📈Applied Impact Evaluation Unit 6 – Statistical Analysis in Impact Evaluation

Key Concepts and Definitions

• Impact evaluation assesses the changes in outcomes that can be attributed to a specific intervention or program
• Counterfactual represents the outcomes that would have occurred in the absence of the intervention
• Treatment group consists of individuals or units that receive the intervention being evaluated
• Control group serves as a comparison and does not receive the intervention
• Selection bias occurs when the treatment and control groups differ systematically in ways that affect the outcome of interest
• Randomization assigns individuals or units to treatment and control groups by chance, helping to minimize selection bias
• Statistical significance indicates the likelihood that observed differences between groups are due to chance rather than the intervention
  • Commonly accepted significance levels include 0.05 (5%) and 0.01 (1%)
• Effect size measures the magnitude of the difference between the treatment and control groups

Types of Statistical Analysis in Impact Evaluation

• Descriptive analysis summarizes and describes key features of the data (central tendency, dispersion, and distribution)
• Inferential analysis uses sample data to make generalizations about the population from which the sample was drawn
• Hypothesis testing evaluates whether observed differences between groups are statistically significant or due to chance
• Regression analysis examines the relationship between the intervention and the outcome while controlling for other variables
• Difference-in-differences analysis compares changes in outcomes over time between the treatment and control groups
• Propensity score matching creates a comparison group that is similar to the treatment group based on observable characteristics
• Instrumental variables analysis uses an external factor that influences participation in the intervention but not the outcome to estimate causal effects
• Regression discontinuity design exploits a cutoff point that determines assignment to the treatment or control group

Data Collection and Preparation

• Develop a clear and comprehensive data collection plan that aligns with the research questions and evaluation design
• Use reliable and valid measurement instruments to capture relevant variables and outcomes
• Ensure that data collection procedures are standardized and consistently applied across all participants or units
• Train data collectors to minimize errors and biases in the data collection process
• Conduct pilot testing to identify and address any issues with the data collection instruments or procedures
• Use appropriate sampling techniques (random sampling, stratified sampling) to ensure representativeness of the sample
• Clean and preprocess the data to handle missing values, outliers, and inconsistencies
  • Techniques include listwise deletion, pairwise deletion, mean imputation, and multiple imputation
• Document and maintain a codebook that describes the variables, their definitions, and coding schemes

Descriptive Statistics and Exploratory Data Analysis

• Calculate measures of central tendency (mean, median, mode) to summarize the typical values in the data
• Compute measures of dispersion (range, variance, standard deviation) to assess the spread of the data
• Examine the distribution of variables using histograms, density plots, and box plots to identify skewness, kurtosis, and outliers
• Explore relationships between variables using scatter plots, correlation coefficients, and contingency tables
• Conduct subgroup analyses to examine differences in outcomes across different categories of participants or units
• Use data visualization techniques (bar charts, line graphs, heat maps) to communicate patterns and trends in the data
• Identify potential data quality issues, such as missing data patterns, measurement errors, and inconsistencies
• Assess the balance between treatment and control groups on key baseline characteristics to ensure comparability

Inferential Statistics and Hypothesis Testing

• Formulate null and alternative hypotheses that specify the expected relationship between the intervention and the outcome
• Select an appropriate statistical test based on the type of data, the distribution of the variables, and the research question
  • Common tests include t-tests, ANOVA, chi-square tests, and non-parametric tests (Wilcoxon rank-sum, Kruskal-Wallis)
• Set the significance level (alpha) to determine the threshold for rejecting the null hypothesis (typically 0.05 or 0.01)
• Calculate the test statistic and p-value to assess the strength of evidence against the null hypothesis
• Interpret the results in terms of statistical significance and practical significance (effect size)
• Adjust for multiple comparisons when conducting multiple hypothesis tests to control the familywise error rate (Bonferroni correction, Holm-Bonferroni method)
• Report confidence intervals to provide a range of plausible values for the population parameter
• Conduct power analysis to determine the sample size needed to detect a meaningful effect with a desired level of statistical power

Regression Analysis Techniques

• Use simple linear regression to model the relationship between a continuous outcome variable and a single predictor variable
• Employ multiple linear regression to examine the relationship between a continuous outcome variable and multiple predictor variables
• Interpret regression coefficients as the change in the outcome variable associated with a one-unit change in the predictor variable, holding other variables constant
• Assess the goodness of fit of the regression model using the coefficient of determination (R-squared) and adjusted R-squared
• Check regression assumptions (linearity, independence, normality, homoscedasticity) using diagnostic plots and tests
  • Residual plots, Q-Q plots, and Durbin-Watson tests can help assess these assumptions
• Use logistic regression to model the relationship between a binary outcome variable and one or more predictor variables
• Interpret odds ratios as the change in the odds of the outcome occurring associated with a one-unit change in the predictor variable
• Employ Poisson regression to model the relationship between a count outcome variable and one or more predictor variables
• Use robust standard errors to account for heteroscedasticity or clustered data in regression models

Interpreting and Reporting Results

• Present results in a clear, concise, and accessible manner, tailored to the intended audience (policymakers, practitioners, researchers)
• Use tables and figures to summarize key findings and illustrate patterns in the data
• Report effect sizes and their interpretation to convey the practical significance of the results
• Discuss the statistical significance of the findings and their implications for the research questions and hypotheses
• Provide context for the results by comparing them to previous research and discussing their contribution to the existing knowledge base
• Acknowledge the limitations of the study and the potential threats to internal and external validity
• Offer recommendations for policy, practice, and future research based on the findings
• Use appropriate language and terminology to communicate statistical concepts and results to non-technical audiences
• Adhere to reporting guidelines (CONSORT, STROBE, TREND) to ensure transparency and completeness of the reporting

Limitations and Ethical Considerations

• Recognize and discuss potential sources of bias (selection bias, measurement bias, confounding) that may affect the validity of the results
• Consider the generalizability of the findings to other populations, settings, or contexts (external validity)
• Address missing data and attrition, and discuss their potential impact on the results and conclusions
• Ensure that the study design and analysis plan are prespecified to avoid data dredging and selective reporting
• Obtain informed consent from participants and protect their privacy and confidentiality throughout the research process
• Consider the potential risks and benefits of the intervention and the evaluation for participants and communities
• Engage stakeholders (participants, community members, policymakers) in the design, implementation, and interpretation of the evaluation
• Ensure that the evaluation is culturally sensitive and respects the values, beliefs, and traditions of the participants and communities
• Disseminate the findings to relevant stakeholders and communities in an accessible and timely manner
• Adhere to ethical guidelines and regulations (Belmont Report, Declaration of Helsinki) and obtain approval from institutional review boards (IRBs) when required