Example

Respondents to a survey were asked to judge the quality of a product on a four-point Likert scale (excellent, good, fair, poor). They were also asked to judge the reputation of the company that made the product on a three-point scale (good, fair, poor). Is there a significant relationship between respondents perceptions of the company and their perceptions of quality of the product?

Since both variables are ordinal, Spearman's method is chosen. The first variable is the rating for the quality the product. Responses are coded as 4=excellent, 3=good, 2=fair, and 1=poor. The second variable is the perceived reputation of the company and is coded 3=good, 2=fair, and 1=poor.

Variable 1 Variable 2
4 3
2 2
1 2
3 3
4 3
1 1
2 1

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Correlation coefficient rho = .830
t-test for the significance of the coefficient = 3.332
Number of data pairs = 7

Probability must be determined from a table because of the small sample size.

See this document, may help you.

第一个问题，最好用伽马(Gamma)相关系数，Kendalls tau-b ， kendalls tau-c 或者Somers d相关系数。

第二个问题年龄段属于ordinal variable（具体年龄属于interval variable）。

Appreciate!

多谢指教！