A Curated Video Resource Guide for Statistics in Public Administration: From Core Concepts to Evidence-Based Decision-Making

This report serves as an essential companion to the university-level course, “Statistics for Public Administration.” It is designed to furnish instructors, curriculum designers, and students with a meticulously curated and annotated guide to high-quality, publicly available video resources that align with the course’s 48-lecture-hour syllabus. The pedagogical philosophy underpinning this guide is that the strategic integration of digital learning tools can profoundly enhance traditional instruction, particularly for an applied field like public administration. Students in this domain are future policymakers, program managers, and analysts; their primary objective is not to become theoretical statisticians but to become critical consumers and producers of quantitative evidence to inform sound governance and effective public service delivery.

The video resources selected for this guide are chosen for their ability to offer diverse teaching styles, foster visual intuition for abstract concepts, and provide practical demonstrations of statistical techniques. This approach is especially valuable for learners who benefit from seeing concepts explained in multiple modalities. The structure of this guide mirrors the course syllabus, progressing logically from foundational principles to the sophisticated framework of hypothesis testing. Throughout, the overarching theme is the empowerment of future public administrators. The goal is to equip them with the statistical literacy necessary to navigate an increasingly data-driven world, enabling them to build robust, evidence-based arguments, critically evaluate policy research, and ultimately, make more informed decisions for the public good.

Section 1: Foundations of Statistical Inquiry

This foundational unit, allocated four lecture hours, establishes the fundamental language, tools, and mindset of statistical analysis. For students of public administration, this is the bedrock upon which all subsequent evidence-based policy analysis is built. The video selections for this unit prioritize conceptual clarity, precise definitions, and a firm grasp of the critical distinction between merely describing a dataset and using it to make inferences about a larger population. Mastering these initial concepts is paramount for understanding the power and limitations of quantitative evidence in the public sector.

1.1 The Role and Language of Statistics in Public Administration

Before any calculations are performed, students must understand the why of statistics. The field provides a systematic framework for collecting, analyzing, interpreting, and presenting data. In the context of public administration, this framework is indispensable for a range of critical functions: assessing public needs, allocating scarce resources, monitoring the performance of government programs, and evaluating the impact of policy interventions. The scope of statistics is vast, encompassing everything from simple data summaries to complex predictive models.

To build this foundational understanding, a blended learning approach leveraging two distinct but complementary video series is recommended. The StatQuest with Josh Starmer – Statistics Fundamentals playlist serves as the ideal starting point for developing conceptual intuition.1 StatQuest’s methodology involves breaking down complex ideas into simple, memorable visuals and analogies, minimizing mathematical jargon in the initial stages. This approach is exceptionally effective for students who may have an aversion to mathematics, as it focuses on the logic and purpose of statistical concepts first.

Once this conceptual framework is in place, students should turn to the Professor Leonard – Statistics (Full Length Videos) playlist for a more comprehensive, university-level lecture experience.2 Professor Leonard’s videos provide the depth, detail, and mathematical rigor necessary for a full academic understanding. They function as complete, unabridged lectures that meticulously walk through definitions, formulas, and examples. The recommended pedagogical sequence is to first watch the relevant StatQuest video to grasp the core idea, and then view the corresponding Professor Leonard lecture to acquire the detailed, formal knowledge. This duality—intuition followed by rigor—provides a robust learning path for the applied learner in public administration.

1.2 Descriptive vs. Inferential Statistics: From Sample Data to Population Insights

The field of statistics is broadly divided into two main branches, and understanding this division is fundamental. Descriptive statistics involves methods for organizing, summarizing, and presenting data in an informative way. Inferential statistics involves methods for using data collected from a small group (a sample) to draw conclusions or make predictions about a larger group (a population).

For a public administrator, this distinction is a matter of daily practice. When a city manager’s office reports that the average response time for the fire department last month was 5.2 minutes, that is a descriptive statistic; it describes the data that was collected.3 However, when a political pollster uses a survey of 1,200 likely voters to predict the outcome of an election involving millions, that is an act of inferential statistics.4 The latter involves a “leap” from the sample to the population, a leap that is governed by the principles of probability and is always accompanied by a measure of uncertainty.

