one sample t-test alternative

#1
Hello,

I hope someone can help me, because I am getting crazy with this. Imagine the following scenario: I have several participants. Each participant has 5 scores in 5 different items. The score in each question is either 1 (correct response) or 0 (incorrect response). Basically would be something like this:

P1 P2 P3 P4
1 1 1 1
1 1 1 0
1 1 0 0
1 0 0 0
0 0 0 0


What I want to explore is whether each participant mean score is bigger than 0.75 (Which would mean a good performance in the task). What can I do?
Thanks a lot!
 

Karabiner

TS Contributor
#2
What I want to explore is whether each participant mean score is bigger than 0.75 (Which would mean a good performance in the task).
According to the title of the thread you want to determine
whether the mean rate of correct responses is > 0.75?

If the number of participants is large enough (n > 30 or
so), then t-test with expected value 0.75 should be possible.
Or, why do you seek for an alternative?

With kind regards

K.
 
#3
According to the title of the thread you want to determine
whether the mean rate of correct responses is > 0.75?

If the number of participants is large enough (n > 30 or
so), then t-test with expected value 0.75 should be possible.
Or, why do you seek for an alternative?

With kind regards

K.
thanks for your reply. I look for an alternative because if you see the data are not normally distributed (I only have 0 and 1).
 

Karabiner

TS Contributor
#4
According to your description, your dependent variable is not 0/1 but on a scale from 0 to 5
(total number of correct responses) or from 0.0 to 1.0 (total number of correct responses
divided by 5), respectively.

With kind regards

K.
 
#5
So maybe I am overcomplicating this. Yes, my DV is the proprortion of correct responses for each participants. So yes, I think that as long as the data are normally distributed I can use a one sample t-test right?

Thanks
 

hlsmith

Omega Contributor
#6
So far I am agreeing with Karabiner. Plot and test these data for normality to better understand the distribution.
 

Karabiner

TS Contributor
#7
So maybe I am overcomplicating this. Yes, my DV is the proprortion of correct responses for each participants. So yes, I think that as long as the data are normally distributed I can use a one sample t-test right?

Thanks
If sample size is large enough, then the t-test is considered
robust against non-normality.

With kind regards

K.
 
#9
By the way, something that I am not sure if it was clear enough is that I am treating each participant as a different measure: I don't want to explore whether the overall performance of all the participant is bigger than.75. I want to explore whether the score of each of the participants is bigger than .75. Don't know if this changes the thing...
 

Karabiner

TS Contributor
#10
So you calculate the correct responses/all responses ratio
for each participant and look whether this is > 0.75 or
not. Then you can say how many subjects were > 0.75 or
<= 0.75, respectively.


With kind regards

K.
 
#12
Thanks again. I think that the best is just to describe the results in terms of ratio.

Rogojel , basically I wanted something to powerful enough to support my hypotheses.

Thanks to both.
 

rogojel

TS Contributor
#13
yes,
that is clear. The question is mre about what your hypothesis is. A t test would be appropriate if you had a hypothesis about a population of which your subjects woukd be a sample and you would want to prove that the population has a performance ratio of 0.75 or higher.

E.g. your population are all the (hypothetical) operators who received a certain kind of training - and you want to prove that the training has the effect of raising the test rate.

If your hypothesis is about each individual I believe a t-test wil not gve you the right answer, and possibly a false one, because it implicitely refers to a population and a sample of that population.

kind regards
rogojel
 
#14
Each participant has 5 scores in 5 different items. The score in each question is either 1 (correct response) or 0 (incorrect response). Basically would be something like this:

P1 P2 P3 P4
1 1 1 1
1 1 1 0
1 1 0 0
1 0 0 0
0 0 0 0

What does these numbers represent? I can only see 4 columns. Is that 4 answers? Or is that 4 participants that has one row for each answer?

(In statistics it is more common to have each respondent=observation as one row and each column for each question.)



What I want to explore is whether each participant mean score is bigger than 0.75 (Which would mean a good performance in the task). What can I do?

For 5 questions I can imagine this number of correct answers: 0, 1, 2, 3, 4, 5.

The proportion correct answers would be: 0, 0.20, 0.40, 0.60, 0.80, 1.00.

Why ask for proportion larger than 0.75?

Do theses questions differ in difficulty? So that question 1 only 10% would answer correct, while in question 5 maybe 70 could be correct?

- - -

Or is it that simple, to just count the number of correct answers an note that participant 1 has got 4 of 5 questions correct, thus 80%, and thus been "good"?