JANUARY 2014

Perspectives from the field

Rigorous evaluation 

of financial capability 

strategies: Why, when 

and how
2 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

Table of contents

1. Introduction: The need for rigorous evaluation of financial 

capability strategies .............................................................................................3

2. When is a randomized controlled trial (RCT) suitable?.....................................6

3. How to conduct a strong study: Solutions to common challenges .................9

3.1 Research design ........................................................................................9

3.2 Research implementation ...................................................................... 12

3.3 Data collection and analysis ................................................................... 14

4. Implications for practice, policy, and funding..................................................17
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1. Introduction: The need for 

rigorous evaluation of 

financial capability strategies

The recent economic downturn raised awareness about the complexity of both our financial 

marketplace and the decisions consumers must make to manage their finances effectively. 

Despite the availability of a wide range of information about managing money and about 

financial products and services, many consumers still struggle to make the financial decisions 

that serve their life goals, a situation which can have significant long-term consequences for 

individuals and families. Therefore, helping consumers make well informed financial decisions 

that will serve them today and in the future is critical to the long term financial well-being of 

Americans. 

The Dodd-Frank Wall Street Reform and Consumer Protection Act mandates that the Consumer 

Financial Protection Bureau (CFPB or Bureau) work to improve the financial literacy of 

American consumers. The Bureau is developing and implementing initiatives to educate and 

empower consumers to make better-informed financial decisions. This requires that we know 

what approaches are effective in improving financial decision making and financial well-being.

While the base of evidence regarding approaches aimed at improving financial decision making 

and outcomes (i.e. financial capability strategies) is growing, there remains too little rigorous 

empirical support. The implication of this is that service providers, financial institutions, policy 

makers, and funders have not been able to draw solid conclusions about which strategies are 

most effective. According to a 2011 Government Accountability Office (GAO) report on financial 

literacy, “[r]elatively few evidence-based evaluations of financial literacy programs have been 
4 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

conducted, limiting what is known about which specific methods and strategies are most 

effective.”1 The Financial Literacy and Education Commission (FLEC),2 comprised of 22 federal 

agencies and of which the Bureau’s Director serves as Vice-Chair, also puts effectiveness at the 

top of its research agenda.3

In order to support and guide efforts to improve the effectiveness and quality of financial 

education, the CFPB is taking up this challenge to provide stronger evidence of what works to 

improve financial decision making and financial well-being, while ensuring the appropriate 

research protections for consumers. This effort will help us and a range of providers improve 

consumer decision making and outcomes. The Office of Financial Education, in coordination 

with the Office of Research, has developed a research program that focuses on (1) determining 

how to measure financial well-being, and identifying the knowledge, skills, and habits associated 

with financially capable consumers, (2) evaluating the effectiveness of existing approaches to 

improving financial decision making and outcomes, and (3) developing and evaluating new 

approaches.

As part of our research program to evaluate the effectiveness of existing approaches, the CFPB 

has contracted with the Urban Institute to engage in rigorous quantitative evaluation of 

promising financial education strategies, and to convene a peer learning network of other 

financial capability researchers and practitioners engaged in rigorous program evaluation using 

randomized controlled trials (RCTs) to measure program impact.

Given the promise that RCTs hold to produce the highest standard of quantitative evidence 

about the effectiveness of an intervention, but also given the difficulty of successfully 

implementing these studies in practical settings, the Urban Institute and the CFPB convened a 

roundtable discussion with a peer learning network on the benefits, challenges and best 

 

1 U.S. Government Accountability Office, GAO-11-614, Financial Literacy: A Federal Certification Process for 

Providers Would Pose Challenges (June 28, 2011), available at http://www.gao.gov/assets/330/320203.pdf.

2 Congress established FLEC in 2003 with the mandate to improve the financial literacy and education of Americans, 

and to coordinate financial education efforts in the federal government. It is chaired by the Secretary of the Treasury.