Two short, focused videos are highly effective for clarifying this concept. The first video, titled “Descriptive vs Inferential Statistics”, uses a simple, direct example: if a study finds that 52% of a sample of people hold a certain opinion, simply reporting this fact is descriptive. The moment one uses that 52% to “project onto the population,” the statistic becomes inferential.4 The second video, with a similar title, reinforces this with relatable examples, such as a teacher calculating the mean, median, and range of test scores for their class (descriptive) versus a business using past sales data to predict future sales (inferential).3 Both videos effectively communicate that the distinction lies not in the calculation itself, but in the intent and scope of the conclusion being drawn.

1.3 Summarizing Public Data: Measures of Central Tendency (Mean, Median, Mode)

The first step in making sense of a raw dataset is often to find its “center” or a typical value. Measures of central tendency provide this summary. The mean is the arithmetic average, the median is the middle value when the data is ordered, and the mode is the most frequently occurring value. Each measure has its strengths and is appropriate in different situations. For example, the mean income of a community can be heavily skewed by a few extremely high earners, making the median income a more representative measure of the typical resident’s financial situation. The mode is useful for categorical data, such as identifying the most common reason citizens contact a municipal service line.

The HelpYourMath – Statistics – Measures of Central Tendency playlist is an excellent resource due to its modular structure.5 It contains short, targeted videos on each specific measure, allowing students to focus on areas where they need clarification, such as “Finding the Median of a Small or Large Data Set” or understanding datasets with multiple modes (“bimodal”).5

For a concise review, the video “How to Find Mode, Median, Mean and Range” provides a clear, step-by-step walkthrough of the calculations for each measure.6 A key benefit of this video is its inclusion of the “range” (the difference between the highest and lowest values). While the range is a measure of dispersion, not central tendency, its introduction here provides a natural and seamless transition to the next critical topic: understanding the variability within a dataset. This illustrates a broader narrative in descriptive statistics—the process of data reduction, where large, complex datasets are systematically summarized into a few key, interpretable numbers.

1.4 Quantifying Variability and Consistency: Measures of Dispersion

Knowing the center of a dataset is insufficient for a complete understanding. Two cities could have the same mean emergency response time, but in one city, all response times are clustered tightly around the mean, while in the other, they are wildly inconsistent. This variability is often as important as the average. Measures of dispersion—such as variance, standard deviation, and the coefficient of variation—quantify this spread or consistency. For a public manager, low variability signifies predictability and equity in service delivery, while high variability may signal a problem requiring investigation.

Two videos effectively explain these concepts and, crucially, the relationships between them.7 The

variance is the average of the squared differences from the mean. A primary challenge with variance is that its units are squared (e.g., dollars squared), which lack intuitive meaning.7 The

standard deviation, which is simply the square root of the variance, resolves this issue by returning the measure of spread to the original units of the data (e.g., dollars). This makes the standard deviation the most commonly reported measure of variability.7

These videos then introduce a more advanced but powerful tool: the coefficient of variation (CV). The CV is calculated by dividing the standard deviation by the mean. Its great advantage is that it is a unitless measure, expressing variability as a proportion of the mean.7 This allows for meaningful comparisons of variability between two datasets that have different units or vastly different means. For instance, a public finance officer could use the CV to determine whether the budget variance in a small department with a budget of thousands of dollars is proportionally larger or smaller than the variance in a large department with a budget of millions. This ability to make standardized comparisons is an invaluable analytical tool.

Section 2: Determining the Bi-Variate Relationship

After mastering the description of single variables, the course progresses over four lecture hours to the analysis of relationships between two variables. This is the heart of much of the social and behavioral research that informs public policy. The core questions in this domain are bi-variate: Does a community policing initiative correlate with a change in residents’ trust in law enforcement? Does a job training program predict an increase in participants’ income? The videos in this section provide the tools to measure and model these relationships.

2.1 Measuring Association: Pearson and Spearman Correlation Methods

Correlation analysis measures the strength and direction of the relationship between two variables. The result, the correlation coefficient, ranges from -1 (perfect negative linear relationship) to +1 (perfect positive linear relationship), with 0 indicating no linear relationship. However, a critical distinction that is often overlooked by novice researchers is the choice between different types of correlation coefficients, a choice dictated by the nature of the data.

The Karl Pearson correlation coefficient is the most common method. It measures the strength of a linear relationship between two continuous (interval or ratio) variables. A key video, “Karl Pearson and Spearman’s Rank correlation,” explains that while this method provides a precise quantitative figure, it has important assumptions: it requires a linear relationship and is sensitive to the influence of extreme values, or outliers.

