Clear Up the Uncertainty

Probability starts from a known model and asks what data it would produce. Statistics starts from data and asks which models are plausible. See Count What Could Happen.

For roughly symmetric data without outliers, the mean works well. For skewed data such as incomes or waiting times, the median better describes a typical value. Often it helps to report both. See Describe What You Observe.

No. Spins are independent and the wheel has no memory. Believing a result is due is the gambler's fallacy.

No. Combining bets that each have negative expected value cannot produce a positive expected value. A system only changes the pattern of wins and losses. On a European roulette wheel the expected loss is about 2.7% of every stake.

A percentage point is the simple difference between two percentages. Going from 40% to 44% is a rise of 4 percentage points, which is a 10% relative increase.

No. The 95% describes the method: across many repeated samples, about 95% of intervals built this way would contain the true value. Any one computed interval either contains it or does not. See Infer with Care.

If the null model were true, results at least as extreme as yours would occur about 3% of the time. It is not the probability that the null hypothesis is true, and it says nothing about the size of the effect.

It depends on how precise you need to be and how variable the data are. For a proportion near 50%, about 1,000 random respondents give a margin of error of roughly 3 percentage points. Quality of sampling matters more than size.

It can be one piece of evidence, but alone it cannot rule out confounding, reverse causation or chance. Randomized experiments give the strongest support for causal claims.

Overfitting happens when a model captures noise in its training data and therefore predicts new data poorly. Testing on held-out data or using cross-validation reveals it. See Test the Model.