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I am struggling with a data analysis. I have made a survey and got the following answers in the first turn, I put them in a frequency table

  • Don't agree at all: 8
  • Don't agree: 6
  • I don't know: 16
  • Agree: 14
  • Totally agree: 6

In the second turn:

  • Don't agree at all: 8
  • Don't agree: 13
  • I don't know: 9
  • Agree: 12
  • Totally agree: 8 I added weights to the answers: 2 for Don't agree at all, 1 for Don't agree, 0 for Don't know, -1 to agree and -2 for totally agree. I need to know whether their opinion is significantly different or not. I have 50 people who wrote these answers. I know firstly I need to know if the data is Normally distributed or not, then I have to test the variance with the two sample F test and only after this I can turn to the T test. My only problem is, that I have to idea how to solve this in Excel (or SPSS), I have only found examples for data in row and not for frequency tables. Could someone please help me?
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  • $\begingroup$ Are the people in the first turn the same as the people in the second turn? If so, can you identify, for any given person, their answer in each turn? $\endgroup$ – Sal Mangiafico Apr 14 at 13:15
  • $\begingroup$ Yes, they are the same people. Unfortunately, no, because they filled it out anonymously. How bad is that? $\endgroup$ – TMoci Apr 14 at 16:04
  • $\begingroup$ I edited by answer below. $\endgroup$ – Sal Mangiafico Apr 14 at 18:50
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Since the the same people were sampled in the first turn and in the second turn, the correct approach would be use a test that takes into account the paired or repeated measures of the data. However, since the identity of the participants was not recorded in a way that allows the observations to be paired, that isn't an option. The only approach I know of in this case is to treat the samples (the two turns) as independent, and make note of this in your write-up.

Treating the data is if your observations are independent: For this kind of data, I wouldn't assume or assess if the data are normally distributed. Nor would I use a t-test. A common test for this situation is the Cochran-Armitage test. This isn't available in SPSS, but because you have only two levels of Turn, you can use the linear-by-linear test of trend in SPSS as described in the answer by Hong-Qiu Gu here. Other alternatives: An ideal approach is ordinal regression. Also, if you have an implementation that handles ties, a Mann-Whitney test will give satisfactory results.

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