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examBoard: AQA
examType: GCSE
lessonTitle: Ratios, Fractions and Percentages
In psychology research, we often need to make sense of numerical data. Whether we're looking at survey responses, experimental results, or statistical analyses, understanding ratios, fractions and percentages is essential for interpreting and communicating findings accurately.
Key Definitions:
Psychologists use these mathematical concepts to:
These concepts help psychologists:
Fractions represent parts of a whole and are commonly used in psychology to express proportions of samples or populations.
Being able to convert between these formats is crucial when analysing psychological data:
Divide the numerator by the denominator:
3/4 = 3 ÷ 4 = 0.75
In a study where 3/4 of participants reported anxiety, this equals 0.75 in decimal form.
Multiply the decimal by 100:
0.75 × 100 = 75%
So 0.75 of participants with anxiety equals 75% of the sample.
Write as a fraction over 100, then simplify:
75% = 75/100 = 3/4
If 75% of participants show a particular trait, that's 3/4 of your sample.
In a memory recall experiment, 24 out of 40 participants correctly remembered a list of words after distraction.
As a fraction: 24/40 = 3/5 (simplified)
As a decimal: 24 ÷ 40 = 0.6
As a percentage: 0.6 × 100 = 60%
The researcher could report: "Three-fifths (60%) of participants demonstrated successful recall."
Ratios express the relationship between two or more values and are particularly useful when comparing different groups or conditions in psychological research.
Ratios are written as numbers separated by colons (e.g., 3:2) and can be simplified like fractions.
If a study has 30 male and 45 female participants:
This is different from saying "2/5 of participants were male" (which is a fraction of the whole).
Ratios help psychologists:
Percentages are perhaps the most commonly used format for reporting psychological findings, as they provide an intuitive way to understand proportions.
There are several types of percentage calculations relevant to psychology:
Formula: (Percentage ÷ 100) × Value
Example: If 35% of 80 participants reported side effects:
(35 ÷ 100) × 80 = 0.35 × 80 = 28 participants
Formula: (Part ÷ Whole) × 100
Example: If 15 out of 60 participants withdrew from a study:
(15 ÷ 60) × 100 = 0.25 × 100 = 25%
Formula: ((New Value - Original Value) ÷ Original Value) × 100
Example: If anxiety scores decreased from 80 to 60 after therapy:
((60 - 80) ÷ 80) × 100 = (-20 ÷ 80) × 100 = -25%
This represents a 25% decrease in anxiety scores.
The difference between two percentages is measured in percentage points, not percentages.
Example: If 45% of Group A and 65% of Group B completed a task:
The difference is 20 percentage points (not 20%).
The percentage increase from Group A to B would be: ((65 - 45) ÷ 45) × 100 = 44.4%
A psychologist tested a new therapy for depression with 50 patients:
This demonstrates how different mathematical representations can describe the same data.
Understanding ratios, fractions and percentages helps psychologists in various aspects of their work:
When designing studies, psychologists need to:
When analysing results, psychologists:
When communicating results, psychologists:
When working with ratios, fractions and percentages in psychology, be careful to avoid these common errors:
A ratio of 1:3 males to females is different from saying 1/4 of participants are male.
The ratio (1:3) compares males to females directly.
The fraction (1/4) expresses males as a portion of the total group.
If a value increases from 40% to 60%:
These distinctions matter when interpreting psychological research.
Ratios, fractions and percentages are essential mathematical tools in psychology that help researchers design studies, analyse data and communicate findings effectively. By understanding how to work with and convert between these formats, you can better interpret psychological research and express your own findings clearly.
Converting between formats:
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