Research Methods & Mathematical Skills

Research methods questions appear on all three papers, not just Paper 2. The Research Methods section on Paper 2 alone is worth 48 marks — half the paper. Across all three papers, research methods and mathematical skills account for a substantial proportion of the total marks. This lesson covers experimental designs, sampling methods, types of data, statistical tests, probability and significance, mathematical skills, data interpretation, and ethical issues.

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Why Research Methods Matter on Every Paper

A common misconception is that research methods are only examined on Paper 2. In reality:

• Paper 1: Research methods questions are embedded within each topic section (e.g. "Design a study to investigate conformity").
• Paper 2: Section C is dedicated to Research Methods (48 marks) — but research methods also appear in the Approaches and Biopsychology sections.
• Paper 3: Research methods questions appear within Issues and Debates and within each option topic.

Key Point: You will encounter research methods questions on every section of every paper. Treat research methods as a cross-cutting skill, not a standalone topic.

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Experimental Methods

Types of Experiment

Type	Description	Strengths	Limitations
Laboratory experiment	Conducted in a controlled environment; the researcher manipulates the IV and measures the DV	High control over extraneous variables; easy to replicate; can establish cause and effect	Low ecological validity; demand characteristics; artificial setting
Field experiment	Conducted in a natural setting; the researcher still manipulates the IV	Higher ecological validity than lab experiments; more natural behaviour	Less control over extraneous variables; harder to replicate; ethical issues (participants may not know they are in a study)
Natural experiment	The IV occurs naturally (the researcher does not manipulate it); the DV is measured	Can study variables that would be unethical or impractical to manipulate (e.g. effects of institutionalisation)	Cannot establish cause and effect (IV not manipulated); potential confounding variables
Quasi-experiment	The IV is based on an existing characteristic of participants (e.g. age, gender, diagnosis)	Allows comparison of existing groups	Cannot randomly allocate participants; differences may be due to confounding variables rather than the IV

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Experimental Designs

The experimental design determines how participants are allocated to conditions.

Independent Groups Design

Each participant takes part in only one condition of the experiment.

Strengths	Limitations
No order effects (practice, fatigue, boredom)	Individual differences between groups may act as confounding variables
Participants are less likely to guess the aim	Requires more participants (one group per condition)

How to reduce limitations: Use random allocation to minimise the impact of individual differences between groups.

Repeated Measures Design

Each participant takes part in all conditions of the experiment.

Strengths	Limitations
Individual differences are controlled (same participants in each condition)	Order effects: participants may perform better/worse in the second condition due to practice, fatigue, or boredom
Requires fewer participants	Participants are more likely to guess the aim (demand characteristics)

How to reduce limitations: Use counterbalancing (ABBA design) — half the participants do Condition A first, then B; the other half do B first, then A.

Matched Pairs Design

Participants are paired on key variables (e.g. age, IQ, gender) and one member of each pair is allocated to each condition.

Strengths	Limitations
Reduces individual differences without order effects	Time-consuming and difficult to match participants effectively
No order effects	Impossible to match on all variables — some unmatched differences may remain

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Sampling Methods

The sample is the group of participants selected from the target population. The sampling method determines how representative the sample is.

Method	How it works	Strengths	Limitations
Random sampling	Every member of the target population has an equal chance of being selected (e.g. drawing names from a hat, random number generator)	Free from researcher bias; most likely to be representative	Difficult and time-consuming with large populations; selected individuals may still decline to participate
Systematic sampling	Select every nth person from a list (e.g. every 5th name on a school register)	Objective and easy to implement	The list may contain a hidden pattern that biases the sample
Stratified sampling	Divide the target population into subgroups (strata) based on key characteristics (e.g. age, gender), then randomly select from each stratum in proportion to the population	Highly representative of key characteristics	Very time-consuming; requires detailed knowledge of the population's characteristics
Opportunity sampling	Select whoever is available and willing at the time (e.g. approaching people in a university corridor)	Quick, easy, and inexpensive	Highly biased — typically overrepresents certain demographics (e.g. students, people in one location)
Volunteer (self-selecting) sampling	Participants put themselves forward (e.g. responding to an advertisement)	Access to willing participants; useful for sensitive topics	Volunteer bias — volunteers may differ systematically from the general population (e.g. more motivated, more extraverted)

Exam Tip: When asked to evaluate a sampling method, always consider (a) whether the sample is representative of the target population, and (b) whether the method introduces any systematic bias.

