Autocorrelation
Does last Wednesday's draw influence today's? For every statistic you can compute about a draw — sum, odd-count, Powerball — we check whether that statistic correlates with itself across the lottery's history. One bar per lag, a confidence band showing where random noise should live.
Sum of the five white balls per draw. Range 15–345, expected mean around 175.
How it works
The test. For a time series x_1, x_2, …, x_n, the autocorrelation at lag k is the correlation coefficient between the series and itself shifted by k steps. If draws are independent, every autocorrelation should be approximately zero.
The confidence band. Under the null hypothesis (no memory), each individual autocorrelation is approximately normal with standard error 1/√n. The shaded band is ±1.96/√n— bars inside are noise; bars outside are candidates for “not noise.” With 30 bars, expect one or two to pop through by chance.
The joint test. The Ljung-Box Q statistic combines all 30 autocorrelations into a single goodness-of-fit test. Its p-value answers the question “taken together, is the whole series more dependent than random?” A p above 0.05 is the null result you'd expect from an honest lottery.