Before we can choose which descriptive or inferential statistics are appropriate, we need to know which level of measurement was used in the data collection. There are four levels of measurement which vary from the most precise to the least precise and this affects the type of statistics that are suitable.
Interval and ratio data are the most precise: They use standardised units where the intervals between data points are always exactly the same; i.e. between 1cm and 2 cm on a ruler there are always 10 small intervals, called millimetres. There are 10 millimetres between every centimetre on a ruler and this never changes.
Ratio data is special because zero means zero!: There are no minus values. You can’t run a race in -65 seconds! Time starts with zero seconds and increases with each second, there is no negative time only positive time. Zero means the clock hasn’t been started yet! Some measurements don’t have a ‘true’ zero, they start at zero but this is simply an arbitrary starting point, e.g. temperature has meaningful minus degrees.
Ordinal data means that the data points can be put into rank order: You could put interval scores into rank order from the person with the most, to the person with the least. You can then assign them a rank, e.g. in a group of 10 participants, the person with the bottom score gets ranked as 1 and the person with the top score gets ranked as 10. As you can see interval data can become ordinal data. However, once a person is given rank score we no longer know how big the gap is between their scores. For example, the intervals might be different now; the difference between the bottom (1) and second to bottom 2) scores might be only 3 seconds, but the difference between the top (10) and second to top (9) scores might be 15 seconds for all we know. You can see now that ordinal data is not as precise as interval data and also that ordinal data cannot become interval data; we have started to lose some of the precision.
In psychology we sometimes decide that our data should be treated as ordinal as it is often hard to say whether the gaps between scores are actually a standard interval, for example if someone remembers 12 items on a memory test is their memory three times as good as someone who remembers only 4, or were some of the test items easier for that person, making them say only twice as good. When someone rates themselves on a scale of 1-10 for how messy they are, might one person’s 6 be another person’s 4? Do you see how some psychological data needs to be treated with a degree of caution; if we want to be rigorous and as scientific as possible, we should err on the side of caution and treat our data as ordinal? If we have used ratings scales such as a Likert scale, then this will generally be treated as ordinal data as the scales are relatively subjective, even when participants are given clear instructions about how ratings should be assigned. This said, many academics who use rigorously standardised psychological measures using Likerts will class the data as interval, but only if the scale has 7 or more points.
Nominal data is the least precise form of data collection; here we are simply counting up frequencies. This is sometimes called category data; maybe we want to know how many people got an A grade, how many B grades, C grades etc. From this we can’t tell who came top (ordinal) and we certainly can’t tell how many points they actually scored (ratio). We might count how many times we observed hitting in the playground from the boys and how many times from the girls, but we don’t know who was the most aggressive or how many times they actually hit anyone!
Having decided which level of measurement was used, you can now choose your descriptive statistics:
|Measure of central tendency||Mode||Median||Mean|
|Measure of dispersion||Variation ratio (percentage of non-modal scores)||Range and/or interquartile range||Standard deviation|