Presentation & Display of Data

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Presentation and Display of Quantitative Data

Quantitative (numerical) data tend to be displayed using graphs and charts. The most common examples are tables, bar charts, and (for correlation) scattergrams.

Tables

When writing up the results of their research, psychologists tend to display findings in graphs and tables.
A table is a simple way to display numerical findings — usually in the form of descriptive statistics such as the mean and standard deviation.
It is often easier for the reader to find information in a table than from a written text.
Tables can also be used to summarise qualitative data.

Charts

A chart shows the data in a more visual way. It can be helpful to illustrate smaller and larger differences between conditions.

Bar chart

The bar chart is the most commonly used type of graph in psychology research:
- The bar chart usually shows the IV along the base (x axis).
- The DV is shown up the side (y-axis), with the height of the bars indicating the mean score.
- Each bar represents one condition of the IV.

Histograms and pie charts

Histograms and pie charts are less frequently used.
A histogram shows a continuous variable along the horizontal (x) axis, such as the age range of different participants, and line graphs have a similar purpose.
A pie chart should represent fractions of a whole. It is not the right choice for showing the DV in a study, but could be used to describe characteristics of a sample.

Scattergrams

Scattergrams are only used to show correlations, not the results of experiments.

Data Distributions

Data are often assumed to be normally distributed, but some sets of data are skewed distributions.

Normal distribution

The normal distribution describes a set of data where scores are very common in the middle of the distribution (close to the mean) and become progressively less common the further they are from the mean.
IQ is an example of a normally-distributed variable.
On a line graph, a normal distribution appears as a bell-shaped curve.

Mathematical properties

A normal distribution has certain mathematical properties:
- 50% of scores fall above the mean, and the other 50% below the mean.
- Approximately 68% of scores fall within one standard deviation above or below the mean.
- Approximately 95% of scores fall within two standard deviations above or below the mean.
- Each tail of the graph gets progressively closer to zero, meaning that they become less and less common as they get further from the mean.

Mathematical properties image

Skewed distribution

A skewed distribution is similar to the normal distribution’s bell-shaped curve but the bulk of scores fall more to one side of the median score, with a longer ‘tail’ on the other.
A very difficult test or exam may result in a skewed distribution, with many low scores and only a few high scores.
Average income is also skewed - most people are at or below the median income, and only a few have very high incomes.

Positive skew

In a positively skewed distribution, the mode is a lower value than the mean and median. The skew is to the right.
- If the distribution of A level results were positively skewed this would mean that more students were achieving the lower grades than the higher grades and the modal grade might be a D. In this case, the exam board might lower the grade boundaries in order to achieve a more normal distribution of results.

Positive skew image

Negative skew

In a negatively skewed distribution, the mode is a higher value than the mean and median. The skew is to the left.
- If the distribution of A level results were negatively skewed this would mean that more students were achieving the higher grades than the lower grades and the modal grade might be a B. In this case, the exam board might raise the grade boundaries in order to achieve a more normal distribution of results.