4.2.3.2 - Presentation and display of quantitative data

Why display quantitative data?

Psychologists collect quantitative data so that behaviour and experience can be summarised numerically. A display turns those numbers into something a reader can inspect. It helps answer questions such as: Which condition had the higher score? How spread out were the scores? Do two co-variables appear to be related?

A display is not the same thing as a statistical conclusion. A bar chart may show that one condition had a higher mean than another, but it does not by itself prove that the difference is significant. A scattergram may show a positive relationship, but it does not prove that one variable caused the other. Good exam answers keep this boundary clear.

For this specification point, AQA names five display terms:

The exam skill is rarely just naming the display. It is usually naming it and justifying why it fits the data. The fastest route is to ask: "Am I comparing categories, showing grouped frequencies, or looking for a relationship between two variables?"

Tables: precise numerical summaries

A table is useful when the reader needs to compare exact numerical values.

Tables are best when the reader needs precise numbers. In psychology, a results table often summarises descriptive statistics, such as means, medians, ranges or standard deviations, for each condition or group. Raw paired scores can also be tabulated before analysis; each row must clearly identify a case or category.

A good table has:

• a clear title that says what the data are about;
• row and column headings that identify the variables, conditions or groups;
• units where needed, such as "seconds", "rating out of 10" or "score out of 20";
• consistent rounding, such as all means to one decimal place;
• enough information to interpret the pattern without clutter.

Constructing a frequency table

For these ten recall scores, 2, 4, 4, 5, 7, 7, 7, 9, 9, 10, list each observed score in order, tally each occurrence once and total the frequencies:

The total must equal the number of observations: $1+2+1+3+2+1=10$. A frequency of 3 at score 7 means three participants each recalled seven words, not that seven people recalled three words. The mode is 7. The mean can be recovered without expanding the list: multiply each score by its frequency, then divide the total score by the total frequency. Here $(2\times1+4\times2+5\times1+7\times3+9\times2+10\times1)/10=64/10=6.4$ words.

Comparing conditions

Table 1. Word recall after two revision conditions, maximum score = 20

This table is useful because it shows exact values. The silent revision condition has the higher mean, so participants recalled more words on average. The phone notification condition has the larger range, so scores were more spread out. A careful interpretation would be:

Participants recalled more words on average after silent revision than after revision with phone notifications. Scores were also less variable in the silent condition. However, the table alone does not show whether the difference is statistically significant.

That final sentence matters. A display helps interpretation, but an inferential test would be needed before claiming a statistically significant difference.

Bar charts: comparing categories

Separate categories can be compared by drawing one bar for each category.

Bar charts are used when the x-axis shows distinct categories rather than a continuous scale. In psychology, common categories include experimental conditions, participant groups, questionnaire response options or types of behaviour.

For a vertical bar chart:

• the x-axis usually names the categories or conditions;
• the y-axis shows the numerical value, such as frequency, percentage or mean score;
• the bars are separated by gaps because the categories are separate;
• the y-axis should usually start at zero when bar height is used to compare size, otherwise the difference can look exaggerated;
• both axes need precise labels, not vague labels such as "result" or "score".

Worked AQA-style example:

A psychologist compares the mean number of aggressive acts shown by children after watching either a violent cartoon or a non-violent cartoon. The violent cartoon group has a mean of 8.4 aggressive acts. The non-violent cartoon group has a mean of 3.1 aggressive acts.

A suitable display would be a bar chart. The x-axis would show the two viewing conditions: violent cartoon and non-violent cartoon. The y-axis would show "mean number of aggressive acts". The bars would be separated because the two conditions are separate categories. The taller bar for the violent cartoon condition would show a higher mean level of aggression.

To draw the chart, choose a y-axis from 0 to 10 with equal 2-unit steps, mark the two condition labels on the x-axis, then draw equal-width separated bars to 8.4 and 3.1. A point at 8.4 lies one fifth of the way from 8 to 10. Give the graph a title and label the y-axis "Mean number of aggressive acts". The source means are represented by bar heights, not by the number or width of bars.

[DIAGRAM: asset_name: Bar chart comparing cartoon conditions; asset_slug: 4_2_3_2_04_bar_chart; description: Separated bars from a zero baseline show mean aggressive acts of 8.4 after a violent cartoon and 3.1 after a non-violent cartoon.]

A histogram would be inappropriate here because the cartoon conditions are separate categories, not numerical intervals.