Trend analysis (evolution & comparison)

[#1]

Hi all,

I have a data set with continous variable (not linked together). I have, over the year, data on the use of 3 products (expressed in DDD) and their efficacy (expressed in %). Annual value for each of the data.

1) I would like to know how to test the evolution of the efficacy/consumption over the years (is it significatively increasing or decreasing and cherry on the cake, when does it become significant)

2) I would like to see if there is a correlation between the evolution of consumption and efficacy.

Can you please help me with the choice of test...

My data set is here enclosed and so far I tried the fit Y by X where X is the year and Y the efficacy or consumption and then I use the Fit line test which gives me an analysis of variance. Not sure this is appropriate or not? Should i use the time series approach? 

Many thanks and kind regards !

[#2]

If this is all the data you have, I don't think time series analysis will add anything and I would not bother with statistical significance - just explore the data graphically.  From a few initial graphs, it looks like efficacy for all 3 products is declining somewhat and sales are declining for products 2 and 3 - but one is increasing substantially.  You haven't said how these 3 products are related - are they substitutes, complements, or unrelated?  I think that is important as it gives some more context about how to look at this data.  From what you have provided, the only thing that seems clear is that the sales for product 1 is on a different path than for products 2 and 3, while efficacy trends seem similar.  To repeat - I don't think conducting any sort of hypothesis tests adds anything to the graphical picture (unless you have more data to work with).

[#3]

Thanks for you reply.

So actually, product 1 has progressively replaced product 2 and 3 (these are different products that could, in some instances, be used for the same thing).

The decline in products 2 and 3 was expected considering the increased use of product 1 but as products 2 and 3 are also used for things product 1 cannot do, we were not sure. It seems important for us to make sure it is the case so we can (or not) emphasie that the use of product 1 will prevent or save the use of product 2 and 3.

The efficacy of each product is linked to their own consumption. The more it is used, the less effective. This is theoritical of course and the speed will depend of the compound. From what we see, the use of product allows a decrease in product 2 and 3 and if we can also restore their activity, that would be very nice to show...

Not sure if my explaination is clear enough...let me know if not!

[#4]

I think your desire to "test" is misguided.  You appear to be looking for a clear answer one way or the other, but the limited data you have will not produce certainty.  I think the graphs are suggestive enough.  It would be better to focus on what decisions need to be made going forward and what data you might track to ensure that things are unfolding as you expected.

[#5]

I may be able to split the data per month instead of year, do you think that it change the approach?

[#6]

If you have monthly data, I would definitely recommend using it.  You certainly can try time series analyses, but you should think carefully about the time structure - e.g., do lagged models make sense, should you focus on differences rather than the raw data, etc.  I still think the idea of looking for statistical significance is a distraction - if you find it, it doesn't mean much more than if you don't.  Exploring the relationships graphically is much more promising.