Descriptive Statistics, Graphs, Reliability and Validity
Turning Data into Meaning
Once a psychologist has collected data, they need to summarise it so that patterns become visible. Descriptive statistics, tables and graphs are the tools that do this. They appear throughout both components — you might be asked to calculate a mean in a Criminal Psychology question just as easily as in the Research Methods section, so these skills need to be secure across the whole course.
Measures of Central Tendency
Measures of central tendency summarise the ‘average’ of a dataset, but the three measures — mean, median and mode — each give a different picture of what is typical.
The mean is found by adding every value together and dividing by the number of values. If five participants scored 7, 8, 6, 9 and 5 on a memory test, the mean is $$\frac{7+8+6+9+5}{5} = \frac{35}{5} = 7$$. The mean uses every score, but a single outlier can pull it up or down.
The median is the middle value once the data is placed in order from lowest to highest. With an even number of values, the median is the mean of the two middle scores. Because it ignores extreme scores, the median is often more useful than the mean when a dataset contains outliers.
The mode is the value that appears most often. It is the only measure that works with categorical data, such as the most common favourite colour in a sample. When data has been grouped into ranges, psychologists refer to the modal class — the group with the highest frequency — rather than a single modal value.
Range
The range shows how spread out a dataset is. It is calculated as the highest value minus the lowest. For the scores 5, 6, 7, 8, 9, the range is \(9 - 5 = 4\). A large range means participants performed very differently from each other; a small range means their scores were similar. Like the mean, the range is sensitive to outliers.
Mean = total ÷ number of values. Median = middle value in ordered data. Mode = most frequent value (or modal class for grouped data). Range = highest minus lowest. Mean and range are both distorted by outliers; the median is not.
Maths Skills: Ratios, Fractions, Percentages and Standard Form
OCR expects you to use basic maths confidently, not just recall it. A ratio compares quantities directly — for example, if 15 out of 20 participants conformed, the ratio of conforming to non-conforming participants is 15:5, which simplifies to 3:1. The same result could be expressed as a fraction (\(\frac{3}{4}\) conformed) or a percentage (75% conformed). Being able to move between these forms — fraction, decimal, percentage — is a skill that is tested directly.
Very large or very small numbers, such as a count of neurons involved in a brain process, are sometimes written in standard form, for example \(3.2 \times 10^4\). When rounding a calculated answer, give it to an appropriate number of significant figures — usually two or three, unless the question tells you otherwise. Always show your working before giving a final rounded answer.
A ratio compares two quantities directly (e.g. 3:1). The same relationship can be shown as a fraction, a decimal or a percentage. Standard form writes very large or small numbers as a value between 1 and 10 multiplied by a power of 10.
Displaying Data: Tables, Charts and Graphs
Frequency tables record how many times each value, or range of values, occurs, and are usually the first step before drawing a chart. A bar chart displays discrete or categorical data as separate bars with gaps between them — for example, the number of participants in each experimental condition. A pie chart shows how a total is divided into proportions, useful for displaying percentages of a sample who hold different views.
A histogram looks like a bar chart but is used for continuous data, such as ages or reaction times grouped into ranges — the bars touch because the underlying scale has no gaps. A line graph plots change over time, such as the number of hours slept across a week. A scatter diagram plots pairs of values as points to reveal whether a correlation exists between two co-variables, such as hours of revision and exam score.
Many psychological variables, when measured across a large population, form a normal distribution. Plotted as a graph, this produces a symmetrical bell-shaped curve. In a normal distribution, the mean, median and mode all sit at the same central point, and scores become rarer the further they are from that centre.
IQ scores and height are classic examples — most people score close to the average, with progressively fewer people at the extremes. The normal distribution matters because it gives psychologists a benchmark: a score close to the mean is typical, while a score in the extreme tail is unusual. Many statistical tests also assume the data being analysed is approximately normally distributed.
Reliability
Reliability asks whether a study or measure is consistent. Internal reliability checks whether a measure is consistent within itself — for example, whether different questions on the same questionnaire produce a consistent pattern of answers. External reliability checks whether a measure gives consistent results when repeated over time or in a different setting, such as a test-retest. Inter-rater reliability checks whether two or more observers scoring the same behaviour agree — high agreement increases confidence that the observation is measuring something real rather than personal judgement.
Validity
Validity asks whether a study genuinely measures what it claims to measure. Ecological validity concerns whether findings from an artificial setting, such as a laboratory, apply to everyday life. Population validity concerns whether findings from one sample can be generalised to the wider population the sample was meant to represent. Construct validity concerns whether a test genuinely measures the underlying psychological concept it is supposed to measure, rather than something else entirely.
Reliability: internal (consistent within the measure), external (consistent over time or settings), inter-rater (consistent between observers). Validity: ecological (applies to real life), population (generalises to the wider population), construct (measures the real underlying concept).