Data Analysis and Descriptive Statistics
Working with Data
Collecting data is only the first step in psychological research. Once a study has been run, the researcher must organise, summarise and display the results so that patterns become visible and conclusions can be drawn. This lesson covers the data-handling and descriptive-statistics skills you need for your exam — including the calculations you are expected to show working for.
Types of Data
Quantitative data is expressed as numbers, allowing direct comparison and calculation — for example, the number of words recalled in a memory test or a score on a rating scale. Qualitative data is expressed in words or descriptions, capturing meaning and detail that numbers cannot — for example, a participant’s account of what they were thinking during a task.
Primary data is collected directly by the researcher for their own study, such as running an experiment or conducting an interview. Secondary data was collected previously by someone else — published statistics or an earlier study, for example — and is re-analysed by the current researcher. It saves time but may not match the current research question exactly.
Quantitative data is numerical; qualitative data is in words. Primary data is collected first-hand by this researcher; secondary data was collected previously by someone else. Any dataset can combine these — for example, quantitative secondary data such as national exam results.
Mean, Median and Mode
The mean is found by adding all the values and dividing by how many there are. 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 every value, so it is sensitive to outliers — one very high or low score can pull it away from the typical value.
The median is the middle value once the data is ordered. With an even number of values, it is the mean of the two middle numbers. Because it ignores extreme scores, the median is a better measure of the ‘typical’ result when outliers are present.
The mode is the value that appears most often. It is the only measure of central tendency that works with categorical data, such as the most common favourite colour in a sample, but it gives little information if scores are spread evenly.
Range
The range shows how spread out a dataset is: highest value minus lowest value. 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 performance was consistent. Like the mean, the range is distorted by a single outlier.
Mean = total of all values divided by how many values there are. Median = middle value once ordered. Mode = most frequent value. Range = highest minus lowest. Mean and range are pulled about by outliers; the median is not.
Ratios, Fractions and Percentages
Edexcel expects you to convert and interpret data using ratios, fractions and percentages — skills tested directly in your exam. If a sample of 30 participants contains 18 women and 12 men, the ratio of women to men is \(18:12\), which simplifies to \(3:2\).
The same data can be expressed as a fraction: \(\frac{18}{30}\) of the sample were women, which simplifies to \(\frac{3}{5}\). Always simplify fractions to their lowest terms where possible — this shows you understand the relationship between the numbers, not just the raw values.
To convert a fraction to a percentage, multiply by 100. \(\frac{18}{30} \times 100 = 60\%\) of the sample were women. Percentages let you compare groups of different sizes fairly — for instance, comparing the proportion of participants who conformed in two studies with different sample sizes.
Ratios compare two quantities with a colon (e.g. \(3:2\)). Fractions show a part out of a whole and should be simplified. Percentages are found by multiplying a fraction by 100 and let you compare proportions across different sample sizes.
Standard Form and Significant Figures
Psychological data can involve very large or very small numbers — for example, the number of neurons in the brain. Standard form writes these more manageably as a number between 1 and 10 multiplied by a power of 10. For example, 86,000,000,000 neurons can be written as \(8.6 \times 10^{10}\).
You are also expected to round answers to an appropriate number of significant figures. A mean of 7.428571 words recalled should usually be rounded to a sensible level of precision, such as 7.4 (2 significant figures), rather than reported with excessive decimal places that imply false accuracy.
Displaying Quantitative Data
Frequency tables record how many times each value, or range of values, occurs. A bar chart displays separate categories as bars with gaps between them, showing the data is discrete. A histogram is used for continuous data, such as reaction times grouped into ranges, and has no gaps between bars because the underlying scale runs continuously.
A scatter diagram plots two variables against each other, with each point representing one participant’s pair of scores. If the points form a rough upward line, the variables show a positive correlation; a downward line shows a negative correlation; a random scatter with no pattern shows no correlation. Scatter diagrams let you translate numerical results into a visual pattern and are the standard way to display correlational data.
The Normal Distribution
Many psychological variables, when measured across a large population, form a normal distribution. This produces a symmetrical, bell-shaped curve when plotted: the mean, median and mode all fall at the same central point, and scores become progressively rarer as you move towards either tail.
Intelligence test scores are a classic example — most people score close to the average, with far fewer people scoring extremely high or extremely low. Psychologists use the normal distribution as a benchmark for judging how typical or unusual an individual score is, and many statistical tests assume the underlying data is approximately normally distributed.