contingency table

Examples of contingency table in the following topics:

• Randomization for two-way tables and chi-square

  • Randomization methods may also be used for the contingency tables.
  • In short, we create a randomized contingency table, then compute a chi-square test statistic.

• Cross Tabulation

  • Cross tabulation (or crosstabs for short) is a statistical process that summarizes categorical data to create a contingency table.
  • Cross tabulation (or crosstabs for short) is a statistical process that summarizes categorical data to create a contingency table.
  • For example, combines multiple contingency tables and tables of averages.
  • A contingency table is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables.
  • Probability can be expressed easily from the contingency table by the relative frequencies.

• Practice 2: Contingency Tables

  • The student will conduct a test for independence using contingency tables.
  • Copy the data provided in Probability Topics Practice 1: Contingency Tables into the table below.

• Comparing Two Populations: Paired Difference Experiment

  • McNemar's test is applied to $2 \times 2$ contingency tables with matched pairs of subjects to determine whether the row and column marginal frequencies are equal.
  • It is applied to $2 \times 2$ contingency tables with a dichotomous trait, with matched pairs of subjects, to determine whether the row and column marginal frequencies are equal ("marginal homogeneity").
  • A contingency table used in McNemar's test tabulates the outcomes of two tests on a sample of $n$ subjects, as follows:
  • A contingency table used in McNemar's test tabulates the outcomes of two tests on a sample of $n$ subjects.

• Student Learning Outcomes

• Contingency tables and bar plots

  • Table 1.32 summarizes two variables: spam and number.
  • A table that summarizes data for two categorical variables in this way is called a contingency table.
  • A table for a single variable is called a frequency table.
  • Table 1.33 is a frequency table for the number variable.
  • If we replaced the counts with percentages or proportions, the table would be called a relative frequency table.

• Practice 1: Contingency Tables

• Row and column proportions

  • Table 1.35 shows the row proportions for Table 1.32.
  • A contingency table of the column proportions is computed in a similar way, where each column proportion is computed as the count divided by the corresponding column total.
  • A contingency table for the spam and format variables from the email data set are shown in Table 1.37.
  • A contingency table with column proportions for the spam and number variables.
  • A contingency table with row proportions for the spam and number variables.

• Contingency Tables

  • A contingency table provides away of portraying data that can facilitate calculating probabilities.
  • The table helps in determining conditional probabilities quite easily.
  • The table displays sample values in relation to two different variables that may be dependent or contingent on one another.
  • Later on, we will use contingency tables again, but in another manner.
  • Complete the probability contingency table.

• Segmented bar and mosaic plots

  • Contingency tables using row or column proportions are especially useful for examining how two categorical variables are related.
  • Segmented bar and mosaic plots provide a way to visualize the information in these tables.
  • A segmented bar plot is a graphical display of contingency table information.
  • A mosaic plot is a graphical display of contingency table information that is similar to a bar plot for one variable or a segmented bar plot when using two variables.
  • In a similar way, a mosaic plot representing row proportions of Table 1.32 could be constructed, as shown in Figure 1.40.