Welcome to Data Analysis!

Once a psychologist has finished their research, they are usually left with a pile of numbers. These numbers are called raw data. On their own, they can be quite confusing! Imagine looking at a list of 100 different heart rates—you wouldn't be able to tell much at a glance.

In this chapter, we learn how to tidy up that data using descriptive statistics. This helps us summarize the "big picture" so we can actually understand what happened in the study. Don't worry if you aren't a "math person"—the Cambridge syllabus focuses on understanding and interpreting these numbers rather than doing long calculations!

1. Measures of Central Tendency

A "measure of central tendency" is just a fancy way of saying we want to find the typical or average score in a set of data. There are three main types you need to know:

The Mode

The mode is the value that appears most frequently in a data set.
Example: In the set of scores \( \{3, 4, 4, 5, 6\} \), the mode is \(4\) because it appears twice.

The Median

The median is the middle value when all the scores are put in order from lowest to highest.
Example: In the set \( \{2, 5, 8, 10, 12\} \), the median is \(8\).
Top Tip: If there is an even number of scores, the median is the halfway point between the two middle numbers. In your exam, you just need to be able to recognize and find it!

The Mean

The mean is what most people think of as the "average." It is calculated by adding up all the scores and dividing by the total number of scores.
Key Requirement: You need to understand what the mean represents and be able to identify it, but you will not be asked to calculate it in the exam.

Quick Review: Which one to use?
  • Mode: Best for categories (e.g., "What is the most common hair color in the study?").
  • Median: Great if there are "outliers" (one or two weirdly high or low scores) because it isn't affected by them.
  • Mean: The most sensitive measure because it uses every single number in the data set.

Key Takeaway: Central tendency tells us where the "center" of our data is.

2. Measures of Spread

While central tendency tells us about the "average," measures of spread tell us how much the scores vary. Are they all clustered together, or are they spread far apart?

The Range

The range is the simplest measure of spread. It is the difference between the highest and lowest scores.
The Formula: \(range = \text{highest value} - \text{lowest value}\)

Example: if the highest score on a test was \(95\) and the lowest was \(40\), the range is \(95 - 40 = 55\).
Advantage: It is very easy to calculate.
Disadvantage: It only looks at the two extreme scores and ignores everything in the middle.

Standard Deviation (SD)

Standard deviation is a more sophisticated measure of spread. It shows the average distance of every score from the mean.

  • A low standard deviation means the scores are all very close to the mean (the participants were very similar).
  • A high standard deviation means the scores are spread out widely (the participants were very different from each other).
Note: You do not need to calculate this. You just need to be able to recognize it and explain what it means when you see it in a results table.

Key Takeaway: Range is simple; Standard Deviation is more detailed but tells us how "consistent" the results were.

3. Presenting Data in Tables

Psychologists use summary tables to show their results clearly. A good table should have:
1. A clear title.
2. Labeled columns and rows.
3. Summarized data (like the mean or SD) rather than every single raw score.

Did you know? In Paper 2, you might be shown a table and asked to "interpret" it. This just means explaining what the numbers tell you in plain English (e.g., "Group A's mean score was higher than Group B's").

4. Visualizing Data: Graphs

Sometimes a picture is worth a thousand numbers! You need to know three types of graphs:

Bar Charts

Used when your data is in separate categories (this is called "nominal" data).
Key Feature: The bars do not touch.
Example: A graph showing the number of people who helped a victim in the Piliavin et al. (subway Samaritans) study based on the victim's race.

Histograms

Used for continuous data (data that fits on a scale, like time or height).
Key Feature: The bars do touch because the data is continuous.
Example: A graph showing the amount of time participants spent sleeping in the Dement and Kleitman study.

Scatter Graphs

Used specifically for correlational research. It shows the relationship between two co-variables.
How it works: Each dot represents one participant's score on both variables.

  • If the dots go from bottom-left to top-right, it's a positive correlation.
  • If the dots go from top-left to bottom-right, it's a negative correlation.
Important: Remember that correlations do not show cause and effect!

Common Mistakes to Avoid:
  • Touching Bars: Don't let your bars touch on a bar chart! That makes it look like a histogram.
  • Labeling: Always label your axes (usually the Independent Variable on the \(x\)-axis and the Dependent Variable on the \(y\)-axis).
  • Misinterpreting SD: If one group has a much higher SD than another, don't just say they "scored higher"—say their scores were "more spread out" or "less consistent."

Final Key Takeaway: Data analysis is all about making results easy to see. Whether you use a mean to find the average or a scatter graph to look for a relationship, the goal is to make the data understandable for everyone!