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Types of Data

Quantitative vs Qualitative Data

Feature	Quantitative Data	Qualitative Data
What it is	Numerical data that can be counted or measured	Non-numerical data expressed in words, descriptions, or categories
Examples	Test scores, reaction times, number of words recalled, heart rate	Interview transcripts, diary entries, open-ended questionnaire responses
Analysis	Statistical analysis (mean, standard deviation, statistical tests)	Thematic analysis, content analysis, coding of themes
Strengths	Easy to analyse statistically; objective; can be replicated	Rich, detailed data; captures participants' experiences in depth
Limitations	May oversimplify complex behaviour; loses depth and context	Subjective; difficult to analyse and replicate; researcher bias in interpretation

Primary vs Secondary Data

Feature	Primary Data	Secondary Data
What it is	Data collected first-hand by the researcher for the purpose of the current study	Data that already exists, collected by someone else for a different purpose
Examples	Data from an experiment, questionnaire, or interview you conduct	Government statistics, published research findings, medical records
Strengths	Tailored to the research question; researcher controls quality and method	Quick and inexpensive to access; large datasets available
Limitations	Time-consuming and expensive to collect	May not perfectly fit the research question; quality may be unknown

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Descriptive Statistics

Measures of Central Tendency

Measure	How to calculate	Strengths	Limitations
Mean	Add all values and divide by the number of values	Uses all the data; most sensitive measure	Distorted by extreme scores (outliers)
Median	Arrange values in order; find the middle value	Not affected by extreme scores	Less sensitive than the mean; does not use all the data
Mode	The most frequently occurring value	Useful for categorical data; easy to identify	May not be representative; there may be no mode or multiple modes

Measures of Dispersion

Measure	How to calculate	Strengths	Limitations
Range	Highest value minus lowest value (sometimes +1)	Quick and easy to calculate	Affected by extreme scores; only uses two values
Standard deviation	A measure of the average distance of each data point from the mean	Uses all the data; gives a precise measure of spread	More difficult to calculate; affected by extreme scores

Exam Tip: You must be able to calculate the mean, median, mode, and range from a data set. You should also understand what the standard deviation means (a high SD = data is widely spread; a low SD = data is clustered around the mean), although you are unlikely to be asked to calculate it from scratch.

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Statistical Tests: Which Test to Use

Choosing the correct statistical test is a common exam question. You need to consider three things:

1. What type of hypothesis? — Test of difference or test of correlation?
2. What experimental design? — Related (repeated measures or matched pairs) or unrelated (independent groups)?
3. What level of measurement? — Nominal, ordinal, or interval/ratio?

The Statistical Test Decision Chart

graph TD
    A[What is the hypothesis?] --> B[Test of Difference]
    A --> C[Test of Correlation]
    B --> D{Related or Unrelated?}
    D --> E[Related Design]
    D --> F[Unrelated Design]
    E --> G{Level of Data?}
    F --> H{Level of Data?}
    G --> I[Nominal: Sign Test]
    G --> J[Ordinal: Wilcoxon]
    G --> K[Interval: Related t-test]
    H --> L[Nominal: Chi-squared]
    H --> M[Ordinal: Mann-Whitney U]
    H --> N[Interval: Unrelated t-test]
    C --> O{Level of Data?}
    O --> P[Ordinal: Spearman's rho]
    O --> Q[Interval: Pearson's r]

Summary Table of Statistical Tests

Test	Difference or Correlation	Design	Level of Data
Sign test	Difference	Related	Nominal
Wilcoxon signed-rank test	Difference	Related	At least ordinal
Related t-test	Difference	Related	Interval/ratio
Chi-squared test	Difference (or association)	Unrelated	Nominal
Mann-Whitney U test	Difference	Unrelated	At least ordinal
Unrelated t-test	Difference	Unrelated	Interval/ratio
Spearman's rho	Correlation	N/A	At least ordinal
Pearson's r	Correlation	N/A	Interval/ratio

Levels of Measurement