Recognise and use expressions in decimal and standard form (to include:…

The idea

Psychology papers print very small and very large numbers compactly, so a reaction time, a hormone concentration or a probability from a computer printout often arrives as a coefficient between one and ten multiplied by a power of ten. To read it, move the decimal point once for every power, to the right for a positive power and to the left for a negative one, so 2.5 times ten to the power of minus three seconds is 0.0025 seconds. That skill is examined in two familiar places. A probability has to be compared against the five percent significance level before a result can be called significant, and a graph has to be drawn from plain frequencies: divide each category total by the grand total, multiply by 360, and label every sector with its category and its percentage.

What earns the marks

• Turning frequencies into sector angles: the frequency in a category, divided by the total number of observations, multiplied by 360 degrees, with the sectors summing to 360 degrees and each one labelled.

Common mistakes and how to put them right

• Moving the decimal point the wrong way for a negative power, so 3.0 times ten to the power of minus two is written as 300 instead of 0.03, which makes a fast reaction time look enormous.

• Reading a probability of 5.0 times ten to the power of minus four as bigger than 0.05 because the coefficient looks bigger, then wrongly retaining the null hypothesis when the result was in fact significant.

• Writing a coefficient that is not between one and ten, such as 25 times ten to the power of three in place of 2.5 times ten to the power of four.

• Drawing the pie chart from percentages that do not total one hundred, or leaving the sectors unlabelled, which loses the display marks however accurate the arithmetic was.

Exam tips

• Expect standard-form values inside a Research Methods results table; convert them carefully before drawing or interpreting the requested display.
• Show the working. A calculation mark is often available for the division and the multiplication even when the final figure is wrong, and an answer with no working scores nothing if it is wrong.
• Give the answer to the accuracy the stem demands and keep the unit, so write 0.03 seconds when two decimal places are asked for, and do not round until the final step.
• If the data are two co variables rather than categories, the display is a scattergram and the test is Spearman's rho, where the observed value of rho must be equal to or greater than the critical value at p less than or equal to 0.05 for that number of pairs.