3 Financial Literacy & Education Commission, Research and Evaluation Working Group, 2012 Research Priorities and 

Research Questions, available at http://www.treasury.gov/resource-center/financialeducation/Documents/2012%20Research%20Priorities%20-%20May%2012.pdf.
5 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

practices of conducting RCTs in the financial capability field in April 2013. In addition to Urban 

Institute and CFPB staff, 26 evaluators, funders, and program staff—all of whom were involved 

in ongoing or recent evaluations of financial capability programs—discussed their experiences 

and shared practical and useful insights into successful strategies and pitfalls of conducting 

rigorous evaluation of financial capability interventions. 

The purpose of this report4 is to share those insights with other researchers, practitioners, and 

funders undertaking or contemplating rigorous research into the effectiveness of different 

financial capability approaches. This sharing is critical because without a growing body of 

rigorous evidence of what works, assessments about whether the programs being offered will 

actually give consumers the skills and tools they need to make better financial decisions will 

continue to be inconclusive.

 

4 This publication is based on a report to the CFPB prepared by Urban Institute researchers Brett Theodos, Margaret 

Simms, Claudia Sharygin, Rachel Brash, and Dina Emam under contract number CFP-12-Z-00006.
6 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

2. When is a randomized 

controlled trial (RCT) 

suitable?

RCT evaluations select units (individuals, schools, neighborhoods, etc.) at random from the 

same population, and assign them to one of at least two groups: treatment (sometimes called 

experimental) or control. Such a process helps to make the treatment and control groups 

equivalent—for example, with respect to motivation, ability, knowledge, socioeconomic and 

demographic characteristics, etc.—at the start of the study. Then, if all goes well, any differences 

in outcomes between the treatment and control groups observed after the intervention can be 

attributed to the intervention specifically. In other words, the control group is the counterfactual 

that helps observers understand what would have happened to the treatment group were it not 

for the intervention.5

However, not all financial capability programs are well-suited to be the subject of such rigorous 

evaluation. Program evaluation—and RCT evaluations in particular—can be time-intensive and 

expensive, and many programs may not have the operational capacity or client volume to justify 

participation in such a study. Even well-established programs with large client bases may find it 

difficult to participate in an evaluation without external support. Further, it is important to 

consider how delaying or denying service to the control group could impact the control 

participants. As described in more detail below, to address this issue, the RCT might be 

conducted as a study of a pilot program or a new service or to perform random assignment 

 

5 For a more thorough explanation of RCTs see Wholey, Hatry, and Newcomer (2010) Handbook of Practical 

Program Evaluation or Shadish, Cook, and Campbell (2002) Experimental and Quasi-Experimental Designs for 

Generalized Causal Inference.
7 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

before individuals are even offered the service. Funding supporting these evaluations is limited, 

which puts more pressure on the studies that are conducted to be well-planned and wellexecuted.

Participants in the convening agreed that, where feasible, the RCT is the preferred way to 

measure a program’s effectiveness. The convening participants identified key criteria for 

determining whether to go ahead with a potential evaluation. The first three criteria are factors 

that cannot easily be addressed in the short run. The final three criteria are likely more 

amenable to change during the process of exploring the possibility and desirability of an RCT in 

a specific situation. 

Scalability and replicability

RCT studies often have high opportunity costs and actual costs, and research funding should be 

directed toward studies whose findings will be widely relevant or replicable to other sites.

Organizational capacity and size

The program itself should be well implemented and managed, and have the operational capacity 

to assist in the implementation of the study. Further, the program should be of sufficient size, or 

be capable of growing to a size large enough, to support an evaluation (in terms of the number of 

individuals enrolled in the study and treated). The minimum number of study participants 

needed depends on the expected size of the effect. The smaller the expected marginal effect of 

the program, relative to outcomes for the control group, the larger the number of participants 

needed to reasonably expect the study to detect an impact on clients.

Program stability

Program design can shift in response to staffing changes or funding mandates. It is often quite 

important that programs demonstrate a track record of stable service delivery, in order to have 

worked out the kinks in implementation before becoming the subject of a rigorous evaluation.

However, an established track record is less critical for interventions that vary a discrete 

component of an program, or if the intervention itself is less complex or less reliant on people 

for the delivery of services, such as an RCT involving a new application of technology.

