Confusing Statistical Terms

Confusing Statistical Term #3: Level

January 21st, 2025 by

Level is a statistical term that is confusing because it has multiple meanings in different contexts (much like alpha and beta).

There are three different uses of the term Level in statistics that mean completely different things. What makes this especially confusing is that all three of them can be used in the exact same analysis context.

I’ll show you an example of that at the end.

So when you’re talking to someone who is learning statistics or who happens to be thinking of that term in a different context, this gets especially confusing.

Levels of Measurement

variable measured at the ordinal levelThe most widespread of these is levels of measurement. Stanley Stevens came up with this taxonomy of assigning numerals to variables in the 1940s. You probably learned about them in your Intro Stats course: the nominal, ordinal, interval, and ratio levels.

Levels of measurement is really a measurement concept, not a statistical one. It refers to how much and the type of information a variable contains. Does it indicate an unordered category, a quantity with a zero point, etc?

So if you hear the following phrases, you’ll know that we’re using the term level to mean measurement level:

  • nominal level
  • ordinal level
  • interval level
  • ratio level

It is important in statistics because it has a big impact on which statistics are appropriate for any given variable. For example, you would not do the same test of association between two variables measured at a nominal level as you would between two variables measured at an interval level.

That said, levels of measurement aren’t the only information you need about a variable’s measurement. There is, of course, a lot more nuance.

Levels of a Factor

Another common usage of the term level is within experimental design and analysis. And this is for the levels of a factor. Although Factor itself has multiple meanings in statistics, here we are talking about a categorical independent variable.

In experimental design, the predictor variables (also often called Independent Variables) are generally categorical and nominal. They represent different experimental conditions, like treatment and control conditions.

Each of these categorical conditions is called a level.

Here are a few examples:

  • In an agricultural study, a fertilizer treatment variable has three levels: Organic fertilizer (composted manure); High concentration of chemical fertilizer; low concentration of chemical fertilizer.So you’ll hear things like: “we compared the high concentration level to the control level.”
  • In a medical study, a drug treatment has three levels: Placebo; standard drug for this disease; new drug for this disease.
  • In a linguistics study, a word frequency variable has two levels: high frequency words; low frequency words.

Now, you may have noticed that some of these examples actually indicate a high or low level of something. I’m pretty sure that’s where this word usage came from. But you’ll see it used for all sorts of variables, even when they’re not high or low.

Although this use of level is very widespread, I try to avoid it personally. Instead I use the word “value” or “category” both of which are accurate, but without other meanings. That said, “level” is pretty entrenched in this context.

Level in Multilevel Models or Multilevel Data

A completely different use of the term is in the context of multilevel models. Multilevel models is a Three level multilevel dataterm for some mixed models. (The terms multilevel models and mixed models are often used interchangably, though mixed model is a bit more flexible).

Multilevel models are used for multilevel (also called hierarchical or nested) data, which is where they get their name. The idea is that the units we’ve sampled from the population aren’t independent of each other. They’re clustered in such a way that their responses will be more similar to each other within a cluster.

The models themselves have two or more sources of random variation.  A two level model has two sources of random variation and can have predictors at each level.

A common example is a model from a design where the response variable of interest is measured on students. It’s hard though, to sample students directly or to randomly assign them to treatments, since there is a natural clustering of students within schools.

So the resource-efficient way to do this research is to sample students within schools.

Predictors can be measured at the student level (eg. gender, SES, age) or the school level (enrollment, % who go on to college).  The dependent variable has variation from student to student (level 1) and from school to school (level 2).

We always count these levels from the bottom up. So if we have students clustered within classroom and classroom clustered within school and school clustered within district, we have:

  • Level 1: Students
  • Level 2: Classroom
  • Level 3: School
  • Level 4: District

So this use of the term level describes the design of the study, not the measurement of the variables or the categories of the factors.

Putting them together

So this is the truly unfortunate part. There are situations where all three definitions of level are relevant within the same statistical analysis context.

I find this unfortunate because I think using the same word to mean completely different things just confuses people. But here it is:

Picture that study in which students are clustered within school (a two-level design). Each school is assigned to use one of three math curricula (the independent variable, which happens to be categorical).

So, the variable “math curriculum” is a factor with three levels (ie, three categories).

Because those three categories of “math curriculum” are unordered, “math curriculum” has a nominal level of measurement.

And since “math curriculum” is assigned to each school, it is considered a level 2 variable in the two-level model.

See the rest of the Confusing Statistical Terms series.

 

First published December 12, 2008

Last Updated January 21, 2025


Charting a Path to Statistical Confidence and Mastery

January 17th, 2024 by

Tell me if you can relate to this:stage 1

You love your field of study, you enjoy asking the big questions and discovering answers. But, when it comes to data analysis and statistics you get a little bogged down. You might even feel a bit lost sometimes.

