Distributions (AQA A-Level Psychology): Revision Notes
Distributions
Normal distribution
A normal distribution represents data that shows an even spread of scores on both sides of the mean. This creates the characteristic bell-shaped curve that is perfectly symmetrical. In a normally distributed dataset, most scores cluster around the central mean value, with progressively fewer scores appearing as you move away from the centre in either direction.
In psychological research, the normal distribution is fundamental because many human characteristics (like height, intelligence scores, and reaction times) naturally follow this pattern, making it essential for statistical analysis.
The normal distribution has several important properties:
- It forms a symmetrical, bell-shaped curve when plotted
- The mean, median, and mode all occur at the same central point
- Approximately 68% of scores fall within one standard deviation of the mean
- The curve never actually touches the horizontal axis, extending infinitely in both directions
Checking for normal distribution
Researchers can determine whether their data follows a normal distribution using three main approaches:
1. Examine visually - Plot the data on a graph to see if most scores cluster around the mean, forming a bell-shaped pattern.
2. Calculate measures of central tendency - Work out the mean, mode, and median. In a normal distribution, these three measures should be very similar or identical.
3. Plot the frequency distribution - Create a histogram to visualise the data shape. A normal distribution will show the characteristic bell-shaped curve with symmetrical sides.
Common Mistake to Avoid: Don't assume data is normally distributed just because it looks roughly bell-shaped. Always use all three checking methods to confirm normality before applying statistical tests that require normal distribution.
Skewed distribution
A skewed distribution occurs when data does not spread evenly on both sides of the mean, creating an asymmetrical shape. This happens when there are extreme scores (outliers) that pull the distribution in one direction.
Positive skewed distribution
A positive skewed distribution develops when there are unusually high extreme scores in the dataset. These high scores stretch the right tail of the distribution, making it longer than the left side. In this type of distribution, most scores are concentrated at the lower end, with fewer high scores creating the extended right tail.
Memory Aid: Think "positive skew = tail points to the positive (right) side of the number line." The extreme high scores create a long right tail.
Negative skewed distribution
A negative skewed distribution forms when there are unusually low extreme scores in the dataset. These low scores extend the left tail of the distribution, making it longer than the right side. Here, most scores cluster at the higher end, with fewer low scores creating the extended left tail.
In skewed distributions, the mean is pulled towards the direction of the skew, while the median remains more centrally located. This means the mean and median will differ, unlike in normal distributions where they coincide.
Bimodal distribution
A bimodal distribution contains two distinct peaks or modes within the same dataset, indicating that there are two separate groups represented in the data. Rather than having one central clustering point like a normal distribution, bimodal distributions show two different score concentrations.
Real-world Examples: Marathon runners' finishing times might show one peak around 2 hours 30 minutes (elite runners) and another peak around 4 hours (recreational runners), creating a bimodal distribution. Similarly, exam scores might show one peak for students who didn't study and another for those who studied extensively.
This pattern often suggests that the sample actually contains two different populations or groups. Sometimes what appears to be a bimodal distribution may actually represent two separate unimodal (single-peaked) distributions occurring within the same dataset.
Introduction to statistical testing
Statistical testing provides methods for analysing data from psychological research. One important test is the sign test, which compares differences between two sets of data to determine if observed differences are statistically meaningful or could have occurred by chance.
The sign test
The sign test is a non-parametric statistical test used when data meets certain conditions:
- The data is at least nominal level (can be categorised)
- A repeated measures design has been used (same participants tested twice)
The test works by examining the direction of difference between paired scores, assigning positive (+) or negative (-) signs to indicate whether each participant's second score was higher or lower than their first score.
Worked Example: Basic Sign Test Process
Step 1: Compare each participant's scores between conditions
- Participant A: Condition 1 = 15, Condition 2 = 18 → Difference = +3 → Sign = +
- Participant B: Condition 1 = 22, Condition 2 = 19 → Difference = -3 → Sign = -
- Participant C: Condition 1 = 14, Condition 2 = 16 → Difference = +2 → Sign = +
Step 2: Count the less frequent sign (this becomes your observed value) Step 3: Compare with critical value from statistical tables
Statistical analysis involves comparing an observed value (calculated from the data) with a critical value (found in statistical tables). If the observed value equals or is less than the critical value, the result is considered statistically significant, allowing researchers to reject the null hypothesis and accept that there is a genuine difference between conditions.
Critical Point: The sign test only looks at the direction of differences, not their magnitude. This makes it less sensitive than parametric tests but more robust when data doesn't meet normal distribution requirements.
Key Points to Remember:
- Normal distributions create symmetrical bell-shaped curves with most scores clustering around the mean
- Skewed distributions are asymmetrical due to extreme scores - positive skew has high extremes, negative skew has low extremes
- Bimodal distributions have two peaks, often indicating two separate groups within the data
- Three methods can check for normality: visual examination, central tendency calculations, and frequency distribution plotting
- Sign tests analyse paired data by examining the direction of differences between conditions