Adequate funding for program operations and evaluation and buy-in from funders

Programs should have sufficient resources to implement the model throughout the evaluation 

period, while remaining faithful to the research design. This may require additional funding to 
8 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

increase the number of individuals served or for gathering and entering data, as well as buy-in 

and support for the study (and its randomized design) from existing funders and board 

members.

Buy-in and research planning participation from front line staff

Front-line staff who will need to be involved in study implementation on a day-to-day basis need 

to be fully invested in the study and involved in designing implementation and data collection 

strategies. This includes the staff responsible for recruiting study participants, assigning 

participants to treatment and control groups, providing the financial intervention, managing 

data. As one researcher said, “I won’t do a research project with a program without the IT 

person signing off.”

Close working relationship between evaluators and providers

Both parties should see the evaluation as a partnership, have an equal commitment to the 

fidelity and success of the study, and be willing to listen and contribute to making it work. Both 

sides should expect a heavy dose of upfront talks during the research design and early 

implementation phases, as well as frequent ongoing communications once the study is up and 

running. 
9 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

3. How to conduct a strong 

study: Solutions to common 

challenges

Researchers face a number of challenges in designing and executing RCT evaluations of financial 

capability programs. The convening participants identified common obstacles to do with 

research design, research implementation, and data collection and analysis, and they offered 

ideas for overcoming these challenges.

3.1 Research design

The first set of obstacles researchers and programs face relate to research design. Can the study 

support an RCT design? What should target enrollment be? How will study participants be 

randomized? Do new partners need to come aboard for the study to be viable? For questions 

such as these, the attendees of the convening identified a number of areas that require special 

attention from researchers and program partners during the study design phase.

Scope of evaluation

One major challenge in research design is determining the appropriate scope of the evaluation—

e.g., how many outcomes to measure and how long to follow study participants. Certain 

outcomes, such as building up savings or improving credit scores, may take months or years to 

develop or may be costly and difficult to measure. Researchers, practitioners, and funders 

should be realistic in approaching the tradeoff between the importance of obtaining data on 

numerous financial behavioral outcomes versus the feasibility of observing change in these 

outcomes within the scope of the study.
10 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

Limited sample size

The biggest challenge facing most RCTs is generating a large enough sample of study 

participants to measure program effects with statistical precision. Limited resources, difficulty 

recruiting participants, and participants dropping out before they attend sessions or complete 

all surveys all hamper evaluators’ efforts to reach target sample sizes. A limited sample size may 

require a research design focused on one or two central outcomes where the largest average 

effect sizes are anticipated across the full study population. Other outcomes might be considered 

or explored but not rigorously tested due to smaller average effects and a limited capacity to 

examine impacts on different subgroups. Many researchers hope that the financial capability 

field will identify one or two “priority” outcomes that measure basic financial capability across a 

broad range of populations, contexts, and interventions—analogous to measuring patients’ 

blood pressure and body mass index in health research.

Small, difficult-to-detect changes in behavior

Often, the expected changes in behavioral outcomes are small, which makes them even more 

difficult to measure. For this reason, it may be prudent to focus on behaviors where single 

decisions or changes at the margin can have substantial long-term effects, and therefore be 

easier to detect. Examples of such behaviors are yes/no decisions such as whether a study 

participant established a savings account or an automatic bill payment, or threshold outcomes 

such as whether a study participant was able to qualify for a standard credit card (to get away 

from predatory lending) or a mortgage refinance (to a lower cost loan). One way to improve the 

likelihood of finding true but relatively small program effects is to enroll a sufficiently large 

number of study participants. The necessary research sample size to detect impacts of varying 

sizes should be clearly discussed between evaluators and program staff in the early stages of 

project feasibility discussions and research design.

Discomfort with denial or delay in service due to randomization

Funders and service providers sometimes balk at the idea of delaying or denying service to 

control participants. To allay this discomfort, the RCT might be conducted as a study of a 

relatively straightforward pilot program or a new variant on an existing service. Another option 

is to perform random assignment before individuals are even offered the service. This approach 

may work best in a setting where individuals show up for other services – such as a workplace 

program, tax filing assistance, or applying for a loan – and the treatment is framed as an 

additional benefit, or where individuals are not the ones initiating contact to begin with. It is 
11 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

also possible to implement “encouragement” designs, in which the service is available to 

everyone but is made more readily available to a random subset.