This same video introduces the essential alternative for social science research: Spearman’s rank correlation. This method is used when the data is ordinal (ranked) or when the relationship between continuous variables is monotonic but not necessarily linear. Much of the data in public administration comes from surveys using Likert scales (e.g., “Strongly Agree,” “Agree,” “Neutral”), which produce ordinal data. In these cases, Spearman’s correlation is the appropriate tool.9 The imperative to first diagnose the type of data before selecting an analytical method is a foundational principle of sound statistical practice. The Initial essentials – Correlation Coefficient playlist provides detailed, step-by-step tutorials for calculating both Pearson’s and Spearman’s coefficients, including the important procedure for handling tied ranks in the Spearman method.

2.2 Introduction to Predictive Analytics: Simple Linear Regression

Where correlation measures the existence of a relationship, regression analysis takes the next step: it attempts to model that relationship to make predictions. Simple linear regression finds the “line of best fit” that describes how a dependent variable (Y) changes as an independent variable (X) changes. The output is a simple equation, Y=a+bX, where the intercept (a) and the slope (b) have direct policy-relevant interpretations. For example, a regression analyzing the impact of public health spending on life expectancy might find a slope of 0.5, suggesting that for every additional dollar per capita spent, life expectancy is predicted to increase by half a year.

The video “Simple linear regression” provides an excellent, non-technical introduction to this topic.11 It demonstrates how to plug values into the regression equation to generate predicted outcomes. Crucially for students of public administration who will be required to produce reports, the video includes a sample APA-style write-up of the results. This demonstrates how to formally present the regression equation, the R-squared value (which measures the proportion of variance in the dependent variable explained by the independent variable), and a clear interpretation of the findings.11 While another video, “Linear Regression with Python Tutorial,” is more technically advanced, its introductory section offers a superb conceptual overview of statistical learning and its goals, providing valuable context for beginners.

It is at this juncture—the transition from correlation to regression—that the most critical mantra in statistics must be emphasized: correlation does not imply causation. A public analyst might find a strong positive correlation between the number of public parks and the crime rate across different neighborhoods. A naive interpretation would be that parks cause crime. However, a lurking variable, such as population density, is a more plausible explanation: denser neighborhoods have more people, which leads to both more parks and more crime. While regression allows for prediction, it cannot, by itself, establish a causal link. This distinction is arguably the single most important statistical lesson for a future policymaker to internalize, preventing the formulation of policy based on spurious relationships.

Section 3: The Logic of Chance: Probability Theory

This unit, allocated a substantial ten lecture hours, delves into the mathematical framework that underpins all of inferential statistics: probability theory. While it may seem abstract, this unit is the theoretical engine that drives estimation and hypothesis testing. It provides the tools to quantify uncertainty, which is the central challenge of making inferences from sample data. For public administration, probability is the basis for risk assessment (e.g., the probability of a natural disaster), program forecasting (e.g., the likely demand for a new service), and, most importantly, understanding the reliability of all sample-based research findings.

3.1 Core Concepts and Approaches to Probability

The unit begins by defining the basic terminology of probability: a sample space is the set of all possible outcomes of an experiment, and an event is a subset of the sample space. The discussion then moves to the different philosophical approaches to defining probability. The classical approach defines probability based on equally likely outcomes (e.g., the probability of heads in a coin toss is 1/2). The relative frequency approach defines probability based on long-run observation or historical data (e.g., estimating the probability of a flight delay based on the airline’s past performance). The subjective approach defines probability based on an individual’s degree of belief or expert judgment, which is often necessary when facing unique, non-repeatable events, such as the likely success of a novel policy initiative.

For students seeking a deep, rigorous, and comprehensive theoretical understanding, the MIT RES. 6-012 Introduction to Probability, Spring 2018 course, available as a playlist, is an unparalleled resource. It offers a full university-level treatment of the subject. For a more accessible introduction focused on applied examples, the Stats4Everyone – Introduction to Probability Theory playlist is highly recommended. Its videos, such as “Counting Methods: Multiplication Rule,” provide clear, step-by-step explanations of the foundational counting principles that are the building blocks for calculating more complex probabilities.

