# Visualizing Statistical Concepts

#### A Collection of Tools for Emerging Music Education Researchers

The web apps that are available from this page are designed to demonstrate and familiarize students with statistical concepts that are commonly encountered in music education research methods courses.

Mastering statistical concepts can often be challenging for graduate music education students who have most recently been out in the field working with children in classrooms. Grappling with statistics can often be overwhelming for those whose last formal mathematics education experiences may have been many years in the past. In my courses, I have found that while clear explanations and practice examples are good – live manipulable demonstrations can be extremely powerful ways for developing insight in regard to statistics.

• Generating Fake Data for Practice Analyses (link)
• This app allows you to create and download a data set consisting of two nominal variables, two ordinal variables, a continuous variable of integer values, and a continuous variable of decimal values. You can set the proportions for the frequencies of the categorical variables, the range of the oridinal variables, and the mean and standard deviation for each of the continuous variables. Once you’ve made your selections, you can download the resulting data set as a .csv file that can be imported into any statistical package.
• This app allows for visualizing basic discrete and continuous probability distributions. You can manipulate a coin-flipping simulation, a dice-rolling simulation, and a normal distribution to examine the probabilities of outcomes of your choosing. All simulations allow you to explore the notion of …in the long run… when thinking about probability by letting you choose the number of indpendent samples drawn. It’s also possible to “weight” the coin to be biased in the flipping simulation.
• This application allows you to visualize correlations of different strengths for scalar (i.e., interval/ratio), ordinal, and binary nominal variables. It’s also possible to adjust the means and standard deviations for the distributions of the scalar variables as well as the ranges for the ordinal variables. Scatterplots of the scalar and ordinal variables and a mosaic plot of the nominal variables are produced along with the resulting coefficient and respective p value.
• Standard Error of the Mean (link)
• This app simulates repeated independent sampling of means from a population with a mean and standard deviation of your choosing. It provides a visualization of how the standard error of the mean can vary given the input parameters for the population and sample size.
• Chi square Test of Independence (link)
• This app allows you to specify the proportions for each cell of a cross-tabulation of two binary nominal variables. The app generates a summary of a Pearson chi square test of the data, a mosaic plot to visualize the proportion of cases in each cell, and a table of the resulting standardized residuals. A plot of a chi square distribution with the respective degrees of freedom is also produced. The critical value of chi square and the observed chi square value are annotated upon the plot.
• This tool provides the opportunity to explore many aspects of the one-sample t-test and inferential statistical tests in general. First, you are able to generate a random sample of data by specifying the sample size, mean, and standard deviation. The mean from the random sample is then compared to a population (i.e., null) mean value of your choice using a one-sample t-test. The t-test results, a plot of the distribution of sample data with respect to the null mean, and a plot of the t distribution for the appropriate degrees of freedom with the critical values of t and the observed t statistic annotated upon it is produced as well. You can then see how specifying different properties of the sample data impacts the confidence interval of the mean, the t distribution, and the t statistic generated.