Program and study enrollment selection effects

Certain kinds of interventions rely on individuals to voluntarily participate. In these cases, 

people who choose to participate in an intervention are likely more concerned about and 

motivated to address their financial behavior than the general population. While the RCT design 

should remove any significant differences between the treatment group and the control group, 

the study participants overall may differ in important ways from the general population. This 

implies that researchers must be cautious in drawing conclusions for the general population 

from these results.

Point of randomization

Researchers acknowledged that in some circumstances, randomly assigning individuals to 

treatment and control groups as they enroll–the “coin-flip” ideal–may be infeasible. Some 

alternatives to this design that preserve the RCT approach include randomly assigning similar 

groups of individuals, or enrolling participants to the treatment group on a first-come firstserved basis and using the waitlist as a control group, if there is good reason to believe that the 

order in which people access a particular service is essentially random. Of course, an RCT need 

not compare an “all or nothing” dichotomy; it is possible to compare interventions with different 

dosages, designs, or durations.

Model fidelity

Many agreed that once a suitable program is chosen, “the less you can mess with standard 

business practice, the better,” as voiced by one convening attendee. A study will be of greater 

usefulness if it evaluates what a program does (or would do, in the case of a new approach) 

during its normal course of business. It is also more likely to be faithfully implemented if it 

places fewer new requirements on program staff. 

Input from program partners

Researchers need to proactively seek staff input on all areas of study design, including 

determining the study timeline, engaging with potential study participants, measuring changes 

in financial decision making among their target population, survey design, and data analysis 

strategies. Staff working directly with clients often provide much needed “reality checks” for the 

research design: will these plans actually work as intended, or will some idiosyncratic factor 
12 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

unexpected to researchers but well known among staff on the ground suggest a change in plans?

(Target gift cards are not useful in an area with no Target stores; proposed survey question 

wording may not be familiar to study participants, etc.) Front-line staff knows the study 

participants and program operations best, and it’s important to make use of this knowledge.

Process/implementation studies

Convening participants agreed that impact evaluations can be strengthened by including an 

implementation study, which is a descriptive account of the organization’s goals, strategies, 

methods, and activities combined with the researchers’ account of the roll-out of the RCT

evaluation. Process studies provide continuous reporting on the evaluation’s progress and help 

to put the eventual study results in context.

3.2 Research implementation

Even the most elegantly designed RCT can face difficulties when study implementation begins. 

Practitioners need the most support when transitioning from planning the study to starting the 

study. Participants had the following insights for moving smoothly from the design to 

implementation phases.

Prepare, prepare, prepare

The transition from planning to implementation should include some preparatory steps if 

possible. These include field testing surveys and doing practice runs of recruitment pitches, 

study consent procedures, randomization tools, and follow-up approaches. Some organizations 

need to hire additional service providers to handle the increased number of clients resulting 

from the study. Staff training and oversight specifically for the study, and making sure that 

staff’s questions are answered quickly and easily, are also important at the outset, and for 

continuing to develop buy-in to the study.

Enlist (and budget for) a research coordinator

Organizations can greatly benefit if they have a dedicated research coordinator whose primary 

responsibility is to manage the evaluation. The additional work associated with a research study 

may be too much for program staff to handle alone, and having a research coordinator who can 

devote significant time to this effort may be the difference between a well and poorly executed 

study. The coordinator might be employed by either the service provider or by the evaluators, 
13 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

though there are some advantages to making the coordinator a part of the organization’s staff 

(or choosing an organization that already has a coordinator on staff). A permanent research 

coordinator gains the experience and authority within the organization to build the capacity to 

participate in rigorous evaluations in the long term. An on-staff research coordinator is better 

able to understand the everyday challenges that practitioners face, particularly in difficult tasks 

like denying or delaying service to control group participants, or asking sensitive and potentially 

upsetting survey questions. Alternatively, there may be some benefits to having the research 

coordinator be directly employed by the research organization, including, potentially, employing 

a coordinator with greater experience in RCT design and implementation. Regardless of who 

employs the research coordinator, it is helpful if the individual has some training and experience 

in program evaluation or field research, as well as an understanding of the program’s 

operations.

