I used SPSS to do a scatter plot for 2 continuous variables and obtained several horizontal lines - there does not seem to be a line of best fit, no positive or negative association, it is unilinear and there are several outliers (see attachment). Does this mean there is no correlation? When I then performed a correlation analysis with the 2 same variables using SPSS (bivariate correlation), I obtained a 2 tailed sig. of .000 and Pearson's correlation (r) of .223. How is this possible ?
It must be a large sample size, right? Large sample size correlates significantly even whit low values Pearson's correlation.
Yup, it sounds like any potential correlation ("the signal") is below the level of noise in your data (assuming you used the various functions correctly).
Or it could be that that the "best fit line" is not included by default in SPSS. Just calculate the correlation between x and y, SPSS should include the P-value for significance of correlation.
The fact that the line of best fit is not shown it is not worrying for itself. The basic feature of SPSS for scatter plot do not include the line of best fit. You can add it in few steps (e.g., http://www.ats.ucla.edu/stat/spss/faq/scatter.htm).
Looking at your data, I have two concerns: 1) is at least one of the two variables normally distributed? This is an assumptions to calculate the correlation coefficient. Better if both are normally distributed. 2) it seems that you have a great concentration of data in the bottom left part of the scatter plot. It is very easy that few data in the up right part of the graph may generate a spurious correlation.
Considering that the variable plotted in the y-axis looks like a discrete numerical variable (1,2,3,etc) more than a continuous one, I would try to perform Spearman rank correlation (Analyze>Correlate>Bivariate>Spearman).
I hope this can help, and let us know!
Many thanks for your replies. Nicola, concerning normal distribution of the variables, indeed the data for the variable plotted in the y axis has very few measurements, ranging from 0 to 8 the majority of which are concentrated around 0 to 2. So can I conclude that this is the reason for the type of scatter plot generated?A.K. Singh, if I understood correctly, even if my scatter plot does not show a correlation between the two variables, I can go ahead and calculate correlation coefficient? I thought the scatter plot was the first step in deciding whether there i a correlation between two variables?
"There is a restriction on the validity of the associated hypothesis test, which is that the two variables are observed on a random sample of individuals and that the data for at least one of the variables have a Normal distribution" (Altman. 2000. Practical statistics for medical research).
Sarah I agree with you that the problems is that your data are severely skewed. It is worthy when you have severely skewed variables to try transformations (e.g., logarithmic, etc). This may make the actual relationship between the two variables clearer. Finally, on this dataset it may be worthy to try the Spearmen Rank Correlation.
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