**Activity.** Actions taken or work performed through which inputs, such as funds, technical assistance, and other types of resources are mobilized to produce specific outputs.

**Alternative hypothesis.** In impact evaluation, the alternative hypothesis is usually the hypothesis that the null hypothesis is false; in other words, that the intervention has an impact on outcomes.

**Attrition.** Attrition occurs when some units drop from the sample between one data collection round and another, for example, because migrants are not tracked. Attrition is a case of unit nonresponse. Attrition can create bias in impact evaluations if it is correlated with treatment status.

**Baseline.** Preintervention, ex-ante. The situation prior to an intervention, against which progress can be assessed or comparisons made. Baseline data are collected before a program or policy is implemented to assess the “before” state.

**Before-and-after comparison.** Also known as “pre-post comparison” or “reflexive comparison,” a before-and-after comparison attempts to establish the impact of a program by tracking changes in outcomes for program beneficiaries over time, using measurements before and after the program or policy is implemented.

**Bias.** The bias of an estimator is the difference between an estimator’s expectation and the true value of the parameter being estimated.

**Census data.** Data that cover all units in the population of interest (universe). Contrast with survey data.

**Cluster.** A cluster is a group of units that are similar in one way or another. For example, in a sampling of school children, children who attend the same school would belong to a cluster because they share the same school facilities and teachers and live in the same neighborhood.

**Cluster sample. **A sample obtained by drawing a random sample of clusters, after which either all units in the selected clusters constitute the sample, or a number of units within each selected cluster is randomly drawn. Each cluster has a well-defined probability of being selected, and units within a selected cluster also have a well-defined probability of being drawn.

**Comparison group.** Also known as a “control group.” A valid comparison group will have the same characteristics as the group of beneficiaries of the program (treatment group), except that the units in the comparison group do not benefit from the program. Comparison groups are used to estimate the counterfactual.

**Cost-benefit analysis. **Ex-ante calculations of total expected costs and benefits, used to appraise or assess project proposals. Cost-benefit can be calculated ex-post in impact evaluations if the benefits can be quantified in monetary terms and the cost information is available.

**Cost-effectiveness.** Determining cost-effectiveness entails comparing similar interventions based on cost and effectiveness. For example, impact evaluations of various education programs allow policy makers to make more informed decisions about which intervention may achieve the desired objectives, given their particular context and constraints.

**Counterfactual. **The counterfactual is an estimate of what the outcome (Y) would have been for a program participant in the absence of the program (P). By definition, the counterfactual cannot be observed. Therefore, it must be estimated using comparison groups.

**Difference-in-differences.** Also known as “double difference” or “DD.” Difference-in-differences estimates the counterfactual for the change in outcome for the treatment group by taking the change in outcome for the comparison group. This method allows us to take into account any differences between the treatment and comparison groups that are constant over time. The two differences are thus before and after, and between the treatment and comparison groups.

**Effect.** Intended or unintended change due directly or indirectly to an intervention.

**Estimate.** See “Estimator” below.

**Estimator.** In statistics, an estimator is a statistic (a function of the observable sample data) that is used to estimate an unknown population parameter; an estimate is the result from the actual application of the function to a particular sample of data.

**Evaluation.** Evaluations are periodic, objective assessments of a planned, ongoing, or completed project, program, or policy. Evaluations are used to answer specific questions, often related to design, implementation, and results.

**External validity. **To have external validity means that the causal impact discovered in the impact evaluation can be generalized to the universe of all eligible units. For an evaluation to be externally valid, it is necessary that the evaluation sample be a representative sample of the universe of eligible units.

**Follow-up survey.** Also known as “post-intervention” or “ex-post” survey. A survey that is fielded after the program has started, once the beneficiaries have benefited from it for some time. An impact evaluation can include several follow-up surveys.

**Hawthorne effect.** The “Hawthorne effect” occurs when the mere fact that units are being observed makes them behave differently.

**Hypothesis.** A hypothesis is a proposed explanation for an observable phenomenon. See also, null hypothesis and alternative hypothesis.

**Impact evaluation.** An impact evaluation is an evaluation that tries to make a causal link between a program or intervention and a set of outcomes. An impact evaluation tries to answer the question of whether a program is responsible for changes in the outcomes of interest. Contrast with process evaluation.

**Indicator. **An indicator is a variable that measures a phenomenon of interest to the evaluator. The phenomenon can be an input, an output, an outcome, a characteristic, or an attribute.

**Inputs.** The financial, human, and material resources used for the development intervention.

**Instrumental variable.** An instrumental variable is a variable that helps identify the causal impact of a program when participation in the program is partly determined by the potential beneficiaries. A variable must have two characteristics to qualify as a good instrumental variable: (1) it must be correlated with program participation, and (2) it may not be correlated with outcomes Y (apart from through program participation) or with unobserved variables.

**Intention-to-treat, or ITT, estimator. **The ITT estimator is the straight difference in the outcome indicator Y for the group to whom we offered treatment and the same indicator for the group to whom we did not offer treatment. Contrast with treatment-on-the-treated.

