Introduction to Distributions, Measurement, and Probability
Welcome! In Psychology, we don't just collect data; we have to make sense of it. To do that, we need to know what "type" of data we have, what "shape" it makes when we graph it, and how likely it is that our results happened by pure luck. This chapter covers the foundations of statistical decision-making. Don't worry if you aren't a "maths person"—we will break this down step-by-step!
Note: This chapter connects closely to "Inferential Testing," where you will learn how to choose specific tests like Wilcoxon or Chi-squared based on the rules we learn here.
1. Levels of Measurement
Before you can analyze data, you need to know its level of measurement. This is essentially a way of categorizing how much information your data gives you. A helpful way to remember the four levels in order is the mnemonic NOIR.
Nominal Data
This is the simplest level. Data is put into categories or named groups. There is no mathematical value to the names.
Example: Asking participants if they are "Obedient" or "Disobedient." You are just counting how many people fall into each category.
Ordinal Data
This data can be put into an order or rank, but the gaps between the ranks aren't necessarily equal.
Example: A finishing order in a race (1st, 2nd, 3rd). You know who was faster, but you don't know if 1st place was one second ahead or ten minutes ahead of 2nd place.
Interval and Ratio Data
These are the most sophisticated levels. Data is measured on a scale with equal units or intervals between each point.
Example: Temperature in Celsius, or the time taken in seconds to recall a list of words. In Psychology, we often treat these as the same when choosing a statistical test.
Quick Tip: If you can measure it with a stopwatch, a ruler, or a standardized test, it is likely Interval/Ratio data.
Key Takeaway: Identifying the level of measurement is the first step in choosing the right statistical test (List B).
2. Distributions: The "Shape" of Data
When we plot our data on a graph (like a histogram), the pattern it forms is called a distribution. In the Pearson Edexcel syllabus, you need to know three types:
Normal Distribution
This is the famous "bell curve." It is perfectly symmetrical.
- The Mean, Median, and Mode all sit exactly in the middle.
- Most people score near the average, with very few people at the extreme high or low ends.
Positive Skew
In a positive skew, the "tail" of the graph points towards the higher/positive end of the scale.
- This happens when there are a few very high scores that pull the Mean up, but most people scored quite low.
- The Mode is the lowest value, followed by the Median, with the Mean being the highest.
Negative Skew
In a negative skew, the "tail" points towards the lower/negative end.
- This happens when there are a few very low scores that pull the Mean down, while most people scored highly.
- The Mean is the lowest value, followed by the Median, with the Mode being the highest.
3. Probability and Significance
In Psychology, we use probability (\(p\)) to decide if our results are "significant." This means we are checking if the difference we found was caused by our Independent Variable or if it was just a fluke (chance).
Levels of Significance
We use decimal numbers to show probability. The standard level used in Psychology is \(p \le .05\).
- \(p \le .05\): This means there is a \(5\%\) (or less) probability that the results were due to chance. We are \(95\%\) confident the effect is real.
- \(p \le .01\): Used when we need to be extra sure (e.g., drug trials). Only a \(1\%\) chance of a fluke.
- \(p \le .10\): A more lenient level (\(10\%\) chance of a fluke), sometimes used in exploratory research.
One-tailed vs. Two-tailed Tests
This depends on your hypothesis (which you learned in the Hypotheses chapter):
- One-tailed test: Used for a directional hypothesis (e.g., "Men will be more obedient than women").
- Two-tailed test: Used for a non-directional hypothesis (e.g., "There will be a difference in obedience between men and women").
Did you know? Using a one-tailed test makes it slightly easier to find a "significant" result, but you must have previous research to justify predicting the direction!
4. Type I and Type II Errors
Sometimes, statistics lead us to the wrong conclusion. We call these errors.
Type I Error (The "False Positive")
This is when you reject the null hypothesis and say there is a significant effect, but actually, the result happened by chance.
Analogy: A medical test saying you are sick when you are perfectly healthy ("Crying wolf").
Risk: This usually happens if your significance level is too lenient (e.g., using \(p \le .10\)).
Type II Error (The "False Negative")
This is when you accept the null hypothesis and say there is no effect, but actually, there was a real effect that you missed.
Analogy: A medical test saying you are healthy when you are actually sick ("Missing the wolf").
Risk: This often happens if your significance level is too strict (e.g., using \(p \le .01\)).
5. Observed and Critical Values
After you perform a statistical test (like Wilcoxon or Spearman's), you get a number called the Observed Value (or Calculated Value).
To see if this number is significant, you compare it to a Critical Value found in a statistical table.
- The table will ask you for:
- Your \(N\) value (number of participants) or df (degrees of freedom).
- Whether your test is one-tailed or two-tailed.
- Your chosen significance level (usually \(p \le .05\)).
Sense-Checking: Always look at your data tables (summary tables) before doing the math. If your mean scores are almost identical, it's very unlikely you'll find a significant difference, no matter what the calculator says!
Quick Review Box
- Levels: Nominal (names), Ordinal (order), Interval (equal scales).
- Distributions: Normal (bell), Positive skew (tail to the right), Negative skew (tail to the left).
- Probability: We usually accept \(p \le .05\).
- Errors: Type I is a false positive; Type II is a false negative.
- Decision: Compare your Observed Value to the Critical Value in the table provided in your exam paper.