Data Presentation, Levels of Measurement and Correlation

Before you can choose a graph, a descriptive statistic or an inferential test, you have to know how precise your data is. AQA identifies three levels of measurement, running from least to most precise.

Level	Description	Example	Precision and test-suitability note
Nominal	Data in named categories, recorded as counts of how many cases fall into each	Number of people who chose tea, coffee or water	Least precise; only frequencies, no order between categories
Ordinal	Data that can be ranked or ordered, but with unequal intervals between the points	Ratings of confidence out of 10; finishing positions in a race	The gap between 1st and 2nd may not equal the gap between 2nd and 3rd
Interval	Data on a scale with equal, fixed intervals between points	Temperature in °C, time in seconds, standardised test scores	Most precise; equal intervals mean the numbers can be treated arithmetically

The key idea is that the level of measurement determines which descriptive statistics and inferential tests are appropriate. Nominal data can only be counted; ordinal data can be ranked; interval data supports the full range of arithmetic, so it unlocks the most powerful analyses.

Read the three levels in order of precision: nominal → ordinal → interval. Each level does everything the one before it does, and adds something more.

Get the distinctions exact, because a single word in the question tells you which level you are dealing with.

Nominal data is purely categorical. You sort responses into named groups and count how many land in each. There is no sense in which one category is "higher" than another. If 12 people preferred tea and 8 preferred coffee, "tea" is not a bigger number than "coffee" — the 12 and the 8 are frequencies.

Ordinal data can be put in order, but the intervals between values are not equal or fixed. A confidence rating of 8 out of 10 is higher than 4, yet you cannot claim it is "twice as much" confidence, because one person's idea of an 8 need not match another's. Positions in a race are ordinal too: the runner-up is behind the winner, but that says nothing about the size of the gap.

Interval data uses a scale with equal, measurable intervals. The difference between 10 °C and 20 °C is exactly the same size as the difference between 20 °C and 30 °C. Time, reaction speed in milliseconds and standardised IQ scores are treated as interval, which is why they are the most precise.

A quick test: if you can only count it, it is nominal. If you can rank it but the gaps are uneven, it is ordinal. If the gaps are equal and fixed, it is interval.

Once data is collected, it is displayed so that a reader can grasp the pattern at a glance. AQA names four forms of display: tables, bar charts, histograms and scattergrams.

Type	What it shows	Key feature
Table	A summary of descriptive statistics, not the raw data	Has a clear title; reports figures such as means and ranges per condition
Bar chart	Discrete or categorical data	Bars have gaps between them; height = frequency or mean
Histogram	Continuous data	Bars touch with no gaps; area represents frequency
Scattergram	A correlation between two co-variables	Each point is one pair of scores

A table in a report summarises the descriptive statistics — the means, ranges or totals for each condition — rather than listing every participant's raw score. It should carry a clear title so the reader knows what is being compared.

A bar chart is for discrete or categorical data, such as the mean recall in two separate conditions of an experiment. The defining feature is the gaps between the bars: the gaps signal that the categories on the x-axis are separate and do not form a continuous scale. The height of each bar shows the frequency or the mean for that category.

The single most tested distinction here is bar chart (gaps, categories) vs histogram (no gaps, continuous). Fix it now and you will not lose marks later.

A histogram displays continuous data — data that can take any value along a scale, such as reaction times or ages. Because the x-axis is a continuous scale divided into equal intervals, the bars touch with no gaps. The area of each bar represents the frequency of scores falling in that interval.

The contrast with the bar chart is deliberate. Gaps mean separate categories; touching bars mean an unbroken continuous scale. If you draw a histogram with gaps, you have contradicted the very thing a histogram is for.

A scattergram is used to display a correlation between two co-variables. Every point plots one participant's pair of scores: their value on one co-variable against their value on the other. The overall pattern of the points shows whether the two co-variables rise together, move in opposite directions, or show no relationship.

Here the points trend downwards from left to right: more sleep is associated with faster (lower) reaction times, so this is a negative correlation.

A correlation measures the relationship between two co-variables. It does not manipulate anything, so it cannot on its own establish cause. The strength and direction of that relationship are summarised by a single number: the correlation coefficient.

A correlation coefficient always falls between -1 and +1:

• +1 is a perfect positive correlation — as one co-variable increases, the other increases in exact step.
• -1 is a perfect negative correlation — as one co-variable increases, the other decreases in exact step.
• 0 means no correlation — no linear relationship between the co-variables.

Two things are encoded in the number. The sign (+ or -) gives the direction; the distance from zero gives the strength. The closer the value is to +1 or -1, the stronger the relationship.

Coefficient	Interpretation
+0.9	Strong positive correlation
+0.4	Weak-to-moderate positive correlation
0	No correlation
-0.8	Strong negative correlation
-0.3	Weak negative correlation

Worked interpretations: -0.8 is a strong negative correlation, and it is stronger than +0.4, because 0.8 is closer to 1 than 0.4 is — the minus sign has nothing to do with strength. Likewise, +0.9 and -0.9 are equally strong; they simply point in opposite directions.

Correlation does not equal causation. Even a coefficient of +0.95 shows only that two co-variables move together, not that one causes the other. A third, uncontrolled variable may explain the relationship.

Not all research produces numbers to begin with. Content analysis studies qualitative material — interview transcripts, adverts, diaries, social-media posts — and turns it into data that can be analysed.

Coding is the technique that makes this possible. It means grouping the qualitative material into categories or units that can then be counted, converting words into quantitative data. For example, a researcher analysing television adverts might code each one by the gender of the main character, then count how many fall into each category.

Once coded, the result is usually nominal data — frequencies in named categories — which is exactly why levels of measurement matter here too. The coded counts can then be displayed in a table or a bar chart.

Coding converts qualitative material into quantitative data by sorting it into countable categories. The categories must be defined clearly enough that a second researcher would code the same material the same way.

1. Using the wrong graph for the data type

A histogram is for continuous data and a bar chart is for discrete or categorical data. Drawing a histogram for categorical data (such as favourite subject), or a bar chart for continuous data (such as reaction times), is a frequent error. Match the graph to the data first.

2. Drawing a bar chart with no gaps

The gaps between bars are what make a bar chart a bar chart — they show the categories are separate. A bar chart drawn with the bars touching looks like a histogram and implies a continuous scale that is not there.

3. Treating ordinal data as interval

Ordinal data can be ranked but its intervals are unequal, so the gap between a rating of 4 and 5 is not guaranteed to match the gap between 8 and 9. Treating ratings-out-of-10 as if they were a true interval scale over-claims the precision of the data.

4. Reading a negative coefficient as weak

A coefficient of -0.9 is a very strong correlation, not a weak one. The minus sign only gives the direction. Strength is judged by the distance from zero, so -0.9 is stronger than +0.4.

5. Saying a scattergram shows cause

A scattergram displays a correlation, and correlation does not establish causation. Writing that the scattergram "proves" one co-variable causes the other ignores the possibility of a third, uncontrolled variable.

6. Confusing the level of measurement with the data itself

The level describes the precision of the measurement scale, not the topic. The same variable (for example, anxiety) can be nominal (anxious / not anxious), ordinal (self-rated 1–10) or interval (a standardised anxiety-scale score) depending on how it is measured. Read how the data was collected before naming the level.