How Do I Calculate Observed Chi?

Observed chi (rhymes with tie) represents how often each level of a categorical variable appears. For example, observed chi can reflect how many people in a sample identify as male or female. You can calculate two versions of observed chi by inputting your data into a simple table and performing a few quick calculations. You can use observed chi to conduct a Chi Square Test of Independence or Goodness of Fit.

Things You'll Need

  • Calculator
  • Microsoft Excel (optional)
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Instructions

    • 1

      Create a table with rows devoted to each level of your categorical variable. Title each row with respect to the level of your categorical variable that it represents. Create an additional row called "Total."

      For example, to examine the proportion of males to females in a classroom, you would create three rows: "Males," "Females" and "Total."

    • 2

      Create two columns for your table. Title your columns "Frequency" and "Percentage."

    • 3

      Input the values for each level of your categorical variable in their respective rows in the "Number" column.

      For example, if you determined that there were 76 males and 87 females in the classroom, you would write 76 in the "Males" row and 87 in the "Females" row.

    • 4

      Add up each value in the "Frequency" column. Input this sum in the "Total" row of the "Frequency" column.

      Following the example of the proportion of males to females in a classroom, you would input 163 (76 + 87) into the "Totals" row.

    • 5

      Divide the value in the "Frequency" column for each level of your categorical variable by the value in the "Total" row. Multiply the quotient from each of these divisions by 100, and input each product in its respective row in the "Percentage" column.

      Following the example of the proportion of males to females in a classroom, you would divide values for males (76) and females (87) in the "Frequency" column by the value in the "Total" row to yield 0.466 for males and 0.534 for females. You would then multiply each of these values by 100 to yield 46.6 for males and 53.4 for females. So, you would input "46.6" into the "Males" row of the "Percentage" column and "53.4" into the "Females" row.

    • 6

      You now have a table containing values of observed chi in two forms: frequency and percentage. You may use the frequency values to complete a Chi Square test; however, it is often most practical to use the percentages. This is because you must compare observed chi with expected values. Expected values are usually expressed as percentages.

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