Correlation and Significance - is this approach valid?

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grain

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Hello,

Could any one please confirm the following;

I have two columns of data (temperature) that I would like to compare. I would like to understand the statistical relationship between the two. I have about 1200 temperature measurements.

Is the following approach valid?

Find the correlation coefficient: ‘r’

I then find the coefficient of determination: ‘r2’

I then find the t value to test significance of a correlation coefficient using this formula:

t = r*Sqrt((n-2)/(1-r^2))

If the value of t is less than the critical value, which is found from a table corresponding to the desired significance level, then the null hypothesis cannot be rejected i.e. there is no relationship. If it’s greater then that level of significance is achieved.

When I use my figures I get a r value of 0.73 and so r2 = 0.53
When I use n = 1200 it gives a t-value = 36.85
When I look up critical values for two tailed significance the 0.0001 significance level is 3.91 for n = 1000 (this was the largest value for n given).

My questions are:

Is this approach correct?

Because 36.85>>3.91 does this mean that indeed there is a very strong positive correlation and also has a very high level of significance??

Does it matter which table of critical values I use i.e. single or two-tailed critical values?

Any help would be greatly appreciated. Thanks.
 
"t"? with 1200 observations? Maybe it's the other 't'.

Do you BELIEVE there is a stong positive correlation?

Not that there is "no" relationship, but that the variation in one dataset is not explained by the variation in the other set.

Why are you using a 2-tailed test? It may be fine, I'm just trying to get you to justify it.

What is the nature of your data? Were they collected sequentially, maybe at regular intervals? Some ARMA model might be more appropriate.
 
Yes I do believe there is a strong relationship.

The two data sets are temperature measurements made every hour over two months. One is the real temperature recorded and the other is temperature for the same place but predicted by my model. I wanted to show mathematically that they have a strong correlation. When I graph them together they look like having a strong correlation.

I followed an example set out here:
http://janda.org/c10/Lectures/topic06/L ... canceR.htm

I'm not sure which test to use two tailed or one-tailed.

Thanks.
 
Ah! You did not say that you were fitting a model. I think you should not be testing correlation. I would lean toward "Goodness of Fit." There are various ways to do that. Give it a search and let's see what you get.
 
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