Introduction: Making Sense of Your Results
You’ve finished your experiment or observation, and you have a pile of data. But how do you know if your results actually prove anything? Did the Independent Variable really cause a change in the Dependent Variable, or was it just a lucky coincidence?
In this chapter, we explore inferential statistics. These are the tools psychologists use to look at a sample of data and "infer" (conclude) whether the findings can be applied to the whole population. Don't worry if you find math intimidating—for this section, the most important skill is knowing which test to use and what the numbers tell you about your hypothesis.
Note: This chapter follows "Data recording, analysis and presentation." If you haven't reviewed Levels of Data (Nominal, Ordinal, and Interval), you might want to take a quick look at those first!
1. Probability and Significance
In Psychology, we can never be 100% certain about anything. There is always a tiny chance that our results happened by fluke. This "chance" is what we call probability.
What is Significance?
If a result is statistically significant, it means the effect we found is strong enough that it is very unlikely to have happened by chance. We use the symbol \( p \) to represent probability.
- The Standard Level (\( p < 0.05 \)): In most psychology research, we use the 5% level of significance. This means there is a less than 5% probability that our results were due to chance. In other words, we are 95% confident that our results are "real."
- Stricter Levels (\( p < 0.01 \)): Sometimes, if the research is very important (like testing a new drug), researchers use the 1% level. This means they are 99% confident.
Top Tip: Think of \( p < 0.05 \) as the "Gold Standard." If your result meets this threshold, you can reject your Null Hypothesis and accept your Alternative Hypothesis.
2. Distribution Curves
When we plot data on a graph, the shape of the curve tells us how the scores are spread out.
Normal Distribution
This is the classic "bell-shaped curve." Most people score in the middle, with fewer people scoring at the very high or very low ends. In a perfect normal distribution, the mean, median, and mode are all exactly the same and sit right in the center.
Skewed Distributions
Sometimes, data isn't symmetrical. This is called a skew:
- Positive Skew: Most scores are low, with a few very high scores "pulling" the tail to the right. (Example: A very difficult exam where most people failed, but a few geniuses got 100%.)
- Negative Skew: Most scores are high, with a few very low scores "pulling" the tail to the left. (Example: A very easy exam where almost everyone got an A, but a few people missed the test.)
3. Choosing an Inferential Test
One of the most common questions in Component 01 Section C will ask you to identify which statistical test is appropriate for a study. To get this right, you only need to know three things:
- Is it a Difference or a Correlation?
- What Experimental Design was used (Repeated Measures or Independent Measures)?
- What Level of Data was collected (Nominal, Ordinal, or Interval)?
The Named Non-Parametric Tests
OCR requires you to know these five tests:
1. Chi-square: Used for a test of difference or association with Nominal data and Independent Measures design.
2. Binomial Sign Test: Used for a test of difference with Nominal data and Repeated Measures design.
3. Mann-Whitney U Test: Used for a test of difference with Ordinal data and Independent Measures design.
4. Wilcoxon Signed Ranks Test: Used for a test of difference with Ordinal data and Repeated Measures design.
5. Spearman’s Rho: Used for a correlation (relationship) between two variables with Ordinal data.
4. Parametric Tests: The "Elite" Tests
The tests listed above are "non-parametric." However, researchers prefer parametric tests because they are more powerful and better at detecting significant results. You don't need to calculate these, but you must know the three criteria for using them:
- Level of Data: The data must be Interval (or Ratio).
- Distribution: The data must be drawn from a population that shows a Normal Distribution.
- Variance: The sets of scores should have similar spreads (known as homogeneity of variance).
5. Using Statistical Tables and Critical Values
Once a test is calculated, it produces 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.
To find the right Critical Value in a table, you usually need to know:
- The significance level (usually \( p \le 0.05 \)).
- The number of participants (represented as \( N \) or \( df \) for "degrees of freedom").
- Whether the hypothesis was One-tailed (directional) or Two-tailed (non-directional).
Key Takeaway: For some tests (like Chi-square), your Observed Value must be greater than the Critical Value to be significant. For others (like Mann-Whitney), it must be lower. You don't need to memorize which is which, as the exam paper will usually provide the rule in a caption!
6. Type 1 and Type 2 Errors
Even with statistics, we can still make mistakes. There are two types of errors you need to know:
Type 1 Error (The "False Positive")
This happens when you reject the Null Hypothesis even though it was actually true. You claim you found a significant effect, but it was actually just a fluke.
Why does it happen? Usually because the significance level was too lenient (e.g., \( p < 0.10 \)).
Type 2 Error (The "False Negative")
This happens when you accept the Null Hypothesis even though it was actually false. You claim there was no effect, but there actually was one—you just missed it!
Why does it happen? Usually because the significance level was too strict (e.g., \( p < 0.01 \)) or the sample size was too small.
7. Mathematical Symbols to Know
In the exam, you may see or need to use these relational symbols. Make sure you recognize them:
- \( = \) : Equal to
- \( < \) : Less than (e.g., \( p < 0.05 \))
- \( << \) : Much less than
- \( >> \) : Much greater than
- \( > \) : Greater than
- \( \propto \) : Proportional to
- \( \approx \) : Approximately equal to
Quick Review: Which Test?
Use this simple checklist for your exam revision:
- Nominal + Independent: Chi-square
- Nominal + Repeated: Binomial Sign
- Ordinal + Independent: Mann-Whitney U
- Ordinal + Repeated: Wilcoxon
- Correlation + Ordinal: Spearman's Rho
Common Mistake to Avoid: Don't mix up the "Sign Test" with "Significance." The Sign Test is a specific mathematical test for repeated measures nominal data; Significance is the overall goal of all inferential testing!