And that is hard to admit.

Because after all, you are supposed to be the expert. Right?

Learning Statistics is Hard but We Make it a Lot Easier

The thing is, statistics is a field unto itself.  But as a researcher, you need to be adept with statistics even though you may only have very basic training in this field. In essence, you learned statistics — a new language — out of context.  You had no real immersion experience to practice this language. You had few opportunities to apply the strange new terms and concepts as you learned them.

At the Analysis Factor, we understand the pain of learning and doing statistics. We have been in the trenches with hundreds of researchers like you across many fields of study. Everyone is struggling to grow their statistical, data analysis, and software skills.

In Statistically Speaking we support and guide you as you learn — every step of the way. We know where to start, where to go next, and next, and next.

We know that your field and research question(s) determine the type of data and complexity of statistical analyses you will choose. And we know that everyone shows up in a different place, and needs different things to help them get where they need to go.

So we have created a treasure trove of resources on hundreds of topics — from data cleaning and research design to logistic regression and structural equation modeling.

And to keep it all about you, we have created a customizable learning platform, one where you make a plan for your own unique journey. We have crafted a series of comprehensive Maps, curated guides on essential topics at each Stage of mastery, offering you a structured pathway through the maze of statistical knowledge.

You create the plan you need, and choose the maps you need to do your research.

Maps

At The Analysis Factor, we classify the statistical content and skills into 4 Stages to help you decide where to begin your learning journey. In Statistically Speaking, the Maps are categorized into these Stages.

Here are just a few examples:

Stage 1: Fundamentals

  • Preparing Data: Understanding the fundamental steps in data preparation, from cleaning and transforming to structuring datasets for analysis.

  • Bivariate Statistics: Grasping the basics of relationships between two variables, laying the groundwork for more complex analyses.

Stage 2: Linear Models

  • Graphing: Learning visualization techniques to represent data and derive meaningful insights.

  • Introduction to Regression: Unraveling the fundamentals of regression analysis, a cornerstone of statistical modeling.

  • Interpreting Results: Developing the skill to interpret statistical results and draw valid conclusions from analyses.

Stage 3: Extensions of Linear Models

  • Count Models: Exploring specialized models for count data analysis, understanding their application and nuances.

  • Logistic Regression: Diving into binary outcome analysis, understanding probabilities, and logistic models.

  • Factor Analysis: Delving into multivariate analysis, understanding latent variables and their relationships.

Stage 4: Advanced Models

  • GLMM: Embracing the complexity of generalized linear mixed models, integrating fixed and random effects.

  • SEM: Venturing into structural equation modeling, exploring complex relationships among variables.

  • Survival Analysis: Understanding time-to-event data, its application in various fields, and survival modeling techniques.

By mapping out the key content and skills you want to learn at each Stage, you’ll gain a clearer understanding of the vast statistical landscape and feel empowered to take on the learning journey ahead.

So, what are you waiting for? Members, head on over to explore the Maps in Statistically Speaking.

And if you are not yet a member, you can sign-up for our waitlist to join Statistically Speaking.  We would love to meet you, learn about your research, and help you get started on your statistical learning adventure.

 


Confusing Statistical Term #13: Missing at Random and Missing Completely at Random

November 22nd, 2022 by

Stage 2One of the important issues with missing data is the missing data mechanism. You may have heard of these: Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR).

The mechanism is important because it affects how much the missing data bias your results. This has a big impact on what is a reasonable approach to dealing with the missing data.  So you have to take it into account in choosing an approach.

The concepts of these mechanisms can be a bit abstract.missing data

And to top it off, two of these mechanisms have really confusing names: Missing Completely at Random and Missing at Random.

Missing Completely at Random (MCAR)

Missing Completely at Random is pretty straightforward.  What it means is what is (more…)


Six terms that mean something different statistically and colloquially

November 8th, 2021 by

by Kim Love and Karen Grace-Martin

Statistics terminology is confusing.

Sometimes different terms are used to mean the same thing, often in different fields of application. Sometimes the same term is used to mean different things. And sometimes very similar terms are used to describe related but distinct statistical concepts.

(more…)


Confusing Statistical Term #10: Mixed and Multilevel Models

April 20th, 2021 by

What’s the difference between Mixed and Multilevel Models? What about Hierarchical Models or Random Effects models?

I get this question a lot.

The answer: very little.

(more…)


Why Statistics Terminology is Especially Confusing

March 16th, 2021 by

The field of statistics has a terminology problem.

It affects students’ ability to learn statistics. It affects researchers’ ability to communicate with statisticians; with collaborators in different fields; and of course, with the general public.

It’s easy to think the real issue is that statistical concepts are difficult. That is true. It’s not the whole truth, though. (more…)