Hundreds of years of statistical analysis by tens of thousands of independent researchers has led to an array of similar sounding names, many of which are often confused. Here are 11 of the most common. Which ones are you guilty of confusing?
1. Chi Square Test for Independence and Chi Square Goodness of Fit Test
To avoid confusion, don't refer to a "chi-square test" [no term], because there are two of them. Both tests use the chi-square statistic and distribution, but they do completely different things.
2. Covariate vs. Covariance
A covariate is a variable observed during analysis, but it's not the focus of analysis and we can't control for it. "Covariate” can be confused with covariance, which has an entirely different meaning: It's a measure of how much two random variables vary together.
3. Sample Space and Event Space
Oft confused are these two types of spaces that describe probability outcomes. They are similar in a way, but if you want to be mathematically precise, make sure you know the difference between the two:
4. False Alarm Ratio vs. False Alarm Rate
A false alarm ratio (FAR) is the number of false alarms per total number of alarms (where a false alarm is given when there's actually not a given event). Unfortunately, the False Alarm Rate (FAR) shares the same acronym, but it has a slightly different meaning: it's the number of times an event didn't happen.
5. Inverse Normal Distribution vs. Inverse Gaussian Distribution
Another name for a Gaussian Distribution is a Normal Distribution. However, the Inverse Gaussian Distribution is not another name for the Inverse Normal Distribution. The inverse Gaussian (which isn't really an "inverse") is a family of continuous probability distributions. On the other hand, the Inverse Normal Distribution is an inverse--it allows you to work backwards to find x-values.
6. Pearson's Coefficient vs. Pearson's Coefficient of Skewness
Pearson's Coefficient [no term] tells you whether two data sets or variables are independent or dependent of each other. Pearson's Coefficient of Skewness is a way to find skew in a sample. To avoid confusion between the two, many people called Pearson's Coefficient the contingency coefficient instead.
7. Positive Predictive Value vs. Sensitivity
The confusion here doesn't stem from the names, but rather what the two terms represent. The Positive Predictive Value tells you the odds of having a disease if get a positive result. Should you panic over that positive Covid-19 test? PPV can be a useful piece of information. On the other hand, the test sensitivity of a test is the proportion of people with the disease who will have a positive result. That little nugget isn't so useful to you, the consumer, but it's useful information for the CDC.
8. Prediction Interval vs. Confidence Interval
Although they are often confused with each other because of their subtle difference, prediction and confidence intervals are not the same thing. Confidence intervals give you a range of values for a population parameter (like the variance). A prediction interval is where you would expect to find a future value. To muddy the waters further, we also have tolerance levels, which cover a particular proportion of the population for a given confidence level. As an example, let's say your factory was producing light bulbs:
9. Probable vs. Plausible
"Plausible" (which basically means reasonable) and "probability" are often interchanged. For example, consider these statements:
“If the probability is large then the null is plausible and we cannot reject the null hypothesis” [1]
“On the other hand, if we report a range of plausible values – a confidence interval – we have a good shot at capturing the parameter.” ~ [2]
Due to the ambiguous language, it's not clear here if plausible means "probable" or "reasonable". To muddle the situation even further, "likelihood" (how well data summarizes parameters.) is also confused with plausible.
10. Relative Absolute Error vs. Relative Error
Relative Absolute Error measures the performance of a predictive model. It has a completely different meaning from relative error, which is a general measure of precision or accuracy for instruments like clocks, rulers, or scales.
11. Reverse Causality vs. Similarity
The definitions for these two terms are very close:
This illustration shows how they relate to each other:
References
[1] Rao, S. (n.d.). Understanding Hypothesis Tests.
[2] Libretexts. Confidence Intervals.
Reverse Causality image by author.
Covariates controlled for in ANCOVA. Image: Makingstats|Wikimedia Commons
Comment
Hey, the logistics performance index of Denmark is 3.78. It indicates a good performance - the logistics system is well prepared and organised, shipments mostly arrive on time and do not suffer damage, and the infrastructure is ready to handle even unpredictably big amounts of traffic as long as it is not overwhelming.
http://www.confiduss.com/en/jurisdictions/denmark/infrastructure/
Posted 12 April 2021
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