How many flips of a coin would it take to know with absolute certainty that a coin is biased (weighted on one side)?

It could be a coincidence that the result is Heads every time with a fair coin, so it's impossible to tell. But, you can tell how big of a coincidence different results would be.

Statistics of Five Coin Flips

• Assume the coin is fair (null hypothesis).
• Flip the coin five times, if the coin lands on heads or tails five times in a row:
• Assuming the null hypothesis is true, what are the odds of a result this extreme?
  • (0.5 ^ 5) * 2 heads or tails, check both ends of the extreme == 6.25%
• 0.0625 is called the p-value
  • How much of a coincidence five heads or tails in a row is if the coin is fair.

Null Hypothesis

The assumption that the experiment is fair.

The assumption that nothing unusual is going on.

Alternative Hypothesis

The hypothesis that the result is unfair.

The hypothesis that the coin is biased or weighted.

P-Value

The smaller the p-value, the more severe coincidence would be required see the same result.

The probability of seeing a result at least this extreme, assuming the null hypothesis is true.

Idiopathic Pulmonary Fibrosis

The goal is to figure out if the differences in gene expression are a coincidence, of if there is a real underlying change in gene expression with the condition.