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Related Concept Videos

Contingency Table01:29

Contingency Table

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A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; The table helps determine conditional probabilities quite quickly and can help systematically organize, analyze and quantify data. The table displays sample values concerning two variables that may be dependent or contingent on one...
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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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In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
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Percentage Frequency Distribution00:57

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A percentage frequency distribution, in general, is a display of data that indicates the percentage of observations for each data point or grouping of data points. It is a commonly used method for expressing the relative frequency of survey responses and other data. The percentage frequency distributions are often displayed as bar graphs, pie charts, or tables.
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Consider a curve representing sample data drawn randomly from a normally distributed population. One must construct confidence intervals to estimate or to test a claim regarding the population standard deviation. For example, a 95% confidence interval covers 95% of the area under the curve, and the remaining 5% is equally distributed on either side of the curve. To achieve such confidence intervals, one must determine the critical values. The critical values are simply the values separating the...
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Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of...
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"Percentaging" contingency tables: It really does matter how you do it.

Thomas R Knapp1

  • 1Professor Emeritus, University of Rochester and The Ohio State University, 78-6800 Alii Dr. #10, Kailua-Kona, HI, 96740.

Research in Nursing & Health
|May 21, 2015
PubMed
Summary
This summary is machine-generated.

Understanding contingency tables requires careful percentaging. This study clarifies how calculating percentages by rows, columns, or total sample size impacts the interpretation of variable relationships.

Keywords:
contingency tablesdependent variablefrequency countsindependent variablepercentaging

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Area of Science:

  • Statistics
  • Data Analysis

Background:

  • Contingency tables are crucial for visualizing co-occurring categorical variables.
  • Interpreting these tables often involves converting frequencies to percentages.

Purpose of the Study:

  • To elucidate the complexities of percentaging contingency tables.
  • To demonstrate how different methods of percentage calculation affect interpretation.

Main Methods:

  • Utilized both artificial and real-world datasets for analysis.
  • Illustrated percentaging techniques by calculating percentages down columns, across rows, and by total sample size.

Main Results:

  • The direction of percentage calculation significantly influences the perceived relationship between variables.
  • Incorrect percentaging can lead to misinterpretation of co-occurrence data.

Conclusions:

  • Proper percentaging of contingency tables is essential for accurate data interpretation.
  • Researchers must be mindful of the chosen percentaging method to avoid analytical errors.