Welcome to Data Recording, Analysis, and Presentation!

In this chapter, we are going to learn how Psychologists turn "messy" information gathered during research into clear, scientific results. Think of it like this: if a researcher just handed you a pile of 500 completed questionnaires, you’d be overwhelmed. We need tools to organize, summarize, and decide what those answers actually mean. Don’t worry if the math seems a bit scary at first—we will take it one step at a time!

1. Raw Data: The Starting Point

Raw data is the "untouched" information you collect before you do any math with it. To keep things organized, psychologists use raw data recording tables. These are simply grids where you write down the results for every participant as you get them.

Numbers and Precision

When recording data, you need to be precise. You will need to understand:

  • Standard Form: A way of writing very large or very small numbers using powers of 10. For example, \( 5,000 \) becomes \( 5 \times 10^3 \).
  • Decimal Form: Using points to show fractions of a whole (e.g., \( 0.75 \)).
  • Significant Figures: The digits in a number that carry meaning. If you are told to give an answer to 2 significant figures, \( 12.34 \) becomes \( 12 \).
  • Estimations: Making a "best guess" before you calculate the exact answer to see if your final result makes sense.

Quick Review: Always design your table before you start your research so you don't lose any data!

2. Levels and Types of Data

Not all data is created equal! We categorize data based on what it is and how "detailed" it is. Use the mnemonic N.O.I.R. to remember the levels of measurement.

The "NOIR" Levels of Measurement

  1. Nominal: Data in separate categories (names). Example: Are you a smoker or a non-smoker?
  2. Ordinal: Data that can be put in an order or rank, but the gaps between them aren't equal. Example: Finishing 1st, 2nd, and 3rd in a race. You know who is faster, but not by exactly how many seconds.
  3. Interval: Data measured on a scale with equal gaps between points. Example: Temperature in Celsius or scores on an IQ test.

Types of Data

  • Quantitative: Data involving numbers (e.g., "How many seconds did it take?").
  • Qualitative: Data involving words and descriptions (e.g., "How did you feel during the task?").
  • Primary: Data you collected yourself for your own study.
  • Secondary: Data someone else collected that you are using (e.g., government statistics).

Key Takeaway: Interval data is the most "scientific" and detailed, while Nominal is the simplest.

3. Descriptive Statistics: Summarizing Data

Descriptive statistics are used to describe the basic features of the data. They don't tell us if our hypothesis is "true," just what the data looks like.

Measures of Central Tendency (The Averages)

  • Mean: Add all scores and divide by the number of scores. (Most sensitive, but affected by extreme scores).
  • Median: The middle score when they are put in order. (Good for ordinal data).
  • Mode: The most frequent score. (The only one you can use for nominal data).

Measures of Dispersion (The Spread)

These tell us if the scores are all bunched together or spread far apart.

  • Range: The difference between the highest and lowest score (High - Low + 1).
  • Variance & Standard Deviation: These measure how much, on average, scores differ from the mean. A large standard deviation means the data is very spread out.

Did you know? Psychologists also use ratios, percentages, and fractions to make comparisons easier (e.g., "60% of participants said yes").

4. Presentation of Data (Graphs)

We use different charts depending on what data we have. Remember: A graph should always have a clear title and labelled axes!

  • Frequency Table: A tally chart showing how often things happen.
  • Bar Chart: Used for Nominal data. The bars do not touch because the categories are separate.
  • Histogram: Used for Interval/Continuous data. The bars do touch because the data is on a scale.
  • Line Graph: Shows how data changes over time or across conditions.
  • Pie Chart: Shows how a whole group is divided into parts.
  • Scatter Diagram: Used for Correlations to show the relationship between two variables.

Common Mistake: Don't use a bar chart for correlational data! Use a scatter diagram instead.

5. Inferential Statistics: Making Decisions

This is where we decide if our results are actually significant (did something real happen?) or just down to luck/chance.

Probability and Significance

Psychologists usually use a significance level of \( p \le 0.05 \). This means there is a 5% (or less) possibility that our results happened by fluke. If \( p \le 0.05 \), we say our results are statistically significant.

Normal and Skewed Distributions

  • Normal Distribution: A "bell-shaped curve" where the mean, median, and mode are all in the center.
  • Skewed Distribution: When the data is pushed to one side. A positive skew has a long tail to the right; a negative skew has a long tail to the left.

The Two Types of Errors

  • Type 1 Error: A "False Positive." You claim your results are significant when they actually happened by chance. (You rejected the null hypothesis when you shouldn't have).
  • Type 2 Error: A "False Negative." You claim your results happened by chance when there was actually a real effect. (You accepted the null hypothesis when you shouldn't have).

Step-by-Step Trick: To avoid a Type 1 error, use a stricter significance level (like \( p \le 0.01 \)).

6. Which Statistical Test to Use?

You don't need to do the complex math for these in the exam, but you must know when to choose which one! To use a parametric test, the data must be Interval level and follow a normal distribution. If not, we use non-parametric tests.

Non-Parametric Tests you must know:
  • Mann-Whitney U: Testing for a difference between two independent groups (Independent Measures).
  • Wilcoxon Signed Ranks: Testing for a difference between the same people in two conditions (Repeated Measures).
  • Chi-square: Testing for a difference or relationship with Nominal data.
  • Binomial Sign Test: Used for a difference with Nominal data and Repeated Measures.
  • Spearman’s Rho: Used to find a relationship/correlation between two variables.

Key Symbols to Learn:
\( = \) (Equal to)
\( < \) (Less than)
\( << \) (Much less than)
\( > \) (Greater than)
\( \propto \) (Proportional to)
\( \sim \) (Approximately)

Key Takeaway: Choosing the right test is like choosing the right tool for a job. If you have nominal data and are looking for a relationship, you must use Chi-square!