POLS 3316: Statistics for Political Scientists
Interactive Lecture Module: Lecture 8
1. The Law of Large Numbers (LLN)
The LLN states that as the number of trials increases, the observed proportion of outcomes will converge on the theoretical probability. In a coin flip, we expect 50% Heads. In the short run (e.g., 5 flips), we might get 80% Heads. Watch how the bars level out as you increase the flips.
2. The Central Limit Theorem (CLT)
This is the magic of statistics. Even if the population is uniform (like a single die roll, which is flat), the distribution of sample means becomes a Bell Curve (Normal) as the sample size increases.
Try increasing the Dice per Roll to see the shape change from flat to mound-shaped.
If n=1, we plot the value of the die. If n=5, we roll 5 dice, average them, and plot the average.
3. Correlation vs. Covariance
Covariance measures the direction of a relationship but is sensitive to scale (units). Correlation (Pearson’s r) is standardized between -1 and 1.
Adjust the “Relationship Strength” to tighten the dots (affecting Correlation). Adjust “Spread/Scale” to change the range of data (affecting Covariance).