Making statistics intuitive
The conjunction fallacy is a cognitive bias that occurs when someone mistakenly believes that two events occurring together are more likely than either of the two events alone. In other words, it’s the mistaken belief that a precisely detailed, multifaced outcome is more likely to occur than a more generalized version of that outcome. [Read more…] about Conjunction Fallacy: Definition & Example
Base rate fallacy is a cognitive bias that occurs when a person misjudges an outcome by giving too much weight to case-specific details and overlooks crucial probability information that applies to all cases in a population. That vital probability is the outcome’s base rate of occurrence in the population. [Read more…] about Base Rate Fallacy Overview & Examples
A quasi experimental design is a method for identifying causal relationships that does not randomly assign participants to the experimental groups. Instead, researchers use a non-random process. For example, they might use an eligibility cutoff score or preexisting groups to determine who receives the treatment. [Read more…] about Quasi Experimental Design Overview & Examples
The residual sum of squares (RSS) measures the difference between your observed data and the model’s predictions. It is the portion of variability your regression model does not explain, also known as the model’s error. Use RSS to evaluate how well your model fits the data. [Read more…] about Residual Sum of Squares (RSS) Explained
Covariance vs correlation both evaluate the linear relationship between two continuous variables. While this description makes them sound similar, there are stark differences in how to interpret them.
Although these statistics are closely related, they are distinct concepts. How are they different?
In this post, learn about the differences between covariance vs correlation and what you can learn from each. [Read more…] about Covariance vs Correlation: Understanding the Differences
What’s the risk? People discuss risk frequently, but it’s not always clearly understood. It is your exposure to danger or adverse outcomes. Statistically, we define risk as the probability of a negative outcome occurring, and there are several ways to calculate it. [Read more…] about Risk Calculations: Relative vs Absolute & Risk Reduction
Omitted variable bias (OVB) occurs when a regression model excludes a relevant variable. The absence of these critical variables can skew the estimated relationships between variables in the model, potentially leading to erroneous interpretations. This bias can exaggerate, mask, or entirely flip the direction of the estimated relationship between an independent and dependent variable. [Read more…] about Omitted Variable Bias: Definition, Avoiding & Example
A case study is an in-depth investigation of a single person, group, event, or community. This research method involves intensively analyzing a subject to understand its complexity and context. The richness of a case study comes from its ability to capture detailed, qualitative data that can offer insights into a process or subject matter that other research methods might miss. Case reports are near the bottom of the level of evidence ranking, offering descriptive insights from individual or small patient series. [Read more…] about What is a Case Study? Definition & Examples
In statistics, the symbols and formulas for basic concepts such as the mean provide a foundational understanding of data analysis. Understanding the mean involves more than just knowing how to calculate an average; it’s about recognizing the nuances that differentiate a population mean from a sample mean. This distinction is crucial in statistical analysis, as the approach and symbol used for each vary (mu vs. x bar). [Read more…] about Sample Mean vs Population Mean: Symbol & Formulas
A correlational study is an experimental design that evaluates only the correlation between variables. The researchers record measurements but do not control or manipulate the variables. Correlational research is a form of observational study. [Read more…] about Correlational Study Overview & Examples
A type 2 error (AKA Type II error) occurs when you fail to reject a false null hypothesis in a hypothesis test. In other words, a statistically non-significant test result indicates that a population effect does not exist when it actually does. A type 2 error is a false negative because the effect exists in the population, but the test doesn’t detect it in the sample. [Read more…] about Type 2 Error Overview & Example
A type 1 error (AKA Type I error) occurs when you reject a true null hypothesis in a hypothesis test. In other words, a statistically significant test result indicates that a population effect exists when it does not. A type 1 error is a false positive because the test detects an effect in the sample that doesn’t exist in the population. [Read more…] about Type 1 Error Overview & Example
A cross-sectional study is an experimental design that analyzes data from a representative sample at a specific point in time. Researchers usually evaluate multiple attributes at once when using this design. Unlike longitudinal studies, these studies don’t track changes over time. [Read more…] about Cross Sectional Study: Overview, Examples & Benefits
A longitudinal study is an experimental design that takes repeated measurements of the same subjects over time. These studies can span years or even decades. Unlike cross-sectional studies, which analyze data at a single point, longitudinal studies track changes and developments, producing a more dynamic assessment. [Read more…] about Longitudinal Study: Overview, Examples & Benefits
Correlation vs causation in statistics is a critical distinction. And you’ve undoubtedly heard that correlation doesn’t imply causation. Why is that the case, what are the differences between them, and why do they matter? Those are the topics of this post! [Read more…] about Correlation vs Causation: Understanding the Differences
Use one way ANOVA to compare the means of three or more groups. This analysis is an inferential hypothesis test that uses samples to draw conclusions about populations. Specifically, it tells you whether your sample provides sufficient evidence to conclude that the groups’ population means are different. ANOVA stands for analysis of variance. [Read more…] about One Way ANOVA Overview & Example
Observational studies and experiments are two standard research methods for understanding the world. Both research designs collect data and use statistical analysis to understand relationships between variables. Beyond that commonality, they are vastly different and have dissimilar sets of pros and cons. [Read more…] about Observational Study vs Experiment with Examples
Goodness of fit evaluates how well observed data align with the expected values from a statistical model. [Read more…] about Goodness of Fit: Definition & Tests
Use the binomial distribution formula to calculate the likelihood an event will occur a specific number of times in a set number of opportunities. I’ll show you the binomial distribution formula to calculate these probabilities manually.
In this post, I’ll walk you through the formulas for how to find the probability, mean, and standard deviation of the binomial distribution and provide worked examples. [Read more…] about Binomial Distribution Formula: Probability, Standard Deviation & Mean
The expected value in statistics is the long-run average outcome of a random variable based on its possible outcomes and their respective probabilities. Essentially, if an experiment (like a game of chance) were repeated, the expected value tells us the average result we’d see in the long run. Statisticians denote it as E(X), where E is “expected value,” and X is the random variable. [Read more…] about Expected Value: Definition, Formula & Finding