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I have used a Likert scale in my survey, where respondents answer statements in terms of 1=strongly agree to 5=strongly disagree. There are 5 items measuring a single type of 'need gratification' and there are 5 different needs.

After summing the five items for each need gratification, a score is obtained between 5 to 25. These scores have been categorised into four "quartiles": 5-10 is Q1 (first quartile) , 10-15 is Q2 , 15-20 is Q3 and 20-25 is Q4 .

How can I test which of the five needs scales has the largest proportion of responses in the 20 to 25 range (Q4)?

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When you say 'quartile' - are those things based on the quartiles in this data (if so, how) or one some external criterion?

Assuming it's some externally determined cut-off point, this simply looks like a comparison of proportions rather than just raw counts ... which is, as you suggest, a chi-square.

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  • $\begingroup$ Quartiles here are with respect to the scores each respondent gets on 5 item, 5 statement scale The score should fall between 5 to 25 and this has been distributed into 4 quartiles. 5-10 is Q1 (first quartile) , 10-15 is Q2 , 15-20 is Q3 and 20-25 is Q4 . There are 5 types of needs and for each need, different number of respondents fall in Q1, Q2, Q3, Q4. Now the statistically significant difference in no. of respondents in each quartile can be calculated with chi square, but if i want to compare the number of respondents who fall in Q4 for all 5 types of needs , then what stat can i use. $\endgroup$
    – user22089
    Commented Mar 17, 2013 at 10:32
  • $\begingroup$ Quartiles here are with respect to the scores each respondent gets on 5 item, 5 statement scale The score should fall between 5 to 25 and this has been distributed into 4 quartiles. 5-10 is Q1 (first quartile) , 10-15 is Q2 , 15-20 is Q3 and 20-25 is Q4 . There are 5 types of needs and for each need, different number of respondents fall in Q1, Q2, Q3, Q4. Now the statistically significant difference in no. of respondents in each quartile can be calculated with chi square, but i want to compare the number of respondents who fall in Q4 for all 5 types of needs $\endgroup$
    – user22089
    Commented Mar 20, 2013 at 17:37

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