# How to test this scenario?

#### JetBonilla

##### New Member
Let's say we have 4 groups of people at a casino -- red hair, brown hair, and blond hair. Each group collectively lost different amounts of money on different games at the casino, and I've calculated those percentages.

For example, red-haired people lost 50% of their losses on blackjack, 25% on craps, and 25% on poker. Brown-haired people lost 60% of their total losses on blackjack, 20% on craps and 20% on poker. Again, the underlying losses are different for each group and there are different numbers of people in each group. I also calculated the % of losses for ALL people collectively on each of the games. How would I determine if each group's losses are statistically different from all people collectively on each of these games?

#### AngleWyrm

##### Active Member
So you have a population of all people, and four samples drawn from that population, called red, brown, blonde, and black. Since this is a problem where sample sizes differ, we should use a z-score that takes sample size into account.

Normal z score = (observation - average)/(standard deviation)
z score scaled to sample size = (observation - average) / (standard deviation / Sqrt(sample size) )

The z score can then be put in this calculator to get the associated percentages and confidence levels

#### JetBonilla

##### New Member
Thanks so much! Sorry to be dense, but I don't really understand how I would do standard deviation when we're just talking about one data point -- the percentage of total loss for each group for each game. So what if it looked like this for the redheads for blackjack:

Sample of redheads lost $100,000 total on blackjack, which is 50% of the groups entire losses at the casino All people in the sample (i.e., redheads + browns + blonds) lost$300,000 on blackjack, which is 30% of their collective losses at the casino.

If I want to know if the redheads subset are statistically different on blackjack from all people in my sample on blackjack losses, how would I plug that into your formula?