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Unlock This CourseDescriptive statistics help psychologists make sense of the data they collect. Instead of looking at endless lists of numbers, descriptive statistics summarise data in a way that's easier to understand and interpret. They're the first step in analysing any research data in psychology.
Key Definitions:
Imagine you've conducted a memory experiment with 30 participants. Without descriptive statistics, you'd have 30 individual scores that are hard to make sense of. Descriptive statistics help you summarise these scores to spot patterns and draw conclusions about memory performance.
Before analysing data, psychologists need to identify what type of data they have:
- Nominal data: Categories with no order (e.g., gender, eye colour)
- Ordinal data: Ranked categories (e.g., 1st, 2nd, 3rd place)
- Interval/Ratio data: Numerical values with equal intervals (e.g., test scores, reaction times)
Measures of central tendency tell us about the "middle" or "average" of our data. There are three main types: mean, median and mode. Each gives us different information about our data set.
The arithmetic average of all values.
How to calculate: Add up all values and divide by the number of values.
Example: For scores 5, 7, 3, 8, 7
Mean = (5+7+3+8+7) ÷ 5 = 30 ÷ 5 = 6
The middle value when data is arranged in order.
How to calculate: Arrange values in order and find the middle one.
Example: For scores 3, 5, 7, 7, 8
Median = 7 (middle value)
The most frequently occurring value.
How to calculate: Identify which value appears most often.
Example: For scores 3, 5, 7, 7, 8
Mode = 7 (appears twice)
Mean: Best for normally distributed data without extreme values.
Median: Better when data is skewed or contains outliers.
Mode: Useful for categorical data or when you want to know the most common value.
While measures of central tendency tell us about the middle of our data, measures of dispersion tell us how spread out the data is. The two main measures are range and standard deviation.
Definition: The difference between the highest and lowest values in a data set.
How to calculate: Highest value - Lowest value
Example: For scores 3, 5, 7, 7, 8
Range = 8 - 3 = 5
Limitation: Only uses two values, so doesn't tell us about the spread of all values.
Definition: A measure of how spread out values are from the mean.
How to calculate:
1. Find the mean
2. Subtract the mean from each value and square the result
3. Find the average of these squared differences
4. Take the square root
Interpretation: A larger standard deviation indicates more variability in the data.
Visual representations help make data more accessible and easier to interpret. Different types of graphs are suitable for different types of data.
Best for: Categorical data or comparing groups
Example use: Comparing anxiety levels across different age groups
Key feature: Bars don't touch, showing distinct categories
Best for: Continuous data showing frequency distributions
Example use: Showing distribution of reaction times
Key feature: Bars touch, showing continuous data
Best for: Showing changes over time or relationships between variables
Example use: Tracking mood changes over a 4-week period
Key feature: Points connected by lines showing trends
Understanding what statistics tell us about psychological phenomena is crucial. Here's how to make sense of the numbers.
Many psychological variables follow a normal distribution (bell curve). In a normal distribution:
- The mean, median and mode are all equal
- Most scores cluster around the middle
- Fewer scores appear at the extremes
This pattern helps psychologists understand how common or rare certain scores are in a population.
Not all data follows a normal distribution. Data can be:
- Positively skewed: Most scores are low, with a few high scores (tail points right)
- Negatively skewed: Most scores are high, with a few low scores (tail points left)
When data is skewed, the mean is pulled toward the tail, making the median often more representative.
A psychology student conducted a memory experiment with 20 participants who were asked to recall as many words as possible from a list of 30 words. Here are the results:
12, 15, 18, 14, 16, 19, 13, 17, 15, 14, 16, 20, 15, 17, 18, 16, 15, 14, 16, 19
Descriptive statistics:
Mean = 15.95 words
Median = 16 words
Mode = 15, 16 words (both appear 4 times)
Range = 8 words (20-12)
Standard deviation = 2.11
Interpretation: The average participant recalled about 16 words. The relatively small standard deviation indicates that most participants performed similarly, with scores clustering around the mean. This suggests the task was of appropriate difficulty – not too easy (which would give a negative skew) or too hard (which would give a positive skew).
Descriptive statistics are essential tools in various areas of psychological research and practice.
Psychologists use descriptive statistics to:
- Summarise experimental results
- Compare performance between groups
- Identify patterns and trends in data
- Communicate findings clearly in research papers
- Determine whether further statistical tests are needed
In clinical settings, descriptive statistics help:
- Track patient progress over time
- Compare a client's scores to normative data
- Evaluate the effectiveness of treatments
- Identify unusual patterns that might need attention
- Communicate outcomes to clients in an understandable way
Descriptive statistics are fundamental tools in psychology that help researchers make sense of their data. By calculating measures of central tendency (mean, median, mode) and dispersion (range, standard deviation), psychologists can summarise complex data sets and identify important patterns. Visual representations like graphs and charts further enhance understanding and communication of findings.
Remember that descriptive statistics are just the first step in data analysis. They describe what the data looks like but don't allow us to draw conclusions about causes or make predictions. For that, we need inferential statistics, which you'll learn about in future lessons.