3.2 The Rules of Probability: Foundational Laws for Inference

 

Building on the basic concepts, this section introduces the fundamental laws that govern how probabilities are combined. The addition rule is used to find the probability of one event or another occurring. The multiplication rule is used to find the probability of two events occurring together. Central to this topic is the concept of conditional probability: the probability of an event occurring, given that another event has already occurred. This concept, denoted as P(A∣B), is vital in many public policy and administration contexts. For example, a public health official might need to know the probability that an individual has a specific disease, given that they have received a positive result from a diagnostic test that is not 100% accurate. Both the MIT and Stats4Everyone playlists provide detailed lectures and worked examples covering these essential rules.13

 

3.3 Theoretical Probability Distributions: Binomial and Normal

 

A probability distribution is a mathematical function that describes the likelihood of obtaining the possible values that a random variable can assume. This unit focuses on two of the most important theoretical distributions.

The Binomial distribution is a model for discrete random variables where there are a fixed number of independent trials, each trial has only two possible outcomes (often labeled “success” and “failure”), and the probability of success is constant for each trial. This is a common scenario in public administration: a grant application is either approved or denied; a citizen either uses a new online service or does not; a project is either completed on time or it is not. The available videos provide excellent, intuitive explanations of the binomial distribution, using examples like the probability of rolling a “1” on a die a certain number of times or the expected number of colorblind men in a sample.15 They demonstrate how to calculate the expected value (mean) and standard deviation for a binomial variable, which are key for making predictions.15

The Normal distribution, often called the bell curve, is the single most important distribution in all of statistics. It is a continuous probability distribution that is symmetrical about its mean, and it serves as an accurate model for a vast number of real-world phenomena in the social and natural sciences. For inferential statistics, its importance cannot be overstated. The video “Normal Distribution Tutorial” provides a clear, practical guide on a core mechanical skill: how to use a standard normal (or “z”) table to find the probability of a value falling within a certain range.17 Another video extends this by connecting the normal distribution directly to the concepts of confidence intervals and hypothesis testing, which are covered in subsequent units.18 This forward-looking connection is critical; it shows students

why they are learning about this distribution. It is the reference against which sample statistics will be compared, forming the basis for statistical inference. A student who does not grasp the concepts in this unit will be unable to understand the logic of the inferential procedures that constitute the remainder of the course.

 

Section 4: From Sample to Population: The Principles of Estimation

 

This unit, allocated five lecture hours, marks the transition from abstract probability theory to the core application of inferential statistics: estimation. The central task is to use information from a sample to estimate the value of a parameter in the broader population. How can a municipal government use a survey of 500 households to estimate the median income for the entire city? How can a federal agency use a sample of tax returns to estimate the proportion of all taxpayers who made a particular error? This unit provides the tools and the logic for making such inferences.

 

4.1 The Foundation of Inference: Sampling Distributions and Standard Error

 

The single most important and often most challenging concept in inferential statistics is the sampling distribution. It is not the distribution of data within a single sample; rather, it is the theoretical probability distribution of a statistic (such as the sample mean) obtained from all possible samples of a specific size (n) drawn from a population. A video titled “Statistical estimation and sampling distribution” provides an exceptionally clear explanation of this concept, carefully distinguishing between the “distribution of the sample data” and the “sampling distribution of the statistic”.19 It uses a powerful visual aid: imagine taking many, many random samples of size 20 from a population, calculating the mean for each sample, and then creating a histogram of all those sample means. That histogram approximates the sampling distribution of the mean.

The Central Limit Theorem, a cornerstone of statistics, states that if the sample size is sufficiently large, this sampling distribution will be approximately normal, regardless of the shape of the original population distribution. The standard deviation of this sampling distribution is called the standard error. The standard error measures the typical amount by which a sample mean is likely to differ from the true population mean, providing a direct measure of the precision of our estimate.

 

4.2 Point vs. Interval Estimation: Balancing Precision and Confidence

 

When we use a sample to estimate a population parameter, we can do so in two ways. A point estimate is a single value used to estimate the parameter. For example, if a sample survey finds that 62% of residents support a new recycling program, “62%” is the point estimate for the entire population’s support.20 While simple, a point estimate is almost certain to be wrong to some degree; the true population value is unlikely to be exactly 62.000%.

For this reason, interval estimates, also known as confidence intervals, are strongly preferred in scientific and policy contexts. An interval estimate provides a range of plausible values for the population parameter, along with a level of confidence that the interval contains the true parameter. For example, a more complete report would state: “We are 95% confident that the true proportion of residents who support the program is between 58% and 66%.”

