# significantly below chance?

#### e.stevens23

##### New Member
im doing a project and someone's performance on a test was 8 out of 48. is there a statistical test i can do to show this was signigicantly below chance?

also, i have the data for the number of correct responses from all the participants to each stimulus that was presented. i want to know if overall performance on each stimulus was higher than chance, how would i do this?

thanks, emily

#### ephialtes

##### New Member
Hi Emily,

I believe that a one-sample T-test will tell you whether a particular mean is significantly different from chance performance. Don't forget to check the assumptions of the t-test (you can do a search and find some help on the net). You can also look at the one-sample K/S or Chi-square goodness of fit if you need a non-parametric.

Since the concept of 'significantly different from chance' performance takes into account variability and a set of scores' distribution as compared to a normal distribution (or some other distribution, I suppose), I don't know that this would be possible with just one score (where there is no variability). You can, of course, still compute probabilities of obtaining a particular score, right?

-e

im doing a project and someone's performance on a test was 8 out of 48. is there a statistical test i can do to show this was signigicantly below chance?

also, i have the data for the number of correct responses from all the participants to each stimulus that was presented. i want to know if overall performance on each stimulus was higher than chance, how would i do this?

thanks, emily

#### Lark

##### New Member
Emily,

If you present more of your data maybe I can help.

For example in your first question, do you know what the data would be "by chance". ie by chance you would expect 13 out of 48; if you have such data, chi-square would be your best way to do this.

Lark

#### Statstastic

##### New Member
Hi,
Another issue is whether the questions are multiple choice or not.
If they are then you would use the binomial distribution to calculate whether the score was significantly different to the chance score.