**Internal validity.** To say that an impact evaluation has internal validity means that it uses a valid comparison group, that is, a comparison group that is a valid estimate of the counterfactual.

**Intra-cluster correlation.** Intra-cluster correlation is the correlation (or similarity) in outcomes or characteristics between units that belong to the same cluster. (In other words, the tendency of units from the same cluster to provide similar answers to our questions). For example, children that attend the same school would typically be similar or correlated in terms of their area of residence or socioeconomic background.

**John Henry effect.** The John Henry effect happens when comparison units work harder to compensate for not being offered a treatment. When one compares treated units to those “harder-working” comparison units, the estimate of the impact of the program will be biased; that is, we will estimate a smaller impact of the program than the true impact that we would find if the comparison units did not make the additional effort.

**Matching.** Matching is a non-experimental evaluation method that uses large data sets and heavy statistical techniques to construct the best possible comparison group for a given treatment group.

**Minimum desired effect.** The minimum change in outcomes that would justify the investment that has been made in an intervention, counting not only the cost of the program and the benefits that it provides, but also the opportunity cost of not investing funds in an alternative intervention. The minimum desired effect is an input for power calculations; that is, evaluation samples need to be large enough to detect at least the minimum desired effect with sufficient power.

**Monitoring.** Monitoring is the continuous process of collecting and analyzing information to assess how well a project, program, or policy, is performing. It relies primarily on administrative data to track performance against expected results, make comparisons across programs, and analyze trends over time. Monitoring usually tracks inputs, activities, and outputs, though occasionally it includes outcomes as well. Monitoring is used to inform day-to-day management and decisions.

**Nonresponse.** That data are missing or incomplete for some sampled units constitute nonresponse. Unit nonresponse arises when no information is available for some sample units, that is, when the actual sample is diff erent than the planned sample. Attrition is one form of unit nonresponse. Item nonresponse occurs when dataare incomplete for some sampled units at a point in time. Nonresponse may cause bias in evaluation results if it is associated with treatment status.

**Null hypothesis.** A null hypothesis is a hypothesis that might be falsified on the basis of observed data. The null hypothesis typically proposes a general or default position. In impact evaluation, the default position is usually that there is no difference between the treatment and control groups, or in other words, that the intervention has no impact on outcomes.

**Outcome.** Can be intermediate or final. An outcome is a result of interest that comes about through a combination of supply and demand factors. For example, if an intervention leads to a greater supply of vaccination services, then actual vaccination numbers would be an outcome, as they depend not only on the supply of vaccines but also on the behavior of the intended beneficiaries: do they show up at the service point to be vaccinated? Final or long-term outcomes are more distant outcomes. The distance can be interpreted in a time dimension (it takes a long timeto get to the outcome) or a causal dimension (many causal links are needed to reach the outcome).

**Output. **The products, capital goods, and services that are produced (supplied) directly by an intervention. Outputs may also include changes that result from the intervention that are relevant to the achievement of outcomes.

**Population of interest.** The group of units that are eligible to receive an intervention or treatment. The population of interest is sometimes called the universe.Power.The power is the probability of detecting an impact if one has occurred. The power of a test is equal to 1 minus the probability of a type II error, ranging from 0 to 1. Popular levels of power are 0.8 and 0.9. High levels of power are more conservative and decrease the likelihood of a type II error. An impact evaluation has high power if there is a low risk of not detecting real program impacts, that is, of committing a type II error.

**Power calculations.** Power calculations indicate the sample size required for an evaluation to detect a given minimum desired effect. Power calculations depend on parameters such as power (or the likelihood of type II error), significance level, variance, and intra-cluster correlation of the outcome of interest.

**Process evaluation.** A process evaluation is an evaluation that tries to establish the level of quality or success of the processes of a program; for example, adequacy of the administrative processes, acceptability of the program benefits, clarity of the information campaign, internal dynamics of implementing organizations, their policy instruments, their service delivery mechanisms, their management practices, and the linkages among these. Contrast with impact evaluation.

**Random sample. **The best way to avoid a biased or unrepresentative sample is to select a random sample. A random sample is asample in which each individual in the population being sampled has aprobability of being selected that is both positive and well-defined. Notice that the selection probability does not need to be the same for all individuals in the population; when this is the case, the sample is called anequal-probability sample. If, furthermore, the individuals are selected independently of each other, the sample is called asimple random sample.

Randomized assignment or randomized control designs.Randomized assignment is considered the most robust method for estimating counterfactuals and is often referred to as the “gold standard” of impact evaluation. With this method, beneficiaries are randomly selected to receive an intervention, and each has an equal chance of receiving the program. With large-enough sample sizes, the process of random assignment ensures equivalence, in both observed and unobserved characteristics, between the treatment and control groups, thereby addressing any selection bias.

**Randomized offering.** Randomized offering is a method for identifying the impact of an intervention. With this method, beneficiaries are randomly offered an intervention, and each has an equal chance of receiving the program. Although the program administrator can randomly select the units to whom to offer the treatment from the universe of eligible units, the administrator cannot obtain perfect compliance: she or he cannot force any unit to participate or accept the treatment and cannot refuse to let a unit participate if the unit insists on doing so. In the randomized offering method, the randomized offering of the program is used as an instrumental variable for actual program participation.