An unconventional but highly effective resource for understanding this distinction is a Reddit discussion thread on the topic.21 The comments from statisticians and practitioners distill the core issue with remarkable clarity. One user notes, “Interval estimates contain information about uncertainty whereas point estimates do not.” Another explains that a point estimate gives the single “best guess,” but an interval estimate provides the “range of values which are also consistent with the data”.21 This quantification of uncertainty is not a flaw; it is the central feature and primary value of inferential statistics. A video resource complements this by providing the formal definitions and the formula for a confidence interval, which is constructed by taking the point estimate and adding and subtracting a margin of error.20 For a public administrator, communicating this “bounded uncertainty” is a core professional ethic. It is far more defensible and honest to provide a range of likely outcomes for a policy than to offer the false precision of a single number.

 

4.3 Practical Research Design: Determining Appropriate Sample Size

 

A critical, practical question that every public manager or researcher faces when commissioning a study is: “How many people do we need to survey?” Determining the appropriate sample size is a crucial step in research design that involves balancing analytical needs with practical constraints like time and budget. The required sample size is determined by three factors:

1. The desired margin of error: How precise does the estimate need to be? A smaller margin of error (e.g., ±2%) requires a larger sample size than a larger margin of error (e.g., ±5%).
2. The desired level of confidence: How certain do we need to be that our confidence interval contains the true population parameter? A higher level of confidence (e.g., 99%) requires a larger sample size than a lower level (e.g., 95%).
3. The variability of the population: A more heterogeneous population requires a larger sample size to achieve the same level of precision.

The video “Determining sample size” demonstrates the formula and clearly illustrates how the required sample size increases dramatically as the desired precision increases or as the population’s standard deviation grows.22 Another video on the topic introduces the practical realities of sampling, such as the formula for adjusting the sample size for a finite population and, more importantly, the unavoidable issue of sampling bias.23 This discussion is vital for public administration students, as it connects the mathematical formula to real-world constraints. A truly random sample of an entire country’s population is often impossible to obtain. Researchers must therefore be aware of potential biases in their sampling method (e.g., surveying only people with landlines) and consider how to mitigate them.23 This framing presents the sample size calculation not merely as a mathematical exercise, but as a strategic planning tool that forces a manager to confront the trade-offs between analytical rigor and available resources.

 

Section 5: The Framework of Statistical Decision-Making: Hypothesis Testing

 

This capstone unit is the most extensive in the course, allocated 25 lecture hours. It integrates all the preceding concepts—descriptive statistics, probability, and estimation—into a formal, structured procedure for making decisions with data. Hypothesis testing provides a framework for answering questions with a “yes” or “no” conclusion based on statistical evidence. Did a new public safety program have a statistically significant effect on crime rates? Is the average satisfaction score for a public service significantly higher this year than last year? This unit equips students with the tools to answer such questions rigorously.

 

5.1 The Hypothesis Testing Framework: Core Concepts and Significance

 

Hypothesis testing can be understood as a form of “statistical proof by contradiction.” The process begins with the formulation of two competing hypotheses. The null hypothesis (H0​) is a statement of the status quo or no effect. The alternative hypothesis (Ha​ or H1​) is the research hypothesis, the statement the researcher hopes to find evidence for. The logic is to temporarily assume the null hypothesis is true and then examine the sample data. If the data are highly unlikely or “surprising” under the assumption of the null hypothesis, we reject the null hypothesis in favor of the alternative.

The jbstatistics – Hypothesis Testing playlist is an outstanding central resource for this entire unit.24 Its series of short, clear videos systematically introduces all the core components of the framework, including the concept of rejection regions, the calculation and interpretation of p-values, and the meaning of statistical significance. A supplementary video provides a quick overview and introduces the modern reality of using statistical software to perform these tests, which is how most analysis is conducted in practice.25

 

5.2 The Language of Testing: Hypotheses, Test Directionality, and Decision Errors

 

Mastering the precise language of hypothesis testing is crucial. A key distinction is between one-tailed and two-tailed tests. A two-tailed test is used when the researcher is interested in any difference from the null hypothesis (e.g., Ha​: the mean is not equal to 50). A one-tailed test is used when there is a specific directional interest (e.g., Ha​: the mean is greater than 50, or Ha​: the mean is less than 50).26 The choice is dictated by the research question; keywords like “different from” or “changed” suggest a two-tailed test, while words like “improved,” “increased,” or “worsened” suggest a one-tailed test.26 A Khan Academy video and its associated comments section provide a deeper, more nuanced discussion that addresses common student questions about this topic.27

