Find Statistical Significance of Binary Data I would like to calculate whether the result of my survey is significant or not. There are two designed interfaces and in the survey, I have asked one question because for example if an interface A is liked 23 over B among 26 people, then interface B is liked 3 over A among 26 people. Therefore I kept the questions just one.
I tried to perform chi-square test but whenever I try to apply the formula, I am stuck because all examples I see require at least 2*2 matrix.





New Interface




Liked
23


Disliked
3




I tried to use the chi-square formula, but I can't do it because of the reason I explained above. I have calculated my conversion rate for the Like as %88.4 and Disliked as %11.5. But I can't do any further since I can't apply an example similar to my situation. I tried to perform the formula below for the chi-square but I got stuck.

I was wondering if anyone could help me with this?
Thanks in advance!

Chi square test requires you have a prior notion of what is "expected".  Under the assumption there is no difference in interfaces, you would expect an equal proportion of people would like and dislike the interface.
Therefore, $E=13$ is the expected number of people who would like the interface (your entire sample multiplied by the expected proportion who would like it).  This is also the expected number of people who would dislike it.
The $X^2$ statistic is then
$$ \dfrac{(23-13)^2}{13} + \dfrac{(3-13)^2}{13} = \dfrac{2}{13}100 \approx 15.3  $$
This test should have one degree of freedom, so we reject the null hypothesis that equal proportions of people like and dislike the interface with a p value far below 0.001.
