Solve simple algebraic equations (to include: calculating the degrees of…

The idea

Degrees of freedom decide which line of the Chi Square table you read; the wrong line gives the wrong critical value and decision. The rule is the number of rows minus one, multiplied by the number of columns minus one, written as (rows - 1)(columns - 1). Count only the cells holding observed frequencies, so a 2 by 2 contingency table has 1 degree of freedom and a 2 by 3 table has 2. Read the critical value at the chosen significance level. The AQA Chi Square table does not require choosing between one and two tails. Compare in the correct direction: Chi Square is significant when the calculated value is equal to or greater than the critical value. The same habit of rearranging a short equation turns a total and a number of participants into a mean.

What earns the marks

• Quoting the rule as (rows - 1)(columns - 1) and showing the numbers put into it, so that a 2 by 3 table gives 1 multiplied by 2, which is 2 degrees of freedom.
• Counting rows and columns from the observed frequencies only, and leaving out the row of totals and the column of totals that a printed table often carries.
• Using the degrees of freedom together with the level of significance to read the critical value from the Chi Square table, noting that this specific table does not use one or two tails.
• Stating the comparison in the right direction, since the calculated Chi Square value must be equal to or greater than the critical value for the result to be significant.
• Rearranging other short equations correctly under exam pressure, such as making the mean the subject by dividing the total of the scores by the number of scores.

Common mistakes and how to put them right

• Using the number of participants, or the grand total of the frequencies, as the degrees of freedom instead of the size of the table.

  Put it right: A study of 60 people set out in a 2 by 2 table still has 1 degree of freedom.

• Counting the totals row and the totals column as data, so a 2 by 2 table is read as 3 by 3 and the critical value is taken from the wrong line of the table.

• Comparing in the wrong direction and calling a small calculated value significant because Mann Whitney U and Wilcoxon T work that way.

  Put it right: Chi Square needs the calculated value to be equal to or greater than the critical value.

• Looking for one-tailed or two-tailed columns in the Chi Square critical values table, which are not present in the AQA specification table.

Exam tips

• Degrees of freedom appear as a calculate question attached to a contingency table, so count the table first and write the substituted rule rather than the bare answer.
• Longer questions ask you to explain whether the result is significant, which needs the degrees of freedom, the level of significance, the calculated value, the critical value and the decision about the null hypothesis.
• Where a table of critical values is printed, point to the exact figure you used, because the marks are for the comparison rather than for the arithmetic.