Because decisions are based on sample data, there is always a risk of error. A Type I Error occurs when we reject a true null hypothesis (a “false positive”). A Type II Error occurs when we fail to reject a false null hypothesis (a “false negative”). A video on this topic uses a powerful and memorable analogy: a courtroom trial.28 The null hypothesis is “innocent until proven guilty.” A Type I error is convicting an innocent person, while a Type II error is acquitting a guilty person. This analogy effectively conveys the trade-off between the two errors. Another video provides a more technical, visual explanation by showing how the probabilities of these errors relate to the distribution curves of the null and alternative hypotheses.29

 

5.3 Large and Small Sample Tests: Z-Tests and t-Tests

 

Different hypothesis tests are used depending on the type of data and the sample size. For testing hypotheses about a population mean or proportion, the primary distinction is between Z-tests and t-tests.

A Z-test is used when the sample size is large (typically n>30) or when the population standard deviation is known.30 It is commonly used for testing population proportions, a frequent task in social science research (e.g., testing if the proportion of a community that supports a new zoning law is significantly different from 50%).31

The t-test is used when the sample size is small and the population standard deviation is unknown, which is a more common scenario in practice. There are different forms of the t-test. The independent samples t-test is used to compare the means of two separate, unrelated groups (e.g., comparing the test scores of students in a new educational program to a control group).32 The

dependent samples t-test (or paired t-test) is used when the two sets of scores are related, such as when comparing the same group of individuals before and after an intervention.33 A comprehensive playlist from

statisticsfun covers all these variations and includes practical tutorials on how to perform the calculations in Microsoft Excel.33

 

5.4 Parametric vs. Non-Parametric Approaches

 

A critical decision point in the analytical process is the choice between parametric and non-parametric tests. Parametric tests, such as the t-test and Z-test, make certain assumptions about the population from which the data were drawn, most notably that the data follow a normal distribution.34 When these assumptions are met, parametric tests are more powerful (i.e., more likely to detect a true effect).

However, data in public administration and social science often do not meet these assumptions. Survey data may be skewed, or the sample size may be too small to confidently assume normality. In such cases, non-parametric tests are the appropriate choice. These tests are “distribution-free” as they do not rely on assumptions about the underlying population distribution.34 One video provides a helpful illustration: data on alcohol consumption is unlikely to be normally distributed, as there will be a large group of people at zero and a long tail of heavy drinkers, making a non-parametric approach more suitable.35 The choice is a fundamental application of the principle of using the right tool for the job.

 

5.5 Analyzing Categorical Data: The Chi-Square Test

 

Many research questions in public administration involve categorical variables (e.g., gender, education level, political affiliation, opinion on a policy). The Chi-square (χ2) test is a versatile non-parametric test used for analyzing this type of data. It has two primary applications.

1. Chi-square goodness-of-fit test: This test compares the observed frequencies of categories in a sample to a set of expected frequencies. For example, a city planner could use this test to determine if the demographic breakdown of people attending a series of public meetings matches the demographics of the city as a whole. A significant result would indicate that certain groups are over- or under-represented.36
2. Chi-square test of independence: This test determines whether there is a statistically significant association between two categorical variables. For instance, a policy analyst could use this test to see if there is a relationship between a respondent’s income bracket and their support for a proposed tax increase.37

The available videos provide a solid introduction to the mechanics of the test, including how to calculate the test statistic, determine the degrees of freedom, and use a Chi-square table to find the critical value for making a decision.36

 

5.6 Comparing Multiple Groups Non-Parametrically: The Kruskal-Wallis Test

 

When a researcher wants to compare the means of more than two independent groups, the standard parametric test is the Analysis of Variance (ANOVA). However, if the assumptions for ANOVA (such as normality and equal variances) are not met, the Kruskal-Wallis H test is the appropriate non-parametric alternative. This test is used to determine if there are statistically significant differences among two or more groups on a continuous or ordinal dependent variable. For example, a program evaluator could use the Kruskal-Wallis test to compare the client satisfaction scores (measured on an ordinal scale) across three different service delivery centers.

