Substitute numerical values into algebraic equations using appropriate…

The idea

A calculation question hands you a table of data and a printed formula, and the marks go to the candidate who puts the right number in the right place. Work through the formula symbol by symbol and write down what each one stands for before any arithmetic. For Chi Square the observed value of a cell is the frequency actually counted there, and the expected value is found by multiplying that cell’s row total by its column total and dividing by N, the total number of scores. For Spearman’s rho the figures to insert are the difference between each pair of ranks, squared and then summed, together with N as the number of pairs of scores. Keep the unit of the original measure, so seconds stay seconds and words recalled stay words recalled, and leave the substitution visible on the page.

What earns the marks

• Writing the formula out and saying what each letter stands for, so the marker can see N identified as the number of scores or the number of pairs of scores rather than the number of conditions or the number of groups.
• Showing the substituted line in full before the answer, because the method mark survives an arithmetic slip while a bare wrong number earns nothing at all.
• Calculating each expected frequency rather than counting it, using the row total multiplied by the column total divided by the overall total, and doing this for every cell of the contingency table.
• Giving the answer to the accuracy the question asks for, usually two decimal places, and carrying the unit of the original measurement wherever the figure has one.
• Squaring each rank difference before summing for Spearman’s rho, so that negative differences do not cancel positive ones.

Common mistakes and how to put them right

• Putting the number of participants into a formula that asks for the number of scores.

  Put it right: In a repeated measures design one participant supplies two scores, and for Wilcoxon the N read against the table is the number of pairs left after every difference of zero has been dropped.

• Substituting raw scores where the formula needs ranks, which happens whenever Spearman’s rho is worked straight from the original measurements without ranking each variable first.

• Mixing units inside one calculation, adding a time recorded in seconds to a time recorded in milliseconds without converting, so the total means nothing.

• Rounding at every intermediate step, which can push the final value across the critical value and reverse the decision about significance.

Exam tips

• For a calculate command, show the values substituted into the equation with their units before simplifying to the final result.
• The table in the stem is the source of every number you use, so label the totals you take from it and check that the row totals and the column totals reach the same grand total before substituting.
• A calculation is often followed by a question asking you to explain why that test was chosen, so be ready to name the level of measurement, the experimental design, and whether a difference or a relationship is being tested.