Determine if coin is fair

I am using a chi-squared test to determine if a coin is fair. Here are my results.

tosses: 10
heads: 6

x: 1.92
Degrees of Freedom: 1

Result: 16.6%

1) Does this mean that the probability of 6 heads in 10 tosses is less than 16.6%?

2) Why doesn't this test take the number of tosses into account? What is the degree of confidence?

3) Bottom line is that I want to know if the coin is fair. How many tosses do I need and what is the result that I'm looking for?



TS Contributor
You can use a chi-square goodness-of-fit test. The "model" distribution would be 5 heads and 5 tails in 10 tosses, and you're evaluating a situation of 6 heads and 4 tails to see if it's "very unusual" (or statistically significant).

Look at this post in the Examples section, which is similar to your problem (scroll down to chi-square test of independence):


New Member
yes, i have used a chi-squared test. my question is on the interpretation of the result. can you answer the three questions from my previous post? thanks.