The video resources for this topic are particularly effective when used in combination. One video provides an outstanding demonstration of how to conduct the test by hand.38 This process, which involves combining all the data, ranking it from lowest to highest, and then summing the ranks for each group, is pedagogically invaluable for understanding the underlying logic of the test. A second video then shows how to perform the same test quickly and efficiently using functions in Microsoft Excel, providing the practical, software-based skill that students will use in their own work.39 This pairing of conceptual understanding with practical application represents an ideal learning model.

The entire hypothesis testing framework is built on a subtle but profound logical point: we can only find evidence to reject the null hypothesis; we can never definitively prove it. A large p-value does not mean the null is true; it simply means we failed to gather sufficient evidence to reject it. This is analogous to a “not guilty” verdict, which is not a declaration of innocence. This requires careful language in reporting results. An analyst cannot claim “the program had no effect.” They must state, “we did not find a statistically significant effect.” This precision is a hallmark of scientific integrity and is essential for preventing policy decisions based on misinterpreted non-findings.

 

Conclusion

 

This guide has systematically mapped a curated selection of high-quality video resources to a comprehensive statistics curriculum designed for students of public administration. The analysis demonstrates that a thoughtful integration of these digital tools can create a powerful and flexible learning environment. By leveraging the distinct strengths of various educational creators—from the intuitive, visual explanations of StatQuest to the rigorous, in-depth lectures of Professor Leonard—instructors can cater to diverse learning styles and build a more robust understanding of statistical concepts.

The progression through the course syllabus, mirrored in this guide, tells a larger story about the role of data in governance. It begins with the fundamental grammar of data reduction in descriptive statistics, moves to the exploration of relationships with correlation and regression, builds a theoretical foundation with probability, and culminates in the formal decision-making frameworks of estimation and hypothesis testing.

Several key themes emerge. First is the imperative for future public administrators to become adept at choosing the appropriate statistical tool for the data at hand, recognizing the critical distinctions between methods like Pearson and Spearman correlation or parametric and non-parametric tests. Second is the ethical and practical necessity of quantifying and communicating uncertainty, favoring the honesty of interval estimates over the false precision of point estimates. Finally, the guide emphasizes the importance of precise, careful language in interpreting and reporting statistical results, particularly the crucial distinction between failing to find an effect and proving the absence of one.

Ultimately, the goal of this course, and by extension this resource guide, is to demystify statistics and reframe it as an indispensable toolkit for evidence-based decision-making. By providing accessible, engaging, and pedagogically sound video resources, we can better equip the next generation of public leaders to analyze data critically, build stronger arguments for policy, and govern more effectively in an increasingly complex world.

 

Appendix A: Master Video Resource Guide for Statistics in Public Administration

 

