Home > Articles > Home & Office Computing > Entertainment/Gaming/Gadgets

Using Excel Tools to Handle Nested and Random Factors in ANOVA

  • Print
  • + Share This
Conrad Carlberg shows you how to use Excel's tools (including both worksheet functions and the add-ins two-factor ANOVA) to handle fixed and random factors, and crossed and nested factors.
Like this article? We recommend

Some experiments rely on settings that are to some degree intact and therefore not subject to experimental manipulation. For example, some medical research takes place in hospitals. It's often true that the experimenter cannot manipulate certain aspects of how the hospital manages health care.

Nested Factors

Suppose that an experimenter wants to investigate the effect of cardiologists' use of digital handheld devices on the success that patients have in managing their blood pressure. If doctors use digital devices to immediately access full in-patient records, modify prescriptions, and arrange changes in diets, hypertensive patients might be able to keep their blood pressure under control more effectively than in hospitals where more traditional procedures are followed.

The difficulty that might confront the experimenter is that hospitals either offer doctors that sort of digital tool or they don't. Only hospitals in transition would have some cardiologists using digital technology; and others relying on paper charts, manual prescriptions, and dietary orders.

So the experimental design might call for a factor called Digital Device Usage, which records whether a participating hospital uses the sort of digital technology that's under evaluation. The experimenter might work with two hospitals that use the technology and two that don't. At each hospital, there might be a random sample of 4 in-patients who have been in treatment for between 7 and 10 days.

What does this design look like? One way to depict it is shown in Figure 1.

Figure 1 This layout ignores Hospital as a factor in the experiment

In a sense, Figure 1 represents the experimental design. There are 16 patients, 8 in each "treatment" category: The doctor either uses digital technology or traditional pencil-and-paper methods.

But the layout in Figure 1 fails to account for any Hospital effect. As described above, there are four hospitals involved. Figure 2 shows a layout that provides hospital information.

Figure 2 This layout includes Hospital as a factor in the experiment, but it does so inaccurately

The design shown in Figure 2 is called a crossed factorial design. The term factorial simply means that there are two (or more) factors involved: Treatment and Hospital. The term crossed means that each level of each factor appears at each level of the other factor. So, for example, Hospital 1 has patients whose doctors use digital equipment and it also has patients whose doctors use traditional storage-and-retrieval methods. Treatment crosses Hospital.

But this is not how the actual design was described. There are four hospitals, not two, and each hospital employs only one level of the treatment: either digital or traditional, and not both. Figure 3 shows an accurate layout of this design.

Figure 3 This layout shows how the Hospital factor is nested within the Treatment factor

The design as described, and as laid out in Figure 3, is termed a nested factorial design. Each level of one factor appears with only one level of the other factor. Here, Hospitals 1 and 2 appear only with the Digital treatment, and Hospitals 3 and 4 appear only with the Traditional treatment.

So why should we care about a Hospital factor at all? The reason is that there may well be something about the medical care at a given hospital (or hospitals) that affects heart patients' response, quite independent of and apart from the technology, digital versus traditional, used by the medical staff.

If we ignore the Hospital factor entirely, as suggested in Figure 1, we miss any effect it may have, either attributing it to the Treatment factor or losing it in the error variance.

We might act as if the layout in Figure 2 represents reality, combining Hospitals 1 and 2, and Hospitals 3 and 4. But that gets us right back to the layout shown in Figure 1.

Therefore, we apply the nested design shown in Figure 3, including some modifications to the statistical analysis.

Nuisance Factors

In the example that this paper has been considering, you can consider Hospital as a "nuisance" factor. The experimenter is not interested in differences in patient outcomes across hospitals. The interest centers on differences in patient outcomes that can be attributed to the use of newer information technologies.

But the nature of the treatment delivery system forces the experimenter to pay attention to Hospital as a factor. At the time when the experiment takes place, only a small subset of hospitals use both traditional and newer technologies, and they do so only because they are in transition.

The experiment, therefore, can't ignore a possible Hospital factor because it might exert an influence on the outcomes achieved by cardiac patients—despite the fact that a Hospital effect isn't of interest to the experimenter. That's why such factors are sometimes termed nuisance factors: You're not really interested in them, but you have to take account of them.

Not all nested factors are nuisance factors, by any means. But it is true that nuisance factors tend to be nested, due to the realities of many experimental test beds.

Random Factors and Fixed Factors

It's also true that the experimenter in this example wants to investigate the differential effects of using handheld digital devices on the effectiveness of cardiac care, versus traditional methods of storing and retrieving patient information. The experimenter isn't interested in any other information management methods. The experiment isn't intended to generalize its findings to other methods: Its purpose is restricted to comparing outcomes that are associated with two specific methods. The Treatment factor in this example is therefore referred to as a fixed factor. The experimenter's interest is fixed on the treatments that are employed in the experiment.

In contrast, the experimenter does not want to restrict the findings to the four particular hospitals in which the research takes place. The four hospitals are randomly selected, from the population of hospitals in which doctors use handheld devices and from the population of hospitals in which the doctors don't. The Hospital factor is therefore termed a random factor.

Designs in which there is just one factor, and that factor is fixed, are among the most frequently used in the literature, whether that literature consists of market research, operations research, medical research or behavioral research. Factorial designs that employ two or more fixed factors, usually fully crossed with one another, are also popular approaches because they often bring about greater statistical power than do single factor experiments, and because they often use scarce resources more efficiently.

Another useful design is called a mixed model. A mixed model uses one or more fixed factors and one or more random factors. The example discussed earlier in this paper is a mixed model: It uses a fixed Treatment factor and a random Hospital factor.

Both mixed models and nested models call for different analysis of variance (ANOVA) computations than does a design with two fixed and crossed factors. Major differences exist in the formulas. If you use calculations that are intended for a crossed design and fixed factors when you should be using the calculations for a nested or mixed design, you can easily mistake an effect that is highly significant for one that few would consider significant.

If you have an equal number of observations in each design cell, however, the ANOVA: Two-Factor With Replication tool (part of Excel's Data Analysis add-in) is easily capable of handling both mixed models and models with a nested factor. A small amount of tweaking, after the fact, is needed.

I describe that additional work in the second paper of this series, Using Excel with Mixed and Nested Models.

  • + Share This
  • 🔖 Save To Your Account

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

Overview


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information


To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

Newsletters

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information


Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.

Security


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

Children


This site is not directed to children under the age of 13.

Marketing


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information


If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

Choice/Opt-out


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information


Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents


California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure


Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

Links


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact


Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice


We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020