One Sample t- test Help

EDINBRO

Hi guys,

Im stuck on my stats for my research project and Im hoping one of ye can help me.

Basically for one part of my analysis my supervisor told me I should me use a One sample t-test.

I have a few questions.

Firstly do I need to test for normality first or is that assumed when using a t-test?

Secondly could anyone give a line or two on why I am using a One sample t-test. What is its actual purpose over other tests? Obviously I can't say because I was told it was the right one

(BTW For my study, I had 20 subjects. each subject had to try to distinguish between 2 stimuli. producing a 2x2 contiguency table from which I calculated their mean d' [sensitivity index])

Thanks in advance! Really hate stats

2Scoops

EDINBRO wrote: »

Firstly do I need to test for normality first or is that assumed when using a t-test?

Technically, you should do it but it's usually not a big deal unless your distribution is very non-normal. It is an assumption of the t-test (i.e. it's supposed to be normal before you run the t-test).

EDINBRO wrote: »

Secondly could anyone give a line or two on why I am using a One sample t-test. What is its actual purpose over other tests? Obviously I can't say because I was told it was the right one

The idea of a one-sample t is that you are comparing your measured distribution to a known standard. Sometimes that is a population mean; in this case, I am guessing you are comparing it to random chance of identifying the stimuli correctly? A chi-square would be better, IMO! :pac:

MathsManiac

EDINBRO wrote: »

(BTW For my study, I had 20 subjects. each subject had to try to distinguish between 2 stimuli. producing a 2x2 contiguency table from which I calculated their mean d' [sensitivity index])

How did you get such a table? Surely each subject either distinguished correctly between the two stimuli or did not. Or is your data set more refined than that?

EDINBRO

Thanks to both of you for your assistance

Just to clarify...

One stimulus was real, the other fake. subjects were asked if they thought it was real or fake. this produces 4 possible outcomes; true positive, false negative, false positive or true negative. From this the sensitivity index d' was obtained.

d' = z(Hit rate)-z(false alarm rate).

so i have a d' for the 20 subjects.

Id expect the mean d' to be around 0 (i.e subjects can't tell the difference between the two stimuli)

so my null hypothesis is that

d' is not significantly greater than d’ = 0.

MathsManiac

So, if I understand you correctly, your d' is simply 2, 0 or -2, depending on whether the subject got 2,1, or 0 answers correct. (Answer correct = person correctly identifies whether the stimulus is real.)

Anyway, it strikes me that the number of people is so small, and given only three possible outcomes per person, this could be analysed with exact combinatoric methods. The total number of correct answers is a whole number between 0 and 40 (i.e. 20 people answering 2 questions each). If the null hypothesis is that people's answers are no better or worse than random answers, the probability of each answer being correct is 1/2, and the total number of correct answers is a binomially distributed variable with n=40 and p = 1/2.

You can, (using a calculator or Excel,) find the exact probability of every value of this variable under the null hypothesis, and hence calculate the exact (one- or two-tailed) p-value corresponding to your observed outcome.