This is a very simple exercise that I'm hoping may help people with limited knowledge in statistical analysis (like myself). I am having trouble deciding what statistical analysis I can perform (in R) to determine whether or not my data are closer to one linear model or another.
For example: I have measurements of sodium and chloride in various dilute solutions:
# Na <- c(1.56, 1.00, 1.60, 3.23, 2.02, 2.81, 2.09, 26.24, 1.59, 0.42) Cl <- c(1.40, 0.91, 1.22, 2.67, 1.67, 3.01, 2.17, 27.42, 1.45, 0.51)
For simplicity, this solution is a dilution of either table salt dissolved in water or natural seawater. For each case, Cl/Na will be a specific ratio that reflects the composition of the original solution. We can visualize this by:
plot(Na,Cl) abline(0,1) # expected slope for table salt dissolved in water abline(0,1.16) # expected slope for natural seawater.
I want to know which model, table salt in water or seawater, is a more statistically accurate fit to the provided data. Linear regression analysis in R gives a line of best fit with a slope of 1.05 (
lm(Cl~Na)), right in between the two models.
So, which solution do I more likely have and why? The line of best fit slope is closer to that of table salt dissolved in water, but that does not seem very statistically sound. Thoughts?
Edit: @whuber mentioned that there is one anomaly in the dataset - in reality, the provided data is just a subset of the original data. There are actually hundreds of data points in between the apparent outlier and the rest of the provided data.
Also, here is a
log(Na)-log(Cl) summary of the complete dataset:
Min. 1st Qu. Median Mean 3rd Qu. Max. NA's -0.46870 -0.06186 0.02654 0.02218 0.12780 0.47510 183
Edit2: As for the "true nature of my investigation": The 'solution' in question is likely a mixture of both table salt water and natural seawater. What I'd like to do is find a definitive way (through statistical analysis) to show that I have more of one or the other. I had hoped that my simplified question/dataset would yield an answer from the community, but it seems I was off base. If it helps, a complete dataset is now hosted below:
Looking at the distribution of the complete data shows I have more Cl/Na about 1.00, but this does not seem 'sound enough' to back up an argument. The probability that I have one solution or the other is unknown. I have the raw data and relevant models for Cl to Na to run with.
For clarification, the original question is still the one I'd like to solve. An alternative question could be: Which solution do I have more of and what analysis did I use to come to that conclusion?