Handling data — AQA A-Level Psychology

The mean is the total of the scores divided by how many scores there are. In an experiment, it is calculated separately for each condition to allow comparison. With eight participants recalling 7, 9, 12, 6, 10, 8, 11 and 9 words in the quiet condition, the total is 72 and the mean is 9.0 words. With 5, 4, 8, 6, 7, 5, 9 and 8 words in the noisy condition, the total is 52 and the mean is 6.5 words, a gap of 2.5 words in favour of quiet. Divide by the number of scores in that condition, never by the total number of people in the study, and keep the unit on the answer. Because every score is used, the mean is the most sensitive measure of central tendency, which is why one extreme score can drag it away from the bulk of the data.

The display has to match the data. Counts of people in named categories, or the mean score of each condition, go in a bar chart, whose bars are drawn with gaps between them because the categories do not run into one another and could be reordered without changing the meaning. Continuous data grouped into equal class intervals, such as reaction times sorted into bands, go in a histogram, whose bars touch because the underlying scale is unbroken and the intervals follow a fixed order. Before either comes the tally: sort the raw scores into categories or intervals, total each row, and check the grand total against the number of participants to construct a frequency table. Every display needs a title, both axes labelled with what they show and their units, and a frequency scale beginning at zero, because a truncated scale makes a small difference look dramatic.

Simple probability is the likelihood of an event occurring, expressed as a number between 0 and 1, a fraction, or a percentage. In psychology, probability (p) determines if results are statistically significant. A significance level is the threshold probability set to decide whether to reject the null hypothesis, representing the maximum acceptable risk of a Type 1 error (rejecting a true null). Psychology normally works at p = 0.05, tolerating a 5% maximum risk of a Type 1 error. The stricter 0.01 level tolerates only a 1% risk and is chosen where a false claim would be costly, such as in drug trials. Tightening the criterion to 0.01 cuts the risk of a Type 1 error but raises the risk of a Type 2 error (retaining a false null).

Sampling determines how well participants represent the target population, dictating the generalisability of scientific data. A random sample gives every member of the target population an equal chance of selection. This requires a complete sampling frame, assigning each a number, and using a random number generator. A stratified sample reflects the exact proportions of relevant subgroups (strata) within the population. Researchers identify these strata, calculate their relative frequencies, and perform random sampling within each stratum. For example, if a population of 1,000 includes 600 females, a sample of 50 must contain 30 randomly selected females. Both methods aim to minimise selection bias and improve representativeness.

Standard deviation measures how far scores typically spread from their mean. First calculate the mean, subtract it from every score, square each deviation and add the squared deviations. Divide by N when the data are treated as the complete population, or by N−1 when estimating a population from a sample, then take the positive square root. For scores 2, 4 and 6, the mean is 4 and the squared deviations total 8: the population standard deviation is √(8÷3), while the sample standard deviation is √(8÷2)=2. State the convention used, show each stage and retain enough precision until the final answer. A smaller value means tighter clustering around the mean; a larger value means greater dispersion.

The three measures of central tendency summarise data differently, dictating their appropriate use at A-level. The mean (total divided by n) uses every value, making it the most sensitive measure, ideal for interval data without outliers. However, extreme scores distort the mean. The median is the middle value of an ordered set (or midpoint of the two central values). It resists outliers, making it suitable for ordinal data or skewed interval data. The mode is the most frequent score, essential for nominal data, though it may be unrepresentative or absent. For reaction times of 210, 220, 230, 240 and 980 ms, the mean of 376 is skewed by the 980 ms outlier. The median of 230 ms better represents the typical performance. In a positive skew, the mean is higher than the median and mode; in a normal distribution, all three are equal.

A scattergram displays the relationship between two continuous co-variables, not a difference between conditions. To plot one, place one operationalised co-variable on each axis, label both with units, and mark one point per participant where their two scores intersect. The pattern reveals the correlation: points sloping upwards from bottom-left to top-right indicate a positive correlation (both variables increase together); a downward slope indicates a negative correlation (one increases as the other decreases); a random scatter shows no correlation. At A-level, this pattern is quantified by a correlation coefficient from -1.0 to +1.0. The sign indicates direction, while the distance from zero indicates strength. Crucially, a strong correlation never establishes causation, as an untested third variable may be responsible.

Choosing a statistical test requires three questions: difference or relationship, related or unrelated design, and level of measurement. Nominal data use Chi-Square (unrelated) or Sign test (related). Ordinal data use Mann-Whitney U (unrelated) or Wilcoxon (related). Interval data use unrelated or related t-tests. Relationships use Spearman's rho (ordinal) or Pearson's r (interval). To use a statistical test, name these features to justify the choice. When calculating a non-parametric test of differences using data from a given experiment, such as the Sign test, follow the specific steps, then compare the calculated value with the critical value to determine significance.

