Data Handling and Descriptive Statistics
Working with Data
Collecting data is only the beginning. Once a psychologist has run a study, they must organise, summarise and display the results in a way that makes patterns visible and allows conclusions to be drawn. Data handling and descriptive statistics are the tools that do this work. They run through every topic in psychology — understanding them unlocks your ability to interpret any study you encounter.
Types of Data
Quantitative data is expressed as numbers. It allows direct comparison and statistical calculation — for example, the number of words recalled in a memory test, a score on an anxiety rating scale, or the time taken to complete a task. Qualitative data is expressed in words or descriptions. It captures meaning, experience and complexity that numbers cannot convey — for example, a participant’s account of what they were thinking during an experiment.
Both types have value. Quantitative data is easier to compare, analyse statistically and replicate. Qualitative data is richer and more contextual but harder to analyse consistently and more open to researcher interpretation.
Primary and Secondary Data
Primary data is collected directly by the researcher for their own study — running an experiment, conducting an interview, carrying out an observation. It is tailored to the research question and provides the most direct evidence, but is time-consuming and expensive to collect.
Secondary data is data collected previously by someone else, often for a different purpose, that the researcher re-analyses. Examples include published statistics, previously conducted studies, or databases. Strength: saves time and resources. Weakness: the data may not perfectly match the current research question, and the researcher cannot control its quality.
Four data types: quantitative (numbers), qualitative (words/descriptions), primary (collected first-hand by this researcher), secondary (collected previously by someone else). Both quantitative and qualitative can be primary or secondary — these are separate classifications.
Descriptive Statistics: Measures of Central Tendency
Descriptive statistics summarise data concisely. The three main measures of central tendency each give a different picture of the ‘average’ in a dataset.
The mean is calculated by adding all values and dividing by the number of values. For example, if five participants recalled 7, 8, 6, 9 and 5 words, the mean is $$\frac{7+8+6+9+5}{5} = \frac{35}{5} = 7$$ words. The mean uses all the data and is sensitive to outliers — a single extreme value can pull the mean up or down significantly.
The median is the middle value when data is arranged in order. If there is an even number of values, the median is the mean of the two middle values. The median is not affected by outliers, making it a better measure of typical performance when extreme scores are present.
The mode is the most frequently occurring value. It is the only measure that can be used with categorical data (e.g. the most common eye colour in a sample) but gives limited information if every value occurs equally often.
Range
The range describes how spread out the data is. It is calculated by subtracting the lowest value from the highest. For the dataset 5, 6, 7, 8, 9, the range is \(9 - 5 = 4\). A large range indicates great variability in the data; a small range indicates participants performed similarly. Like the mean, the range is sensitive to outliers — one extreme value will inflate it.
Mean = sum of all values ÷ number of values. Median = middle value in ordered data. Mode = most frequent value. Range = highest minus lowest. Mean and range are sensitive to outliers; median is not.
Displaying Quantitative Data
Data is often displayed visually to make patterns clearer. Frequency tables show how many times each value (or range of values) occurs. A bar chart uses separate bars to represent each category; gaps between the bars show that the categories are discrete. A histogram is used for continuous data (such as ages or heights grouped into ranges), with no gaps between bars because the underlying scale is continuous.
Many psychological variables, when measured in large populations, form a normal distribution. This produces a symmetrical, bell-shaped curve when data is plotted. The key characteristics of a normal distribution are: the mean, median and mode are all the same value (the centre of the curve); the distribution is symmetrical about this central point; most scores cluster around the mean, with fewer and fewer scores as you move towards the extremes.
Intelligence test scores and height are classic examples: most people score near the average, with progressively fewer people at the extremes. The normal distribution is important in psychology because many statistical tests assume data is approximately normally distributed, and because it provides a reference for understanding how typical or unusual any given score is. A score at the extreme tail of the distribution is rare; a score near the centre is typical. This is why psychologists often use the normal distribution as a benchmark when evaluating individual results.