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How to Work Chi Squares

Scientific investigation requires the creation and running of experiments to test and validate models. Once an experiment is complete the collected data needs to be compared to data predicted by models. A number of statistical tests can do this, but the most commonly used is known as the chi-squared test. This allows the calculation of a chi-squared value. This value can be looked up on a table to check if there is a statistical discrepancy between the model and experimental data.

Things You'll Need

Paper
Calculator

Instructions

- 1
  Make a five-column table of the experimental and theoretical data. Label the heading of the first column "Experimental Data", the heading of the second column "Theoretical Data", the heading of the third column "Experimental minus theoretical", the heading of the fourth column "(Experimental minus theoretical )squared", and the heading of the fifth column is "( Experimental minus theoretical)squared/theoretical".
- 2
  Write the experimental and theoretical data into the first two columns. Using a calculator calculate the values of the other columns. The formula's for the remaining columns are given in the headings.
- 3
  Calculate the sum of the values in the fifth column. This is known as the chi squared value. Determine a standard for deciding whether or not the experimental and theoretical values match. For example, it may be decided that if the experimental and theoretical values are within 5 percent (0.05) of one another, then they are in agreement. Determine the number of degrees of freedom. This is the number of categories with 1 subtracted. There are only two categories (Experimental and theoretical) in this example, so the degrees of freedom is equal to 1.
- 4
  Look up the value of chi squared for number of degrees of freedom and the acceptable percentage value. Following the example, find the degrees of freedom =1 row, and the percentage value=0.05 column. Find the value where these row and columns intersect.
  If the calculated value for chi squared exceeds the value found in the table, then experimental and theoretical data are in agreement to within 5 percent. If the calculated value for chi squared is less than the value found in the table, then there is a discrepancy between the experimental and theoretical data of more than 5 percent.

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