how to apply chi-square on test result

Question

I have a test result and want to compare this based on the performance of different gender students. By analyzing this result, I should be able to say the difference is statistically significant.

In this test, 6 questions were asked male and female students and their accuracy were collected as follows:

You can assume that the same question was asked to two students at the same time, one is male and the other is female.

Question_NO   Gender     Accuracy
1              Male      70%
1              Female    50% 
2              Male      80%
2              Female    20%
3              Male      90%
3              Female    30%  
4              Male      60%
4              Female    20% 
5              Male      70%
5              Female    20% 
6              Male      100%
6              Female    30% 

How to apply chi-square method on my data set. I tried to use this to calculate the chi-square http://www.physics.csbsju.edu/stats/contingency_NROW_NCOLUMN_form.html

but, the thing is that if i put my each student' accuracy in a row, the df (degrees of freedom) will be too high(5) which does not make sense. Since, the df should not be affected by data size. Let's say if i have 1000 students results and the df will be 999, right?

So, how many rows and columns should i select? Number of Column is obvious which is two(male and female) but what about number of row?

OR how to form my data so that chi-square can be applied regardless of number of student?

Answer 1

You seem to have not have your data well formed:

Question_NO   Gender     Accuracy
1              Male      70%
1              Female    50% 
2              Male      80%
2              Female    20%
3              Male      90%
3              Female    30%  
4              Male      60%
4              Female    20% 
5              Male      70%
5              Female    20% 
6              Male      100%
6              Female    30% 

Seems to be

Male     Female
70%      50%
80%      20%
90%      30%
60%      20%
70%      20%
100%     30%

The average for each score is (approximately)

Male     Female
78       28

And the average of them together is 53

In the chi-square paradigm, the null hypothesis is that there is no relationship between the categories (gender and scores), ie they are independent of each other. If there is no relationship, the expected value for each gender's average score would the average of the scores. Thus the expected value for each gender is about 53%. Since the chi-square is far outside the rejection region, reject the null hypothesis with a very high degree of confidence.

r × c Contingency Table: Results

The results of a contingency table X2 statistical test performed at 19:19 on 26-NOV-2013

data: contingency table

       A      B

1     78     28    106
2     53     53    106

     131     81    212



expected: contingency table

        A          B

1    65.5       40.5    
2    65.5       40.5    


chi-square = 12.5
degrees of freedom = 1
probability = 0.000