**Randomized promotion.** Randomized promotion is a method similar to randomized offering. Instead of random selection of the units to whom the treatment is offered, units are randomly selected for promotion of the treatment. In this way, the program is left open to every unit.

**Randomized selection methods. **“Randomized selection method” is a group name for several methods that use random assignment to identify the counterfactual. Among them are randomized assignment of the treatment, randomized offering of the treatment, and randomized promotion.

**Regression. **In statistics, regression analysis includes any techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. In impact evaluation, regression analysis helps us understand how the typical value of the outcome indicator Y (dependent variable) changes when the assignment to treatment or comparison group P (independent variable) is varied, while the characteristics of the beneficiaries (other independent variables) are held fixed.

**Regression discontinuity design (RDD). **Regression discontinuity design is a no-experimental evaluation method. It is adequate for programs that use a continuous index to rank potential beneficiaries and that have a threshold along the index that determines whether potential beneficiaries receive the program or not. The cutoff threshold for program eligibility provides a dividing point between the treatment and comparison groups.

**Results chain.** The results chain sets out the program logic that explains how the development objective is to be achieved. It shows the links from inputs to activities, to outputs, to results.

**Sample.** In statistics, a sample is a subset of a population. Typically, the population is very large, making a census or a complete enumeration of all the values in the population impractical or impossible. Instead, researchers can select a representative subset of the population (using a sampling frame) and collect statistics on the sample; these may be used to make inferences or to extrapolate to the population. This process is referred to as sampling.

**Sampling. **Process by which units are drawn from the sampling frame built from the population of interest (universe). Various alternative sampling procedures can be used. Probability sampling methods are the most rigorous because they assign a well-defined probability for each unit to be drawn. Random sampling, stratified random sampling, and cluster sampling are all probability sampling methods. Non-probabilistic sampling (such as purposive or convenience sampling) can create sampling errors.

**Sampling frame. **The most comprehensive list of units in the population of interest (universe) that can be obtained. Differences between the sampling frame and the population of interest create a coverage (sampling) bias. In the presence of coverage bias, results from the sample do not have external validity for the entire population of interest.

**Selection bias.** Selection bias occurs when the reasons for which an individual participates in a program are correlated with outcomes. This bias commonly occurs when the comparison group is ineligible or self-selects out of treatment.

**Significance level.** The significance level is usually denoted by the Greek symbol, α (alpha). Popular levels of significance are 5 percent (0.05), 1 percent (0.01), and 0.1 percent (0.001). If a test of significance gives a p value lower than the α level, the null hypothesis is rejected. Such results are informally referred to as “statistically significant”. The lower the significance level, the stronger the evidence required. Choosing the level of significance is an arbitrary task, but for many applications, a level of 5 percent is chosen for no better reason than that it is conventional.

**Simple random sample.** A random sample (see above) in which all units of the population are selected with the same probability, and independently of each other.

**Spillover effect.** Also known as contamination of the comparison group. A spillover effect occurs when the comparison group is affected by the treatment administered to the treatment group, even though the treatment is not administered directly to the comparison group. If the spillover effect on the comparison group is negative (that is,if they suffer because of the program), then the straight difference between outcomes in the treatment and comparison groups will yield an overestimation of the program impact. By contrast, if the spillover effect on the comparison group is positive (that is, they benefit), then it will yield an underestimation of the program impact.

**Statistical power.** The power of a statistical test is the probability that the test will reject the null hypothesis when the alternative hypothesis is true (that is, that it will not make a type II error). As power increases, the chances of a type II error decrease. The probability of a type II error is referred to as the false negative rate (β). Therefore power is equal to 1 − β.

**Stratified sample. **Obtained by dividing the population of interest (sampling frame) into groups (for example, male and female), and then drawing a random sample within each group. A stratified sample is a probabilistic sample: every unit in each group (or stratum) has a well-definedprobability of being drawn.

**Survey data.** Data that cover a sample of the population of interest. Contrast with census data.

**Treatment group.** Also known as the treated group or the intervention group. The treatment group is the group of units that benefits from an intervention, versus the comparison group that does not.

**Treatment-on-the-treated (effect of).** Also known as the TOT estimator. The effect of treatment on the treated is the impact of the treatment on those units that have actually benefited from the treatment. Contrast with intention-to-treat.

**Type I error.** Error committed when rejecting a null hypothesis even though the null hypothesis actually holds. In the context of an impact evaluation, a type I error is made when an evaluation concludes that a program has had an impact (that is, the null hypothesis of no impact is rejected), even though in reality the program had no impact (that is, the null hypothesis holds). The significance level determines the probability of committing a type I error.

**Type II error.** Error committed when accepting (not rejecting) the null hypothesis even though the null hypothesis does not hold. In the context of an impact evaluation, a type II error is made when concluding that a program has no impact (that is, the null hypothesis of no impact is not rejected) even though the program did have an impact (that is, the null hypothesis does not hold). The probability of committing a type II error is 1 minus the power level.

**Variable.** In statistical terminology, a variable is a symbol that stands for a value that may vary.