TABLE 1: RESEARCH COORDINATOR ROLES

Research coordinators can...

Understand both the program’s need to keep their primary focus on providing services, and the 

research staff’s requirements to push the evaluation forward and maintain fidelity to the research 

design.

Translate the relative importance of each side’s priorities.

Mediate between the program staff and researchers when the requirements of each may come 

into conflict.

Minimize the evaluation’s disruptive effects on program operations.

Provide oversight and quality control for research implementation and fidelity to evaluation 

design.

Improve the program’s ability to internally track its performance. 

Align data collection efforts

In most studies, evaluators are responsible for collecting the data that will be used in the 

analysis. Evaluators should coordinate with organization staff to minimize duplicative data 

collection and duplicative contact with participants. Automated randomization and data 

collection tools that can sync easily with the organization’s existing tracking system reduce data 
14 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

entry burden, ensure fidelity to the research design, and alleviate the stress of randomization, 

are important components.

Expect bumps along the way

Even with ample preparation, it is entirely normal for things to go wrong. Both evaluators and 

program staff need to be prepared for pitfalls like lower-than-expected rates of participation in

the study, difficulty tracking down participants to receive services, important survey questions 

being misunderstood or skipped entirely, and IT problems. Good communication between 

researchers and practitioners is key to moving past these problems. Problems at start-up are less 

likely to derail an evaluation as long as they are documented and dealt with as soon as they 

arise.

3.3 Data collection and analysis

Convening participants recommended that data analysis not only be considered as the capstone 

of the research effort, but be sufficiently incorporated into the planning and research design 

stages and expand as study data become available. They offered the following advice on the use 

of data, from the early stages of a study to the final analysis.

Look at data early and often

Researchers first use program data to determine whether the program is a good candidate for 

evaluation, and to design their own data collection tools to complement the programs’ existing 

intake forms and tracking instruments. Study coordinators can also use participants’ data to 

troubleshoot the randomization, data collection, and data entry processes. Initial responses to 

financial knowledge and behavior questions can also highlight areas where the follow-up survey 

may need to be revised.

Don’t undervalue intermediate results

Program and research funders are also interested in short-term and intermediate study results

to keep the conversation active around ongoing evaluation projects and to help fulfill 

responsibilities to their stakeholders. These results may also be of interest to practitioners and 

policymakers. Research designs that incorporate theories of change for improving financial 

decision making, and logic models for the impact of program interventions, allow evaluators to 

connect early data to potential long-term outcomes.
15 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

Choose data sources deliberately

Administrative data collected by third-party organizations, and other forms of what one funder 

referred to as “naturally renewable data sources,” are increasingly useful to evaluations and to 

financial capability training more generally, but it cannot be assumed that such data will 

necessarily be available to researchers. For example, it is becoming standard practice for 

financial capability programs to review individuals’ credit reports as a part of understanding 

their financial history and how their behaviors affect their ability to obtain credit. Programs or 

interventions operated by financial institutions or third-party personal financial management 

firms frequently download information from participants’ financial accounts. However, the right 

to use such data for research purposes must be clearly established in the context of a specific 

study.

6 Additionally, researchers suggested caution in prioritizing measures that are convenient 

to collect from administrative sources but that might not reflect appropriate goals or likely 

outcomes for all participants. 

Expect realistic effects

Researchers, practitioners, policy makers, and funders stressed the importance of setting 

expectations for the evaluation’s results, both at the outset and in the data analysis stage. All 

interventions exist in a complex world with other factors affecting the outcomes of interest, and 

in many cases the results of an intervention may be statistically significant but small. To avoid 

mischaracterization of the study’s conclusions, all parties should give significant thought to how 

the results will be framed.

