Lesson 2 Defense Prep

Statistical Concepts

Explain your analysis choices in plain language

Examiners will ask why you used specific tests and what the numbers mean. You don't need to recite formulas — you need to explain why each test was chosen and what it tells you.

The Analysis Flow

Collect data
Check normality
Shapiro-Wilk
Choose test
Wilcoxon (primary)
Report effect size
Cohen's d (reference)

The Tests You Used

Shapiro-Wilk Test

What it tests: Are the paired score differences normally distributed?

Your result: Non-normal (reject null of normality).

Why it matters: If differences are non-normal, parametric tests (paired t-test) may be less reliable. This is why Wilcoxon became your primary test.

How to say it: "We first checked whether the paired score differences were normally distributed using the Shapiro-Wilk test. Because the test indicated non-normality, we used the Wilcoxon signed-rank test as the primary analysis."

Wilcoxon Signed-Rank Test

What it tests: Is there a statistically significant difference between two related groups (pre vs post), without assuming normal distribution?

How it works: It looks at the ranks of the differences, not the raw values. This makes it robust to non-normal distributions and outliers.

Your result: Significant (p < 0.05).

How to say it: "The Wilcoxon signed-rank test showed a significant within-group increase from pre-test to post-test, indicating a positive score direction after the Kit-Build activity."

Key distinction: This tests whether there is a difference, not how big the difference is. For that, you need effect size.

Paired t-test (Reference)

What it tests: Same question as Wilcoxon, but assumes normal distribution of differences.

Your role for it: Reference/robustness check only. Report it alongside Wilcoxon to show the result is consistent across methods.

How to say it: "A paired t-test was also conducted as a reference comparison and confirmed the same direction of result."

Cohen's d

What it measures: The standardized magnitude of the mean difference between two paired measurements.

Interpretation:

Why "reference": Because your primary test is non-parametric (Wilcoxon), Cohen's d (a parametric effect size) is reported as a reference, not the primary effect size estimate.

How to say it: "Cohen's d was reported as a reference effect size for the mean paired difference. The effect size [was small/medium/large], consistent with the score direction observed."

Hedges' g

What it measures: Like Cohen's d but corrected for small sample bias. More accurate for N < 20.

Where you used it: For the median-split comparison (low vs high pre-test groups), which had smaller subgroups.

How to say it: "Hedges' g was used instead of Cohen's d because the subgroups were small. The effect size was large."

Spearman's rho vs Pearson's r

Spearman rho: Measures rank correlation. Does not assume linear relationship or normal distribution. Used for Kit-Build score vs score change.

Pearson r: Measures linear correlation. Assumes normal distribution and linear relationship. Used for pre-test score vs gain.

Your result: Spearman showed no significant relationship between Kit-Build score and score change. Pearson showed a significant negative correlation between pre-test score and gain.

How to say it: "We used Spearman's rho because we did not assume a linear relationship between Kit-Build reconstruction score and comprehension score change. The correlation was not significant."

Key Interpretation: The Ceiling Effect

Your most important statistical finding to explain:
The negative correlation between pre-test score and gain (lower pre-test → bigger gain, higher pre-test → smaller gain or decline) is a ceiling effect. Participants who scored high on the pre-test had less room to improve. This is a known pattern in educational measurement — not a flaw in the intervention.

This matters because examiners might ask: "Why did some students decline?" The honest answer: they were already near the ceiling, so any small random variation looks like a decline. The median-split analysis confirms this: low pre-test group gained, high pre-test group declined slightly.

What to Say When You Don't Know

If an examiner asks about a statistical detail you've forgotten:

"That's a good question. I'd need to check the exact value, but the direction was [positive/negative/not significant]. The key takeaway is [main finding]."

This is always better than guessing. Examiners respect honesty about what you know vs. what you'd need to verify.

⚡ Quick Check

1. Why was Wilcoxon chosen as the primary test instead of the paired t-test?

2. A student asks: "Why did students with high pre-test scores decline?" What's your answer?

3. What's the difference between "statistically significant" and "large effect size"?

Primary Source

Read Field (2018), Chapter 6 (Correlations) and Chapter 8 (Comparing two means) — specifically sections on choosing between parametric and non-parametric tests.

Reminder

Ask me anything. If you want me to re-explain Shapiro-Wilk, effect sizes, or any specific test in simpler terms, just say so.