Significant difference between two groups in a right /wrong quiz

I did an exam, which the comment given was that my answers to two questions were too "short" or lacking… (I do not know what was lacking). I would like to learn and understand. As I remember I think I used something called an on line calculator for categoric values when I came to my answers.

The exam questions were:

1. Students representing two different geographical ares had a quiz test.

• group 1 had 36 right and 13 wrong
• group 2 had 29 right and 19 wrong

Is there a significant difference between these groups (p<0,05)?

2. What if the quiz result where like this:

• group 1 360 right, 130 wrong
• group 2 290 right, 190 wrong

Is there a significant difference between this groups (p<0,05)?

1. Yes there is a significant difference
2. No there is not a significant difference.

My questions to you are:

• And what is the proper way of showing how you get to this/ or correct answer (without using a calculator)?

Meaning, what are the steps I need to take to solve this kind of questions?

I am most grateful if anyone have time to explain this to me.

• Please check you didn't make a transcription error (who the heck uses a significance level of $\frac{1}{2}$??) – Glen_b Sep 1 '13 at 23:54
• The question is more interesting when the test is conducted at a level of $0.5\%$ rather than $5\%$ or $0.5=50\%$. That is because (2) is very strongly significant whereas (1) is significant between the $1.7\%$ and $3.5\%$ levels, depending on how it is tested ($\chi^2,$ Fisher, or a permutation test). As far as its efficacy in assessing the underlying concepts goes, the question would be far better replacing $13$ by $18$ and $130$ by $180$: then it can be answered rigorously with almost no calculation. – whuber Sep 25 '13 at 22:28

What counts as a good answer would depend on the instructions you received, the learning goals and contents of the course associated with the exam (if any). In some courses, you are expected to document the whole procedure and do all relevant computations by hand. In others, just printing out the right output from a statistical package is enough.

• The name of the test and a succinct explanation of the reasons you think it is appropriate.
• A list of the assumptions of the test and why they are reasonable.
• A statement of the hypotheses being tested.
• An explicit formula for the test statistic/computation of the test statistic.
• The name and parameters of the relevant statistical distribution, if applicable.
• A p-value/critical value for the statistic, justifying your conclusion that the difference is or is not significant.

Also, your answers are obviously incorrect. I don't know how comfortable you are with these notions but you can realize that by thinking about the link between power and sample size, even without looking at any computation or specific test result.

• Thank you very very much for your respond. This makes me understand more. – Heta Aug 2 '13 at 11:44
• But since you say my answer is incorrect that basically means that I did not use the calculator correct, or that I should not have used it at all? – Heta Aug 2 '13 at 12:05
• Difficult to know without more details. Maybe you used incorrectly, maybe it was not appropriate to use it in this situation, maybe it claims to be appropriate for your situation but it's faulty in some way (this is also not uncommon, everybody can put a calculator on the web). In any case, even if the calculator could be used to perform the test in other circumstances, it was perhaps not the best approach for learning/answering exams because you are treating the whole thing as a black box instead of gaining more understanding. – Gala Aug 2 '13 at 12:11
• PS: If answers are helpful, you might vote them up (using the little arrow/normal distribution on the left of the answer). – Gala Aug 2 '13 at 12:12
• Hello Gaël Laurans. I have study a lot the last weeks, and I understand much more. And I finally got the right answers/how to create a good rapport. I just wanted to thank you again for your respond, it was truly useful. – Heta Sep 25 '13 at 22:08

Your answers were incorrect so your teacher might have given you some points if you had more information. You're probably supposed to observe something about the differences between the two sets of data and why the significance changes (or doesn't). Why do you think it might change? What have you tried? Where was the online calculator? Do any of the analyses listed here look like familiar names from class or the website calculator?

• First, thank you so very much for responding. The Chi-squared test part of the class. – Heta Aug 2 '13 at 11:36
• I understand more now, I did not test anything, I just "answered" the question. So my lack of understanding became very clear to me now. But I could have gone more into it than I did, but I did not understand enough to see that that would be the right thing to do. Thank you very much again. – Heta Aug 2 '13 at 11:42
• There are lots of places you can find on the internet if you just type in, "how to calculate the chi-square test". I tried it in two search engines and the first results that came up were all OK. Looking for a chi-square calculator is not nearly as fruitful from an education point of view as looking for understanding on the test. – John Aug 2 '13 at 11:46