (like the first part). Excel printouts are fine as long as they are neatly formatted.

You should do the second part (the quantitative analysis) prior to doing the first part (the executive summary). Be sure to read through the entire case at least once before proceeding.

Analysis
DATA
The data for this case is provided in the Quality Alloys Data spreadsheet. The data is collected over weekly intervals for the period May 25, 2008-August 29, 2009, unless otherwise indicated. The number of visits per week, as well as some visit-related information captured by Google Analytics, is in the Weekly Visits worksheet. (The meaning of each variable is provided in the glossary at the end of this document.) Financial data, collected via the Enterprise Resource Planning (ERP) system at QA is provided in the Financials worksheet. (The revenue and profit variables are self- explanatory; the pounds sold variable represents the total number of pounds of material sold that week, and the inquiries variable captures the total number of inquiries received by the sales staff at QA. The records do not indicate which of these inquiries were generated directly from the website.) The Lbs. Sold worksheet contains pounds of material sold data over a broader time span, from January 2005-mid-July 2010. (This is the only data collected over a time frame other than May 25, 2008-August 29, 2009.) The Daily Visits worksheet contains, as you might expect, the number of daily visits to the QA website. Various "demographic" data for site visitors, also from Google Analytics, is provided in the Demographics worksheet.

DESCRIPTIVE STATISTICS
Start by getting a better sense of the data in each of the four periods.

1) Using data in the Weekly Visits and Financials worksheets, create four column charts (like Figure 1: Visits to the QA Website per Week) for unique visits over time, revenue over time, profit over time, and pounds sold over time. You do not have to indicate on these charts the cutoffs for the four periods.

2) Using the same data, calculate the following summary statistics for visits, unique visits, revenue, profit, and pounds sold: mean, median, standard deviation, minimum, and maximum, for the initial, pre-promotion, promotion, and post-promotion periods. So, for each period you should provide 25lvuaes: five summary measures for each of five variables, as per the table below for the initial period.

That is, you should create four such tables, one for each period.
Suggestion: It's probably easiest to start by copying the data for these five variables to a new spreadsheet. Then either:
a) Use the Descriptive Statistics tool for the data for each period, and then create the four tables from this output, or

b) Create a (blank) table like the one above to the right of the initial period data. Use the Excel functions to calculate the summary measures for visits for the initial period. You can then copy these values across to complete the table for the initial period. Now create another blank table for each additional period and repeat.

3) Create a column chart of the mean visits over the four periods-that is, your chart should have four columns, the first representing the mean visits during the initial period, the second representing the mean visits during the pre-promotion period, etc. Create four more such charts, this time using the mean unique visits, mean revenue, mean profit, and mean pounds sold statistics.

Suggestion: Create another (blank) table on the same worksheet that looks like the one below. Type the cell addresses for the mean visits for each period (that you already calculated) into the appropriate cells in the first column, then copy these values across to complete the table. Creating the column charts from this table is straightforward.

4) Write one or two paragraphs summarizing your findings thus far. Be sure to describe the behavior of each variable. Indicate what the results seem to show about the relationships between the variables, and the apparent effect(s) of the promotion. (In the next section you'll explore this further; feel free to make any conjectures here that seem reasonable.) Be sure to support your verbiage with your analysis results.

RELATIONSHIPS BETWEEN VARIABLES

Up until now, you've analyzed each variable separately. It would seem reasonable to look at pairs of variables and see what happens to one as the other varies.

5) Start by taking a look at revenue and pounds sold. (Before proceeding, what does your intuition say about the relationship between these two variables?) Create a scatter diagram of revenue versus pounds sold. (Revenue should be on the y, or vertical, axis.) Determine the correlation coefficient of revenue and pounds sold.

6) Now create the scatter diagram of revenue versus visits. (Given your previous work, what do you expect this plot to look like?) Determine the correlation coefficient of revenue and visits.

7) Summarize your results. In particular, elaborate on the implications of the relationship between revenue and number of visits to the website. Feel free to examine any other variable pairs you think might be important.

8) QA is interested in modeling data critical to their business. For example, if data for a particular variable appears to be reasonably approximated by a normal distribution, with a predictable mean and standard deviation, future values for that variable can be reasonably estimated. The purpose of the following exercise is to pursue this modeling process.
The Lbs. Sold worksheet contains the pounds of material sold per week from January 3, 2005, through the week of July 19, 2010.
a) Determine the following summary values for this data: mean, median, standard deviation, minimum, and maximum.
b) Create a histogram of the pounds of material sold data.

c) Describe the histogram. Does it appear bell-shaped?
Generally, simply examining the histogram has limitations for judging how well a data set follows the normal distribution. (Bear in mind, for example, that while all normal distributions are unimodal and symmetric, not all unimodal and symmetric distributions are normal.) An additional approach is to see how well the data follows the Empirical Rule.
d) Determine how well this data follows the Empirical Rule by completing the following table.

e) Refine your analysis by completing the following table for the pounds sold data.

f) How well does the data for pounds of material sold seem to follow the normal (bell-shaped) distribution? Support your response from your results in parts a through e. (I realize you don't have a standard here against which to assess "goodness of fit"-just use your best judgment.)

g) Determine the skewness and kurtosis for the pounds sold data. Are these values consistent with your analysis of the pounds of material sold data?

9) As part of the analysis, the number of daily visits to the QA website over the period May 25, 2008-August 29, 2009, was also collected. The material below is the output for the daily visits data using the same analysis you did in the previous problem for the pounds of material sold per week data. Your task in this problem is to use the two sets of output to write a paragraph or two comparing the distribution of the pounds sold data with that of the daily visit data. That is, is one more "normal" than the other? How do you know? (Note that the daily visit data is provided in the Quality Alloys Data spreadsheet; however, you may rely here solely on the output below.)

SUMMARIZING DATA/SUMMARIZING DATA GRAPHICALLY
The data in the Demographics worksheet is included to (a) more fully provide you with a sense of the type of web data that can and is collected and (b) give you with a more complete picture of QA's customers and its website.

10) Represent each set of data graphically. In each case, write a sentence or two capturing the main conclusion(s) you draw.

Attachment:- Case Workshop - Quality Alloy Inc Excel.xlsx

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