An order-of-magnitude calculation estimates the scale of a value using powers of ten and provides a quick plausibility check. To estimate a mean, divide the overall total by the number of participants after rounding both to convenient values. For example, 4,850 words recalled by 97 participants is approximately 5,000 divided by 100, or 50 words per participant. In scientific notation this is $5 × 10^1$, so its order of magnitude is $10^1$. Compare the estimate with the precise calculation: a large discrepancy signals that the arithmetic, decimal position or units should be checked. An estimate is deliberately approximate, so report it with an appropriate unit and limited precision.

Psychology sorts data by how much information the numbers carry, and this decision drives subsequent analysis: which measure of central tendency is reported and which inferential test is run. Data sorted into named categories and counted, such as how many participants said yes or no, carry the least information and support only the mode. Data that can be put into rank order but whose gaps are not equal, such as a self-report rating of anxiety out of ten, carry more information and support the median. Data measured in units of equal and precisely defined size, such as seconds, grams, or the number of items recalled, carry the most information and support the mean alongside a standard deviation.

A frequency distribution is the shape a set of scores makes when the scores run along the horizontal axis and the frequency up the vertical one. The bell shaped curve is symmetrical about its centre, so the mean, the median and the mode all sit together under the peak, the tails get closer to the axis without ever touching it, and roughly 68 percent of scores fall within one standard deviation of the mean with roughly 95 percent within two. Asymmetry pulls those three averages apart. A long tail of high scores drags the mean out towards the tail and leaves the mode under the hump, so reading from left to right the order becomes mode, median, mean, and a long tail of low scores reverses that order.

Three questions settle the choice, and a mark scheme wants all three answered from the stem. Is the researcher testing for a difference between conditions or for an association between two co variables? If it is a difference, was the design related, meaning repeated measures or matched pairs, or unrelated, meaning independent groups? What level of measurement did the dependent variable produce? Nominal and unrelated gives Chi Square, ordinal and unrelated gives Mann Whitney U, interval and unrelated gives the unrelated t test. Nominal and related gives the sign test, ordinal and related gives Wilcoxon, interval and related gives the related t test. A correlation takes Spearman's rho for ranked data and Pearson's r for interval data.

An inferential test produces an observed value, and a table of critical values decides whether that value is unlikely enough to count. Reading the table needs three facts from the study: the level of significance, normally 0.05, whether the hypothesis was directional and so one tailed or non directional and so two tailed, and either the number of participants or of pairs or the degrees of freedom. Then the comparison runs in a direction fixed by the test. Chi Square, Spearman's rho, Pearson's r and both t tests need the observed value to be equal to or greater than the critical value. Mann Whitney U, Wilcoxon and the sign test need the observed value to be equal to or less than the critical value before the null hypothesis can be rejected.

Two conditions can share a mean and still describe completely different sets of participants, which is why a measure of dispersion is reported alongside every average. The range takes the smallest score away from the largest. It is quick but fixed by two scores only. The standard deviation uses all scores, representing the average distance of each score from the mean. A large standard deviation means scores are widely spread; a small one means participants behaved consistently. Standard deviation is a more useful measure of dispersion than the range for a given set of scores when there is an outlying score, because the range is entirely distorted by extremes, whereas standard deviation incorporates every value.

Numbers that record how much or how many, such as reaction times, scores on a memory test or tallies of aggressive acts, are quantitative. Material expressed in words or images that carries meaning, such as what a participant said in an interview, an answer to an open question or a diary entry, is qualitative. The exam usually asks for the bridge between the two, and that bridge is content analysis. The researcher reads the material, agrees coding categories in advance, works through applying them, and counts how often each category appears, turning words into frequencies that can be graphed and tested with Chi Square. What is gained is comparison and statistical analysis; what is lost is the depth and the context of what was actually said.

The distinction is about who gathered the information and for what purpose, not about whether it is numbers or words. Information a researcher obtains at first hand, from people they tested, questioned or observed for the investigation now being reported, belongs to the first category. Information that already existed because somebody else gathered it for their own purposes, and is then reused, belongs to the second: official statistics, hospital records, the published results of earlier studies. First hand collection fits the aim exactly and the conditions stay under the researcher's control, but it costs time and money. Reused information is quick and cheap and may cover far more people, yet it was never designed for this hypothesis and its quality cannot be checked directly. A meta analysis rests entirely on it.