Inferential statistics and qualitative analysis: probability and significance, the five Edexcel inferential tests, Type 1 and Type 2 errors, the normal and skewed distributions, and the analysis of qualitative data through thematic analysis and grounded theory.

What this dot point is asking

Paper 3 (Psychological Skills) requires you to handle data: to explain probability and significance, choose and interpret the correct inferential test, recognise Type 1 and Type 2 errors, read the normal and skewed distributions, and analyse qualitative data through thematic analysis and grounded theory. These are synoptic skills tested across novel scenarios drawn from any topic.

The answer

Probability and significance

A null hypothesis predicts no difference or no relationship; the alternative (experimental) hypothesis predicts one. An inferential test produces a calculated value, which is compared with a critical value from a table (using $N$, whether the test is one- or two-tailed, and the significance level). If the result passes the test, we reject the null hypothesis. A one-tailed hypothesis predicts the direction of the effect; a two-tailed hypothesis does not, and uses a more conservative critical value.

Choosing the inferential test

For the sign test, Wilcoxon and Mann-Whitney, the result is significant when the calculated value is equal to or less than the critical value. For chi-squared and Spearman, the result is significant when the calculated value is equal to or greater than the critical value. Mixing up these two rules is the most common error.

Type 1 and Type 2 errors

The significance level controls the trade-off. A lenient level (for example $p < 0.10$) makes a Type 1 error more likely; a strict level (for example $p < 0.01$) reduces Type 1 risk but raises Type 2 risk. The conventional $p < 0.05$ balances the two.

The normal and skewed distributions

The normal distribution is a symmetrical, bell-shaped curve where the mean, median and mode coincide at the centre, with most scores clustered around the mean and the tails thinning symmetrically. Many psychological variables (IQ, reaction time) approximate it.

A distribution is skewed when scores bunch at one end:

• Positive (right) skew. A long tail to the right (high scores). The mode is lowest, the mean is pulled highest by the tail, so $\text{mode} < \text{median} < \text{mean}$.
• Negative (left) skew. A long tail to the left (low scores), so $\text{mean} < \text{median} < \text{mode}$.

Skew matters because the mean is distorted by extreme scores, so the median is a better measure of central tendency for skewed data.

Analysis of qualitative data

Qualitative data (interviews, open questions) are analysed for meaning rather than counted:

• Thematic analysis identifies patterns of meaning. The researcher reads the data, assigns codes to segments, then groups codes into broader themes that capture something important about the data, illustrated with quotations. It is flexible and rich but can be subjective, so reliability is checked through a second coder.
• Grounded theory builds theory inductively from the data rather than testing a pre-set hypothesis. Through constant comparison (comparing each new piece of data with earlier codes) and successive coding, categories emerge until theoretical saturation (no new categories appear), at which point a theory grounded in the data is proposed.

Evaluation (GRAVE)

• Generalisability. Inferential statistics let researchers generalise from a sample to a population, but only if sampling was sound.
• Reliability. Standardised tests and decision rules make quantitative analysis highly reliable and replicable; qualitative analysis needs inter-rater checks to be reliable.
• Application. Choosing the right test underpins every Paper 1 and Paper 2 data question and real published research.
• Validity. Thematic analysis and grounded theory preserve the richness and meaning of data, raising validity where reducing experience to numbers would lose it.
• Ethics. Researchers must not "p-hack" (run many tests to find a significant one), which inflates Type 1 errors and is a form of misreporting.

Examples in context

Example 1. Reading reaction-time data that are skewed. Reaction times usually show positive skew, because a few slow trials create a long right tail. Reporting the mean would overstate the typical response time, so a psychologist reports the median instead, and may treat the data as ordinal, pushing the analysis towards a non-parametric test such as Mann-Whitney. This shows how the shape of the distribution drives both the descriptive measure and the inferential test.

Example 2. Thematic analysis of interviews about exam stress. A researcher interviews 15 students, codes phrases such as "I couldn't sleep" and "my mind went blank", then groups them into themes like "physical symptoms" and "cognitive disruption", illustrating each with a quotation. A second researcher codes a sample independently to check agreement. The output is a structured account of how students experience stress that a questionnaire's numbers could not capture, demonstrating the value (and the subjectivity) of qualitative analysis.

Try this

Q1. State the significance level used in psychology and explain what it means. [2 marks]

• Cue. $p < 0.05$: there is less than a 5 per cent probability the result is due to chance if the null hypothesis is true.

Q2. A study correlates two sets of ranked scores. Name and justify the inferential test. [3 marks]

• Cue. Spearman's rho, because the data are ordinal and the aim is to measure a relationship (correlation) rather than a difference.

Q3. Outline the difference between thematic analysis and grounded theory. [4 marks]

• Cue. Both code qualitative data, but thematic analysis identifies patterns (themes) within data, while grounded theory builds a new theory inductively from the data through constant comparison until saturation.