Welcome to Data Recording, Analysis, and Presentation!
Hello! Don't let the title of this chapter scare you. While it sounds very "maths-heavy," it is actually about how psychologists turn messy human behaviour into clear, understandable information. Think of this as the "Storytelling" part of research—you’ve collected your data, and now you’re learning how to tell everyone what it means.
Whether you love numbers or find them a bit tricky, these notes are designed to walk you through the process step-by-step. We will cover how to record data, the different types of data you’ll encounter, and the "magic" formulas used to find patterns.
1. Raw Data: The Starting Point
Raw data is simply the "unprocessed" information you collect during an experiment or observation before you do anything else with it.
Design and Use of Recording Tables: Before you start, you need a clear place to put your results. A good recording table should have clear headings so that anyone looking at it knows exactly what was measured.
Standard and Decimal Form: Sometimes numbers are very big or very small.
Standard form is a way of writing these using powers of 10. For example, 5,000 becomes \( 5 \times 10^3 \).
Decimal form is the standard way we write numbers, like 0.05.
Significant Figures: This is about rounding numbers to the most important digits.
Example: If a calculation gives you 12.34567, rounding it to 3 significant figures gives you 12.3.
Estimations: Sometimes, psychologists make a "best guess" based on the data to see if their final results look reasonable.
Quick Review:
• Raw data = The "messy" first results.
• Recording tables = The "buckets" we put data into.
• Significant figures = Keeping only the digits that matter.
2. Types of Data
Not all data is created equal! Psychologists use four main categories:
Quantitative Data: This is data in the form of numbers.
Example: A score of 8/10 on a memory test.
+ Strength: Easy to compare and turn into graphs.
- Weakness: Lacks detail; it doesn't tell us *why* someone got that score.
Qualitative Data: This is data in the form of words, descriptions, or meanings.
Example: A transcript of an interview where someone describes their feelings.
+ Strength: Very rich and detailed.
- Weakness: Hard to summarise or compare across different people.
Primary Data: Data you collected yourself for your specific study.
Example: You conduct a survey on your classmates.
Secondary Data: Data that someone else collected that you are using.
Example: Using government statistics on crime rates.
Takeaway: Quantitative is about quantity (how many), and Qualitative is about quality (what is it like).
3. Levels of Measurement (Levels of Data)
This is a way of "ranking" how precise your data is. You can remember this with the mnemonic NOI.
1. Nominal Level Data: The most basic level. Data is put into categories or named groups.
Example: Counting how many people are "Left-handed" vs. "Right-handed."
2. Ordinal Level Data: Data that can be put in an order or rank, but the gaps between the ranks aren't equal.
Example: Finishing 1st, 2nd, and 3rd in a race. You know who is faster, but the person in 1st might be 10 seconds ahead of 2nd, while 2nd is only 1 second ahead of 3rd.
3. Interval Level Data: The most precise. Data is measured on a scale with fixed, equal intervals.
Example: Temperature in Celsius. The gap between 10°C and 11°C is exactly the same as the gap between 20°C and 21°C.
4. Descriptive Statistics: Summarising the Data
Once you have your numbers, you need to summarise them. We use Measures of Central Tendency (the middle) and Measures of Dispersion (how spread out they are).
Measures of Central Tendency
• Mean: The mathematical average. Add all scores and divide by the number of scores.
Formula: \( \bar{x} = \frac{\sum x}{n} \).
• Median: The middle score when you put them in order.
• Mode: The most frequent score.
Measures of Dispersion
• Range: The difference between the highest and lowest score (usually plus 1).
• Variance: A calculation showing how much scores deviate from the mean.
• Standard Deviation: The most popular measure. It shows the average distance of every score from the mean.
Analogy: If the mean height of a class is 160cm, a small standard deviation means everyone is roughly 160cm. A large standard deviation means some are very short and some are very tall.
Other Maths Bits
• Ratio: Comparing two quantities (e.g., 2:1).
• Percentage: A fraction out of 100.
• Fractions: Parts of a whole (e.g., 1/4).
• Frequency Tables: Often called a "tally chart," used to count how often things happen.
5. Presenting Data: Graphs
Don't worry if you aren't an artist! Just remember which graph goes with which data:
Bar Charts: Used for Nominal (categories) data. The bars should not touch.
Histograms: Used for Interval data. The bars must touch because the data is continuous.
Scatter Diagrams: Used for Correlations. You plot dots to see if there is a relationship between two variables.
Line Graphs: Used to show how something changes, often over time.
Pie Charts: Used to show proportions of a whole (percentages).
Common Mistake: Students often draw bar charts for continuous data. Remember: If it’s separate categories (like "Cats vs Dogs"), leave a gap!
6. Analysis of Qualitative Data
What do we do with all those words? We can convert qualitative data into quantitative data.
This is usually done through Content Analysis. You look at the words (like an interview transcript) and count how many times certain themes or "codes" appear.
Example: If you interview people about school, you might count how many times they say the word "stressful." Suddenly, your words have become numbers!
7. Inferential Statistics: Are the results "Real"?
This is the part that helps psychologists decide if their results happened because of their IV (the thing they changed) or just by "fluke" (chance).
Probability and Significance
Psychologists usually use a significance level of \( p \le 0.05 \). This means there is a 5% (or less) probability that the results happened by chance. If \( p \le 0.05 \), we reject the null hypothesis and accept the alternative hypothesis.
Distributions
Normal Distribution: A symmetrical "bell-shaped" curve where the mean, median, and mode are all in the middle.
Skewed Distributions: When the results are bunched at one end.
Positive Skew: Most scores are low (the "tail" points to the right).
Negative Skew: Most scores are high (the "tail" points to the left).
Choosing a Statistical Test
You need to know the criteria for choosing these five non-parametric tests:
1. Mann-Whitney U: Use for Independent Measures design and Ordinal data.
2. Wilcoxon Signed Ranks: Use for Repeated Measures design and Ordinal data.
3. Chi-Square: Use for Independent groups and Nominal data.
4. Binomial Sign: Use for Repeated Measures and Nominal data.
5. Spearman’s Rho: Use when looking for a Correlation.
Errors in Research
Type 1 Error (False Positive): You claim your results are significant, but they actually happened by chance. (You were too lenient).
Type 2 Error (False Negative): You claim your results are not significant, but there actually was an effect. (You were too strict).
Section Takeaway:
• Inferential tests tell us if we can trust our results.
• p ≤ 0.05 is the magic number.
• Type 1 error = Seeing a ghost that isn't there.
• Type 2 error = Missing a ghost that is standing right behind you!
Symbols to Know
You must be able to recognise and use these symbols in your exam:
= Equals
< Less than
<< Much less than
>> Much greater than
> Greater than
∝ Proportional to
~ Approximately
≥ Greater than or equal to
≤ Less than or equal to