Consult practitioners on interpretation of findings

Researchers should gather input from practitioners and policy makers, including ones not 

directly involved with the study, to assist the researchers in understanding the meaning and 

implication of the findings. In some cases, a “negative” result might mask a positive outcome. In 

one example referenced at the convening, researchers found that debt levels increased among 

program participants, which initially seemed like a failure to improve financial behavior. When 

the researchers discussed the results with the program staff, they realized that the result was 

driven by low-income participants who now had access to credit, which allowed them to smooth 

 

6 For example, the agreements that financial capability programs have with providers of credit reports may not allow 

for the data that programs access for clients to be transferred to researchers for analysis.
16 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

financial disruptions by borrowing. Looking at these individuals’ credit reports, researchers saw 

that they were using credit responsibly. Flexibility, thoughtfulness, and communication are key 

to interpreting findings.
4. Implications for practice, 

policy, and funding

Researchers, practitioners who run financial capability programs, policymakers, and funders 

can take a number of concrete steps to expand rigorous, data-driven, experimental research on 

financial capability programs. A number of key themes emerged from conversations during the 

convening about how these different groups can prime the field for future evaluations in this 

space.

For practitioners, key steps included:

 Encourage a “culture of data” in their operations, and prioritize detailed tracking of

program activities and outcomes.

 Use data to isolate key impact metrics—those indicators that programs feel that they are 

able to move the needle on.

Programs that build this internal data collection and analysis capacity will also be able to 

document their efforts, refine their approaches, and communicate the value of their work to 

external stakeholders without a formal, external evaluation. Some programs that have 

participated in rigorous (RCT) evaluation have found that the heighted attention to data and 

metrics required by study participation helped them notice less successful elements of their 

program operations that they would not have otherwise been aware of, leading to meaningful 

improvements in their service to clients.

For evaluators, funders and policymakers, key steps included:

 Developing strategies and systems to make data collection easier, faster, less 

expensive, and more efficient. Both researchers and practitioners will benefit from 

standardized, affordable, and easy-to-use data collection and management programs.
18 RIGOROUS EVALUATION OF FINANCIAL CAPABILITY STRATEGIES

 Working with programs to develop a set of “priority outcomes”— accepted financial 

capability outcomes shared across evaluation studies.7

 Designing standardized data collection efforts around the priority outcomes, once 

established, and making sure that these outcomes are included in subsequent 

evaluations.

Practitioners need to be supported financially in their efforts to expand their data collection and 

analysis capacity. There exists something of a chicken-and-egg problem: Programs need funding 

to set up data collection systems, but have trouble fundraising without data-driven evidence of 

their program’s impact. Reducing the expense and complexity of installing these systems will 

help to address this issue. Access to a set of priority outcomes, accepted by researchers, 

practitioners, and funders, can motivate funders to help programs adopt these practices, and the 

CFPB8 and others are currently engaged in this area.

Policymakers are interested in the potential benefits of integrating financial capability strategies 

into other programs and services. Some attendees suggested supporting return on investment 

studies into the costs and benefits of such integration. Others were interested in seeing how the 

programs’ impact varies by individuals’ initial behavior and attitudes in addition to their 

demographic characteristics.

Finally, all participants emphasized that external, rigorous evaluations are often expensive and

time-consuming. It is important, therefore, to choose evaluations strategically, focusing on those 

with the most potential to further knowledge in the field.

 

7 The value and practical challenges associated with establishing and collecting consumer financial outcome metrics 

are described in detail in the CFPB’s November 2013 publication “Empowering Low Income and Economically 

Vulnerable Consumers: Report on a National Convening,” available at 

http://files.consumerfinance.gov/f/201311_cfpb_report_empowering-economically-vulnerableconsumers.pdf. 

8 The CFPB’s ongoing work to develop and advance measures of financial well-being and related outcomes is 

described on page 47 of the 2013 “Financial Literacy Annual Report,” available at

http://www.consumerfinance.gov/reports/financial-literacy-annual-report/, and on page 75 of “Empowering 

Low Income and Economically Vulnerable Consumers: Report on a National Convening,” available at 

http://files.consumerfinance.gov/f/201311_cfpb_report_empowering-economically-vulnerableconsumers.pdf.