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Statistical Topic

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  • This paper comes from researchers at the NASA Langley Research Center and College of William & Mary.  

    "The experience of retinex image processing has prompted us to reconsider fundamental aspects of imaging and image processing. Foremost is the idea that a good visual representation requires a non-linear transformation of the recorded (approximately linear) image data. Further, this transformation appears to converge on a specific distribution. Here we investigate the connection between numerical and visual phenomena. Specifically the questions explored are: (1) Is there a well-defined consistent statistical character associated with good visual representations? (2) Does there exist an ideal visual image? And (3) what are its statistical properties?"

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  • This program visualizes the effects of outliers to regression lines. The user may pick up a point with the mouse and move it across the chart. The resulting regression line is automatically adjusted after each movement, showing the effect in an immediate and impressive way. The program Leverage allows one to experiment with the leverage effect. You can create a random sample of data noisy points on a line. Dragging one of the points away from the regression line immediately shows the effect, as the regression line is recalculated and moves according to the current data set. Not online: user has to download the program.

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  • In these activities designed to introduce sampling distributions and the Central Limit Theorem, students generate several small samples and note patterns in the distributions of the means and proportions that they themselves calculate from these samples. Outside of class, students generate samples of dice rolls and coin spins and draw random samples from small populations for which data is given on each individual. Students report their sample means and proportions to the instructor who then compiles the results into a single data file for in-class exploration of sampling distributions and the Central Limit Theorem. Key words: Sampling distribution, sample mean, sample proportion, central limit theorem

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  • This website is compilation of data from sources such as the CIA World Factbook, UN, and OECD. You can generate maps and graphs to statistically compare and research Nations.

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  • Which is more robust against outliers: mean or median?  This app demonstrates the (in)stability of these descriptive statistics as the value of an outlier and the number of data points change.

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  • The Caesar Shift is a translation of the alphabet; for example, a five-letter shift would code the letter a as f, b as g, ... z as e. We describe a five-step process for decoding an encrypted message. First, groups of size 4 construct a frequency table of the letters in two lines of a coded message. Second, students construct a bar chart for a reference message of the frequency of letters in the English language. Third, students create a bar chart of the coded message. Fourth, students visually compare the bar chart of the reference message (step 2) to the bar chart of the coded message (step 3). Based on this comparison, students hypothesize a shift. Fifth, students apply the shift to the coded message. After decoding the message, students are asked a series of questions that assess their ability to see patterns. The questions are geared for higher levels of cognitive reasoning. Key words: bar charts, Caesar Shift, encryption, testing hypotheses

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  • The goal of this text is to provide a broad set of topics and methods that will give students a solid foundation in understanding how to make decisions with data. This text presents workbook-style, project-based material that emphasizes real world applications and conceptual understanding. Each chapter contains:

    • An introductory case study focusing on a particular statistical method in order to encourage students to experience data analysis as it is actually practiced.
    • guided research project that walks students through the entire process of data analysis, reinforcing statistical thinking and conceptual understanding.
    • Optional extended activities that provide more in-depth coverage in diverse contexts and theoretical backgrounds. These sections are particularly useful for more advanced courses that discuss the material in more detail. Some Advanced Lab sections that require a stronger background in mathematics are clearly marked throughout the text.
    • Data sets from multiple disciplines and software instructions for Minitab and R.

    The text is highly adaptable in that the various chapters/parts can be taken out of order or even skipped to customize the course to your audience. Depending on the level of in-class active learning, group work, and discussion that you prefer in your course, some of this work might occur during class time and some outside of class. 

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  • CODAP provides an easy-to-use web-based data analysis platform, geared toward middle and high school students, and aimed at teachers and curriculum developers. CODAP can be incorporated across the curriculum to help students summarize, visualize and interpret data, advancing their skills to use data as evidence to support a claim.

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  • This online software allows you to load data and make professional-looking graphs with it. Graph types are basic (scatterplot, line plot, bar charts, etc.), statistical (histograms, box plots), scientific (error bars, heat map, contour), 3D charts, and financial (e.g. time series). Other graphs are available with the paid pro version. Log in is required, which allows you to upload data and save it for next use.

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  • This online application allows the user to import data from online resources such as Facebook, Google Analytics, GitHub, as well as spreadsheets on their own computers. They can then drag-and-drop variables to make graphs automatically. The basic version is free, but you can upgrade to a paid version which allows combining data across services and, if the data come from an online resource, the user has the choice to have Data Hub keep the graphs updated as the data changes.
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