Use ratios, fractions and percentages (to include: calculating the…

The idea

A structured observation produces tallies in behavioural categories, and raw tallies rarely compare fairly because the totals behind them differ. Converting a count into a proportion of its own total puts unequal samples on one scale: 18 aggressive acts out of 45 in one nursery and 24 out of 80 in another become 40 percent and 30 percent, which is the comparison the researcher actually wants. The same relationship can be written as parts, so 18 aggressive against 27 non aggressive acts is 2 to 3, or as a part of the whole, which is two fifths. Keep the raw counts alongside the converted figures, because an inferential test on nominal data works from the frequencies themselves and never from the percentages.

What earns the marks

• The method stated plainly: the count in the category, divided by the total number of recorded behaviours, multiplied by 100, with the percent sign written in the answer.
• Saying why the conversion is made: percentages standardise, so behaviour tallied for different lengths of time, or in groups of different sizes, can be compared directly.
• Distinguishing the three forms: a ratio compares part with part in its simplest terms, such as 2 to 3, while a fraction and a percentage both express a part of the whole, such as two fifths or 40 percent.
• Converting between them accurately: divide the top of the fraction by the bottom to get 0.4, then multiply by 100 to reach 40 percent, and reverse the steps to recover a raw frequency from a reported percentage.

Common mistakes and how to put them right

• Running Chi Square on percentages rather than on the raw frequencies.

  Put it right: Chi Square compares observed counts with expected counts, so feeding it percentages changes every expected value and the whole calculation is void.

• Dividing by the wrong total, typically by the number of children observed rather than by the number of behaviours recorded, which produces a figure that cannot be a percentage of anything.

• Confusing a ratio with a fraction, so 2 to 3 is reported as two thirds of all behaviour when the aggressive acts were in fact two fifths of it.

• Dropping the percent sign or the required decimal places, so a correct calculation is written as 40 with no percent sign, or as 38 percent when one decimal place was specified.

Exam tips

• When a table gives observation tallies, write the category count divided by the total count and multiplied by 100 before stating the percentage.
• When asked to explain why the researcher reported percentages rather than the tallies, answer in terms of comparing groups with different totals, not in terms of it being easier to read.
• If the follow up asks which test, say Chi Square and justify it as a test of difference or association with nominal data and independent groups. Degrees of freedom are the number of rows minus one, multiplied by the number of columns minus one, and the observed value of Chi Square must be equal to or greater than the critical value for the result to be significant.
• Note the contrast in direction between tests, because examiners ask for it: Chi Square and the t tests need the observed value to be equal to or greater than the critical value, while Mann Whitney U and Wilcoxon need the observed value to be equal to or less than it.