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I am analysing data from questionnaires. I have 344 valid responses. When I run the spearman's rho correlation test to see if there's any correlation between students' home province and their attitudes to a number of other criteria I get low coefficient values (mostly positive but some negative) but high p-values. The coefficient values and their corresponding p-values are: 

0.037/0.496,
0.014/0.795,
-0.049/0.363,
0.03/0.574,
0.029/0.597,
-0.026/0.636,
0.104/0.053,

I think that in most of these cases the coefficient values mean that the correlation is slightly positive or negative (depending) and the high p-values mean that there is strong evidence to support the null hypothesis. Is it accurate of me to argue that while the correlation coefficient values are low they could be seen as significant as there is a large number of responses (344). Would that be a correct understanding of this data?

gung - Reinstate Monica
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Rob D
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    Please clarify how you are using Spearman's test for this purpose. That test compares two variables that have ranks, and it's not clear how you could put ranks on the home provinces. – EdM Jun 21 '16 at 14:38
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    Welcome to CV. Based on the brief description, it sounds to me like you may be misusing the correlation coefficient. Home province is nominally scaled or categorical information, even if it's given a number from, e.g., 1 to 5. You need to elaborate more on how you're doing your analysis. – Mike Hunter Jun 21 '16 at 14:38

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Both @EdM and @DJohnson are right to point that it is not clear that you can use Spearman's test on this data, because home province is a categorical variable. An alternative approach you might want to use is to compare the mean responses to a question for students of different provinces to see if province might influence their attitudes.

Beyond this, you also seem to ask about how to read p-values and this is the part of your question that I am trying to answer below.

Whether or not something is "significant" depends on the choice you made of what is a "significant" result. Basically, you define a priori a p-value below which you will consider a correlation significant. It is possible that your field has a "traditional" level often used for sigificance.

Most of the p-values that you report above are very high and therefore it indicates that you do not have enough evidence to reject the null hypothesis which is that there is no correlation between your different variables. Therefore you should conclude that you have not found any significant correlations, if it weren't for the fact that probably your first issue here is that you should use a different test.

There is a lot of discussion around p-values and their use. One thing to keep in mind is that with enough data, every relationship is likely to appear significant (meaning it will get a small p-value in a correlation or regression context), but that might not mean that it has practical relevance (because more data will allow you to detect effects that are smaller in size).

Two places to start learning more about p-values:

Understanding p-value

p-value related posts on Andrew Gelman's blog

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Antoine Vernet
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  • I've ranked the provinces from 1 to 30 with 1 corresponding to the province with the highest average rate of disposable income and 30 corresponding to the province with the lowest average rate of disposable income. My field is Applied Linguistics. This is my first time doing statistical analysis and I'm still trying to figure out SPSS, what scales to apply to different variables. Thank you very much Antoine for those links. – Rob D Jun 21 '16 at 17:03
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    @RobD So what you're *really* doing is a rank-based correlation between mean home province disposable income and attitude, which is a reasonable analysis. From the original post, it seemed that provinces had no particular ordering, which would be a big problem for correlation analysis (since changing the arbitrary ordering would give different results). – Nuclear Hoagie Nov 21 '18 at 15:28