Statistical Analysis Playground

Sample Size ?Sample Size (n) — How many patients or observations are in your study. Larger samples give more reliable results. Try changing from 50 to 500 and watch how the convergence chart stabilizes!

100

True Probability (%) ?True Probability (p) — The actual chance of success in the population. For example, 35% means 35 out of 100 patients would have the condition. The simulation generates random data based on this value.

30%

Click Generate to simulate a study with your settings

Statistical Methods ?Click any method below to see its analysis in the Method Analysis card. Each method examines your data from a different statistical perspective.

Law of Large Numbers

More data → closer to truth

Maximum Likelihood Est.

Best guess for the true parameter

Confidence Interval

Range where the true value likely falls

Hypothesis Testing

Is the difference real or by chance?

Linear Regression

Find the trend line in your data

Distribution Analysis

Shape & spread of your results

Live Stats ?These numbers update every time you generate data. They summarize your simulated study at a glance — just like a real research paper's results section!

Total Samples ?The number of patients/observations in your simulated study. In real research, this is your n.

Success Count ?How many patients had a positive outcome (e.g., cavity present, implant successful). This is your x in x/n.

Observed Rate ?Success Count ÷ Total Samples × 100. This is your sample proportion (p̂) — your best estimate of the true probability from the data you collected.

Error Margin ?The gap between what you observed and the true value. Smaller error = more accurate study. Try increasing sample size to see this shrink!

📊 Data Distribution ?What is this? A bar chart showing how many successes vs failures occurred in your simulated study. Think of it like: "Out of 200 patients, how many had cavities vs didn't?" Hover over bars for exact counts.

💡 How to read: The green bar = successes (e.g., patients with condition). Red bar = failures. Hover over each bar to see the count and percentage.

📈 Convergence Analysis ?What is this? Shows how your observed probability changes as you add more patients. The blue line (observed) should gradually approach the red dashed line (true value). This is the Law of Large Numbers in action!

💡 How to read: Blue line = your running estimate. Red dashed line = the true probability. Notice how early samples are "noisy" but the line stabilizes with more data — that's why bigger studies are more reliable!

🔔 Normal Approximation ?What is this? Shows the bell curve (normal distribution) that approximates where your success count should fall. The red triangle marks where your actual result landed. If it's near the peak, your result is typical; if it's far out in the tails, it's unusual!

💡 How to read: The purple bell curve shows expected outcomes. The red triangle (▲) is your actual result. If the triangle is near the center → typical result. If far from center → unusual/surprising result.

🔬 Method Analysis & Results ?What is this? Detailed statistical analysis of your data using the method selected in the left panel. Each method looks at the same data differently — try switching between them to see how statisticians interpret results from multiple angles.

📊 Statistical Analysis Playground