Unit & Topic	Primary Video Recommendation	Secondary/Alternative Video	Key Concepts Covered	Pedagogical Notes & Relevance to Public Administration
Unit 1.1: Introduction, Scope	StatQuest with Josh Starmer – Statistics Fundamentals 1	Professor Leonard – Statistics (Full Length Videos) 2	Statistics definition, scope, significance, application	StatQuest provides excellent conceptual intuition (the “why”). Professor Leonard provides rigorous, university-level depth (the “how”). Essential for setting the stage.
Unit 1.2: Descriptive vs. Inferential	Descriptive vs Inferential Statistics 4	Descriptive vs Inferential Statistics 3	Descriptive statistics, inferential statistics, sample, population	Short, focused videos using clear, relatable examples. Crucial for understanding the fundamental division in statistical methods and the limits of data.
Unit 1.3: Measures of Central Tendency	HelpYourMath – Measures of Central Tendency Playlist 5	How to Find Mode, Median, Mean and Range 6	Mean, weighted mean, median, mode, bimodal	Playlist offers a modular approach for targeted learning. The single video is a great summary and introduces “range,” linking to the next topic.
Unit 1.4: Measures of Dispersion	Variance, Standard Deviation and Coefficient of Variation 7	Variance, Standard Deviation and Coefficient of Variation 8	Variance, standard deviation, coefficient of variation (CV)	Explains the relationships between the measures. Highlights the value of standard deviation (interpretable units) and CV (comparing datasets with different means/units).
Unit 2.1: Correlation Analysis	Karl Pearson and Spearman’s Rank correlation 9	Initial essentials – Correlation Coefficient Playlist 10	Pearson’s r, Spearman’s rho, linearity, outliers, monotonic relationships, ordinal data	Directly compares the two methods and their assumptions. Vital for social science, where ordinal survey data is common. The playlist provides calculation details.
Unit 2.2: Simple Linear Regression	Simple linear regression 11	Linear Regression with Python Tutorial (Intro only) 12	Regression equation, line of best fit, slope, intercept, R-squared	Focuses on practical application: making predictions and writing up results in APA format. Invaluable for students who will write research reports.
Unit 3.1: Probability Concepts	Stats4Everyone – Introduction to Probability Theory 14	MIT RES. 6-012 Introduction to Probability 13	Combination, event, sample space, classical, relative frequency, subjective approaches	Stats4Everyone is accessible with clear examples. The MIT course is for advanced students seeking deep theoretical knowledge.
Unit 3.3: Binomial Distribution	Binomial Distribution Explained 15	The Binomial Distribution 16	Binomial distribution, discrete probability, expected value, standard deviation	Both videos offer clear, intuitive explanations with simple examples (colorblindness, dice rolls). Covers both theory and calculation.
Unit 3.3: Normal Distribution	Normal Distribution Explained 17	The Normal Distribution and Z-Scores 18	Normal distribution, standard normal distribution, z-score, probability calculation	17 teaches the core mechanical skill of using a z-table. 18 connects the concept to future topics like confidence intervals, showing its importance.
Unit 4.1: Sampling Distribution	Statistical estimation and sampling distribution 19	N/A	Sampling distribution, distribution of sample data, standard error, Central Limit Theorem	Exceptional video that clearly explains the most critical (and often confusing) concept in inferential statistics using a great visual approach.
Unit 4.2: Point vs. Interval Estimates	Reddit Discussion: “Why does point estimates get such a bad rap?” 21	Point vs interval estimates 20	Point estimate, interval estimate, confidence interval, margin of error, uncertainty	The Reddit thread provides rich conceptual understanding from practitioners. The video provides the formal definitions and formulas. A powerful combination.
Unit 4.3: Determining Sample Size	Determining sample size 22	How To Calculate The Sample Size 23	Sample size calculation, margin of error, confidence level, population variability, bias	22 explains the formula and trade-offs. 23 introduces crucial real-world issues like sampling bias, connecting theory to practice.
Unit 5.1: Intro to Hypothesis Testing	jbstatistics – Hypothesis Testing Playlist 24	Introduction to hypothesis testing 25	Hypothesis testing, null hypothesis, alternative hypothesis, p-value, significance	The jbstatistics playlist is the recommended core resource for the entire unit due to its clarity and systematic coverage of all key concepts.
Unit 5.2: Test Types & Errors	One-Tailed and Two-Tailed Tests 26	Statistics 101: Visualizing Type I and Type II Error 29	One-tailed test, two-tailed test, Type I error (false positive), Type II error (false negative)	26 provides clear definitions. For errors, the courtroom analogy video 28 is highly recommended for its memorability and intuitive power.
Unit 5.3: Large Sample Tests (Z-test)	Z-test for a Population Proportion 31	Z-Test for Population Mean and Proportion 30	Z-test, population mean, population proportion, large samples	Provides clear, step-by-step instructions for conducting Z-tests, which are common for analyzing survey data and proportions.
Unit 5.3: Small Sample Tests (t-test)	t-tests of Independent and Dependent Groups Playlist 33	The t-test for independent samples 32	t-test, independent samples, dependent (paired) samples, degrees of freedom	The playlist is comprehensive, covering both major types of t-tests and including practical Excel tutorials.
Unit 5.4: Parametric vs. Non-Parametric	Parametric vs Non-parametric tests 34	Parametric and Non-Parametric Tests 35	Parametric assumptions (normality), non-parametric tests, distribution-free tests	Provides a clear, high-level overview of the distinction. Crucial for guiding the selection of the appropriate statistical test based on data characteristics.
Unit 5.5: Chi-Square Test	Chi-Square Test for Independence 37	Chi-Square Test 36	Chi-square (χ2) test, goodness of fit, test of independence, categorical data, expected frequencies	Covers both major applications of the Chi-square test and explains the mechanics of calculation and interpretation using the Chi-square table.
Unit 5.6: Kruskal-Wallis Test	How to conduct a Kruskal-Wallis H test by hand 38	How to perform the Kruskal-Wallis H test in Excel 39	Kruskal-Wallis H test, non-parametric alternative to ANOVA, ranked data	Combining these two videos is ideal: 38 provides deep conceptual understanding through manual calculation, while 39 provides the practical software skill.

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