Statistics

Visualizing oneway ANOVA

I spent a little while over this winter break expanding upon how I might use Shiny to help demonstrate and familiarize students with statistical concepts in music education research methods courses. In general, it seems to me that clear explanations are needed, practice examples are good, but “live” manipulable demos are really, really great.

I built an app that allows students to visualize and manipulate a hypothetical experimental scenario so that they can see how the oneway ANOVA procedure partitions variation into “group (i.e., model)” and “residual” sources or more colloquially, “between” and “within” group sources. The plot at the top shows stripcharts of three groups of hypothetical experimental participants in blue, and a single stripchart of all of the hypothetical participants at once in red. Below the strip chart are controls for manipulating the data.

Students can play with the means of three groups and watch the between sums of squares go up and down. When students manipulate the standard deviations of the groups, they’ll see the within sums of squares go up and down. The numbers corresponding to the between, within, and total sums of squares appear reactively in the sub-title of the plot on top.

Below the controls are (a) a corresponding ANOVA table that updates reactively with each change the student makes and (b) a density plot to depict the overlap among the groups a bit more clearly.

This app is similar in design to “this ANOVA handout” I use in my courses.

Click this link or the image below to access the app:

https://petemiksza.shinyapps.io/Visualizing_oneway_ANOVA/

Let me know what you think if you have a moment or have any suggestions if you’d like to use this or something like it and I can be of help.

onewayANOVAapp

PS…

I’ve updated the previous “standard error of the mean” app I built to be cleaner and easier to use (see the previous post)

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 Vince Guaraldi’s Music from “A Charlie Brown Christmas”

A Festive Analysis

It’s the holiday season and catchy tunes are in the air! Vince Guaraldi’s score to A Charlie Brown Christmas stands out even among the many, many traditional favorites that appear on the radio these months.

Offered here is an analysis of the tracks from this album using the data provided by Spotify and the R package “spotifyR”. The variables that are involved in the analyses are labeled and described as follows (more info can be found by clicking here: Spotify Developer Page

  • “danceability”
    • How suitable the track is for dancing, based on tempo, rhythmic stability, beat strength, and regularity
  • “track popularity”
    • An accounting of how often the tracks are played (updated relatively often)
  • “tempo”
    • Estimated tempo in beats per minute (BPM)
  • “energy”
    • Perceptual measure of intensity and activity
  • “valence”
    • Degree of musical “positiveness” conveyed by a track

CBKableDataSummary

But Can You Dance To It?

The Peanuts kids dance a bit in the show, but what does spotify think about it?

CBdanceability

Are the Tunes You Can Dance To More Popular?

Do people listen to the songs that are easier to dance to more than they do those that are harder to dance to?

CBprediction

What are the Emotional Signatures of the Tunes?

How do these tunes match up with common indicators of musical affect, valence (e.g., the degree of positiveness or negativeness present) and arousal (e.g., the amount of energy present)?

CBcircumplex

My First Data Visualization Toy

I made a toy!

I made a fun little web app for visualizing some interesting things about sampling distributions and the standard error of a mean (pictured below). The app allows you to change parameters with the sliders on the left to see how sample size and standard deviation affect the standard error of a mean — and how sampling distributions of the mean approach normality as the number of samples drawn from a population increases.

You can play with it at this link (or click the picture): 

https://petemiksza.shinyapps.io/standard_error_of_mean_app/

semAPP

I built this app in R

I’ve recently been enjoying learning about the possibilities that the free, open-source statistical computing and graphics language “R” offers. It’s an amazingly flexible platform for organizing, visualizing, and analyzing data. Working in R requires acquiring some fluency with basic programming language. However, there is an astounding amount of free learning resources available on the web in the form of websites, books, blogs, tutorials, etc. There are also great web-based courses (https://www.datacamp.com/) that often have free trials.

The program can be downloaded here:

https://www.r-project.org/

Many recommend also using R Studio, a platform to help organize workflow when using R. The free version of R-Studio is what I use, and I’m fairly sure it has all that most of the folks in music education would likely every need.

https://www.rstudio.com/

More to the point… …R Studio has an integrated web app builder called “shiny“. Shiny makes building data visualization tools and web-based dashboards for exploring data fairly straight-forward. The apps that are produced with shiny are built in roughly the same type of code that is used to run analyses and make plots in R in general.

https://www.rstudio.com/products/shiny/

Why R?

Music ed research folks may wonder why use R instead of say, SPSS, or another commercial statistical package? Well, that could probably be a rather lengthy discussion of pros and cons. However, here’s a short list of some simple things that R is nice for:

  • It’s free and open-source with an immense community of users and developers which keeps it well-documented and up-to-date, as well as relevant to the needs of contemporary analysts.
  • The R community is very helpful. You could google almost any kind of problem you may be having and would be likely to find a few forums where people offer solutions.
  • It’s modular such that there is a package or more than a few packages to do any kind of data wrangling or analyses or plotting you’d ever want to do. For example, there was a point when I would toggle back and forth between SPSS, Stata, and Lisrel depending on what sorts of analyses I was doing. Now I can do it all in R.
  • The graphing capabilities are very impressive. It’s fairly easy to get nice-looking, presentation and/or publication ready figures and you can customize any aspect of a graph.
  • Organizing the coding for analyses with code in scripts allows you to create a very clear reproducible record of all of the work you do to arrive at your results in any given project. This saves lots of time in the long run and is good scientific practice in general.

