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Related Concept Videos

Probability in Statistics01:14

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Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
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A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
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 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
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Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
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A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
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Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
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A New Visualization for Probabilistic Situations Containing Two Binary Events: The Frequency Net.

Karin Binder1, Stefan Krauss1, Patrick Wiesner1

  • 1Mathematics Education, Faculty of Mathematics, University of Regensburg, Regensburg, Germany.

Frontiers in Psychology
|June 13, 2020
PubMed
Summary
This summary is machine-generated.

New frequency nets improve statistical reasoning, performing comparably to existing methods for conditional probabilities. Frequency-based visualizations consistently outperform probability-based ones for Bayesian reasoning tasks.

Keywords:
Bayesian reasoningconditional probabilitiesfrequency netjoint probabilitiesnatural frequencies

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Area of Science:

  • Statistics Education
  • Cognitive Psychology
  • Data Visualization

Background:

  • Traditional visualizations for dichotomous characteristics include 2x2 tables and tree diagrams, used with probabilities or frequencies.
  • Frequency visualizations significantly aid Bayesian reasoning compared to probability visualizations.
  • Existing methods like 2x2 tables and tree diagrams have limitations in representing both joint and conditional probabilities simultaneously.

Purpose of the Study:

  • To introduce and evaluate a novel visualization, the 'frequency net', capable of depicting both absolute frequencies and all probability types.
  • To compare the effectiveness of the frequency net against traditional 2x2 tables and tree diagrams in statistical reasoning tasks.

Main Methods:

  • Theoretical analysis of the frequency net's properties.
  • An empirical study involving 249 university students assessing reasoning performance with different visualizations (2x2 tables, double-trees, net diagrams) and formats (frequencies vs. probabilities).
  • Analysis of error patterns across visualizations and formats.

Main Results:

  • Frequency-based visualizations (2x2 tables, double-trees, net diagrams) were superior for conditional probability questions.
  • The frequency net performed comparably to frequency double-trees for conditional probabilities; familiar frequency 2x2 tables yielded the highest performance.
  • For joint probability questions, all visualizations aided performance, with probability 2x2 tables and probability net diagrams showing the highest effectiveness.

Conclusions:

  • The frequency net is a viable tool for teaching probability, offering advantages in visualizing both frequencies and probabilities.
  • Frequency visualizations are generally more effective for Bayesian reasoning, particularly for conditional probabilities.
  • Recommendations are provided for teaching probability, emphasizing the benefits of frequency-based representations and specific visualization types based on the probability type (joint vs. conditional).