# Thread: Is this a Covariance application?

1. ## Is this a Covariance application?

Hi,

I have data from a satisfaction survey and want to see how much responses differed between two questions, the responses ranging from 1(Lowest) to 5(Highest). i.e. If the responses are very close, one will be omitted in future surveys.

I think it would be the Covariance between the two, but am not sure. I entered the data into Excel and calculated the Covariance between the two columns, which was 0.92.

Is this the correct way to go about it, or is there a more appropriate calculation?

Thanks.

2. ## Re: Is this a Covariance application?

Hey SC313.

What specific difference are you testing? You could use a correlation statistic as well to test the relationship between the two sets of paired random variable observations.

3. ## Re: Is this a Covariance application?

Originally Posted by chiro
Hey SC313.

What specific difference are you testing? You could use a correlation statistic as well to test the relationship between the two sets of paired random variable observations.
Basically, to see if people generally answered the same for both questions, which would indicate that the two questions are too similar and redundant.

What if I took a regression line?

4. ## Re: Is this a Covariance application?

Have you considered using a form of a Pearson Chi-Square test with attention to the order of observed answers? (i.e. Chi-square goodness of fit for paired data)?

5. ## Re: Is this a Covariance application?

Originally Posted by chiro
Have you considered using a form of a Pearson Chi-Square test with attention to the order of observed answers? (i.e. Chi-square goodness of fit for paired data)?
Hi,

I calculated the Chi-test from the Excel command "=chitest(A2:A77,B2:B77)." This gave 1.

Also, I calculated the following:

a) Mean of Difference: 0.18
b) Slope of Regression: 0.79
c) Intercept of Regression: 0.91
4) Chi-Test: 1

From these, what can I conclude? Have I used the correct Chi-test you are referring to?

Thank you!

6. ## Re: Is this a Covariance application?

Can you explain what chi-test returns and performs (I am not familiar with this function in Excel) with regard to the test-statistic and comparisons involved in the calculation?

7. ## Re: Is this a Covariance application?

Hi,

According to Microsoft, the Chi-Test uses the following formula:

$\chi^2=\sum_{j=1}^{r}\sum_{j=1}^c\frac{(A_{ij}-E_{ij})^2}{E_{ij}}$, where $A_{ij}$ is the actual frequency in the i-th row, j-th column, $E_{ij}$ is the expected frequency in the i-th row, j-th column, and r is the number of rows and c is the number of columns.

Is this the one you were referring to before?

8. ## Re: Is this a Covariance application?

This will test whether there is a statistically significant enough difference between the distributions themselves, but it won't give information about specific relationships between paired data.

Do you need to get information about relationships between paired observations or not?

9. ## Re: Is this a Covariance application?

Originally Posted by chiro
This will test whether there is a statistically significant enough difference between the distributions themselves, but it won't give information about specific relationships between paired data.

Do you need to get information about relationships between paired observations or not?
To be honest, I do not know. All I need to determine is whether or not people answered both questions similarly enough.

For example:

Person 1: Question 1=5, Question 2=5
Person 2: Question 1=5, Question 2=4.5

In this case, I would remove one of the questions, because the responses were so similar...

Does that make somewhat sense?

Thanks, by the way for helping.

10. ## Re: Is this a Covariance application?

Are you just considering the frequency of answered questions or does the relationship between pairing and possibly through question number make a difference?

If the answer is the former, then what you have been doing should be OK but if not you will need more advanced analyses.

11. ## Re: Is this a Covariance application?

Originally Posted by chiro
Are you just considering the frequency of answered questions or does the relationship between pairing and possibly through question number make a difference?

If the answer is the former, then what you have been doing should be OK but if not you will need more advanced analyses.
Yeah, basically to see how people answered the two questions, specifically if they answered the questions nearly identically...Still not making sense?

12. ## Re: Is this a Covariance application?

Is it just the frequency information of questions answered that matters?

If the answer is yes, then what you have done is right. You can use the chi-square test primarily to test this and get a p-value for the test statistic and if its less than say 0.05 then reject the hypothesis that the distributions are the same.

13. ## Re: Is this a Covariance application?

Originally Posted by chiro
Is it just the frequency information of questions answered that matters?

If the answer is yes, then what you have done is right. You can use the chi-square test primarily to test this and get a p-value for the test statistic and if its less than say 0.05 then reject the hypothesis that the distributions are the same.
No, it matters if person A chose 5 for each of the two questions, and person B chose 4 for both of the two questions, etc.

What would a Chi-Square of test of 1 indicate then?

14. ## Re: Is this a Covariance application?

I don't know if the test is just a yes/no answer (I think it is but I would need to read the documentation), but what it does intuitively is test the variation between distributions by relating frequency information for each bin together.

It generates a test-statistic that is large if there is more of a difference between the two distributions and small if the differences are smaller.

If the difference is big enough then you reject the hypothesis that the two distributions are the same and conclude that both question processes are different.