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How to Calculate the Expected Value of a Chi-Square

    • 1). Organize data into cells with rows and columns, with a number in each cell. For example, if you want to know if there is a relationship between hot and cold months and whether or not people like ice cream. You survey 220 people, and classify each month as either a hot month or a cold month. Your variables are month's temperature and ice cream preference, using a two-by-two table with four cells that may look like this:

      Hot Months/Like = 100

      Hot Months/Not like = 10

      Cold Months/Like = 5

      Cold Months/Not Like = 105

    • 2). Add the number of people who voted in each category for that row to derive a row total and a column total.

      In this example:

      Hot Months = 110

      Cold Months = 110

    • 3). Add together the number of people who voted in one category for all rows to derive a column total.

      In this example:

      Like = 105

      Dislike = 115

    • 4). Multiply the column total by the row total.

      In this example:

      Like/Hot/Cold: 110x105=11,550

      Not Like/Hot/Cold: 110x115=12,650

    • 5). Divide each column/row total by the total number of observations. In this example:

      Hot Months/Like = 11,550/220 = 52.5

      Hot Months/Not like = 12,650/220 = 57.5

      Cold Months/Like = 11,550/220 = 52.5

      Cold Months/Not Like = 12,650/220 = 57.5

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