Statistics By Jim

Making statistics intuitive

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Regression to the Mean: Definition & Examples

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What is Regression to the Mean?

Regression to the mean is the statistical tendency for an extreme sample or observed value to be followed by a more average one. It is also known as reverting to the mean, highlighting the propensity for a later observation to move closer to the mean after an extreme value. The concept applies only to random variation in a process or system and does not pertain to interventions or events that affect the outcome. [Read more…] about Regression to the Mean: Definition & Examples

Self Selection Bias Overview & Examples

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What is Self Selection Bias?

Self selection bias can occur when individuals choose to participate in a study, survey, or experiment. The bias exists when volunteers have different characteristics than those who do not participate. It is a form of sampling bias stemming from using a nonprobability sampling method, such as volunteer or convenience sampling. [Read more…] about Self Selection Bias Overview & Examples

Attrition Bias: Definition & Examples

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What is Attrition Bias?

Attrition bias in research occurs when study participants who drop out have characteristics that differ significantly from those who remain. This selective dropout can lead to skewed results and misinterpretations if the researchers don’t adequately address it. This threat is higher for longitudinal studies and those with relatively high attrition rates. [Read more…] about Attrition Bias: Definition & Examples

Conjunction Fallacy: Definition & Example

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What is the Conjunction Fallacy?

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

Covariance vs Correlation: Understanding the Differences

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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

Omitted Variable Bias: Definition, Avoiding & Example

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What is Omitted Variable Bias?

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

Sample Mean vs Population Mean: Symbol & Formulas

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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

Type 2 Error Overview & Example

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What is a Type 2 Error?

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

Type 1 Error Overview & Example

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What is a Type 1 Error?

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

Observational Study vs Experiment with Examples

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Comparing Observational Studies vs Experiments

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

Expected Value: Definition, Formula & Finding

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What is the Expected Value?

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

Placebo Effect Overview: Definition & Examples

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What is the Placebo Effect?

The placebo effect occurs when a fake medical treatment produces real medical benefits psychosomatically. In short, believing in the treatment and the power of the mind can help someone feel better. The placebo effect can be so powerful that it mimics genuine medicine. Consequently, scientists need to control for it when conducting clinical trials. [Read more…] about Placebo Effect Overview: Definition & Examples

What is P Hacking: Methods & Best Practices

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P-Hacking Definition

P hacking is a set of statistical decisions and methodology choices during research that artificially produces statistically significant results. These decisions increase the probability of false positives—where the study indicates an effect exists when it actually does not. P-hacking is also known as data dredging, data fishing, and data snooping. [Read more…] about What is P Hacking: Methods & Best Practices

Likert Scale: Survey Use & Examples

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What is a Likert Scale?

The Likert scale is a well-loved tool in the realm of survey research. Named after psychologist Rensis Likert, it measures attitudes or feelings towards a topic on a continuum, typically from one extreme to the other. The scale provides quantitative data about qualitative aspects, such as attitudes, satisfaction, agreement, or likelihood. [Read more…] about Likert Scale: Survey Use & Examples