 

 

Research reads to keep you warm on cold winter nights

Because, really, what’s more comforting in the middle of winter than curling up with a great book on quantitative research design and/or statistical analysis!

🙂

This semester I have the pleasure of teaching a course on quantitative research methods for music education. In preparation for this class, I’ve been looking at all kinds of resources that could be helpful for the students (and me) to dig into compelling issues of research design and analysis. A couple of standouts from the pile of books I was wading through are listed below. In addition to being clearly written and approachable in style, each book does a great job elaborating on issues related to quantitative research that are often difficult to digest. These books aren’t designed to be suitable as a text for a music education research methods course, but, they’re certainly excellent supplements.

photo

(snowflake courtesy of Lucy Miksza, 5 yrs old)

Stanovich, K. E. (2001). How to think straight about psychology (6th ed.). Needham Heights, MA: Allyn & Bacon.

  • This book is a terrific, down-to-Earth read about some of the most basic characteristics of scientific inquiry. I particularly enjoy the discussions of scientific inquiry as a converging process, the importance of falsification, and the challenges inherent in probabilistic thinking. Being focused on the social science of psychology, it comes across as a good introduction to issues of scientific activity that comes across in a way that I think is relevant to many of the types of questions that music ed researchers may be interested in.

Abelson, R. (1995). Statistics as principled argument. Hillsdale, NJ: Erlbaum Associates.

  • This is a humorous and plain-spoken collection of wisdom for those who are writing about statistical findings. The first chapter, “making claims with statistics,” raises a host of simple, yet important considerations for stats folk. All of the chapters, though, will be helpful – especially when thinking about developing a writing style.

Jaeger, R. M. (1990). Statistics as a spectators sport. Newbury Park, CA: Sage Publications.

  • I’ve relied on this book for one reason or another many times since getting bitten by the music ed research bug. This book lays out basic and intermediate statistical topics in an easy-to-grasp, conceptual manner. Jaeger’s explanations could be a great help for those who find that math and formulas seem to get in the way of understanding how statistical analysis techniques could serve music ed researchers. Or, if you’re looking for a book that ties together some loose ends and fills conceptual gaps – this could really help.

Need summer reading ideas for nerds? Look no further!

Are you a nerd looking for a good read? This is a quick post about the reading I’ve been lucky enough to squeeze in this summer, maybe your nerdy side will enjoy some of it too.

It’s been a great summer of family time at home, trips to see friends and family afar, outdoor activity, research, writing, teaching – and – having a little bit of extra time each week to read purely for the sake of pleasure!

Here’s a quick list of some of the books I had a chance to read for fun since the spring semester wound down along with a silly synopsis of my take on each of them.*

AvidReader

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The Future of Music Education: Continuing the Dialogue about Curricular Reform

I’m excited to report the publication of a recent article I wrote for the Music Educators Journal titled: “The future of music education: Continuing the dialogue about curricular reform”

The heart of this article is captured in the opening quote: “The art of progress is to preserve order amid change and to preserve change amid order.” Alfred North Whitehead

In this article I highlight several trends regarding critical arguments that have recently been raised when discussing the secondary large-ensemble tradition in the public schools. In support of secondary school ensembles, I argue for a discussion of curricular reform that avoids polemical rhetoric, straw men, and hasty generalization. I also suggest taking special care when considering the incorporation of new technologies and popular music idioms in music education curricula.

I describe how critical energies might be redirected to what I see as urgent needs for the profession such as:

  • Directing advocacy efforts towards increasing access to music education for underserved populations of children
  • Focusing advocacy efforts towards enhancing support for foundational elementary music experiences
  • Transforming teaching to maximize what’s possible from within the large-ensemble model without needlessly tearing it down by:
    • Increasing the breadth of comprehensive musicianship experiences possible
    • Increasing the degree of individual student empowerment
    • Broadening the range of collaborative approaches to music-making that teach­ers and students could engage in
    • Broadening the inclusiveness of repertoire in large-ensemble curricula

After briefly, yet sincerely, acknowledging the certain need to expand curricular offerings for music in the secondary schools, I close with the following:

“…it will be necessary to cultivate dispositions of patience and reflection with visions of curricular transformation if we hope for significant and lasting changes in the nature and quality of music education for all.”

Please check out the full article here (free to all NAfME members – or email me if you’d like to read it):

Miksza, P. (2013). The future of music education: Continuing the dialogue. Music Educators Journal, 99, 45-50.

Arts Ed: Reasons to Advocate and Levers to Pull

Reasons to advocate: Inspiring stories

The collegiate chapter of the National Association for Music Education at IU (see their blog!) recently participated in the music advocacy groundswell event (found here) by collecting stories from children about why music matters to them. They made efforts to contact public school teachers in the greater Bloomington area and reached out to the teachers from their hometowns. They ended up collecting nearly 18,000 words worth of inspirational stories of how music has played an essential role in kids’ lives across the country.

The comments the children made are powerful to say the least… they speak of many benefits of music that we, as musicians and teachers, know to be true – finding a place to belong, uncovering a special talent, learning about themselves, developing a means of self-expression, bringing them closer together with friends and family, connecting to a greater community, music as a release and a joy, the acquisition of skills and dispositions that are benefits in other areas of life, etc.

Here is a word cloud from the collection of stories that emphasizes the sentiments the students most commonly expressed – click on it for a close-up:

Better wordle 2

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