How to interpret decomposition plot and check for seasonality

I'm new to this and I have a question about the results that I get from checking whether my data contains seasonality or not. I have a csv file which contains date, period and year. However, R reads the date as a factor and I didn't know how to deal with is. So I extracted the frequencies per month, so I have very little points now. The point contain the frequencies of the years 2012 and 2013.

My code:

k <- c(1110,989,1141,674,790,739,842,1004,751,765,1246,1045,
1106,1078,1012,965,978,991,856,703,784,639,821,518)

z <- ts(k, start =c(2012,1), frequency =12)

plot(decompose(z))


I really don't know how to read this an whether I can draw a conclusion about seasonality by this methods or not.

Smoothing procedures like that implemented in decompose are not intended to check for the presence of seasonality (or at least it is not straightforward to use it to that end). You should first use other methods to decide whether seasonality is present (for example a plot of the autocorrelation, periodogram, statistical tests,...). If you conclude that seasonality is present then it makes sense to apply decompose on the data. See this post.
• I think two years of data is not enough information to conclude that seasonality is strong. Also, using this kind of methods to test for the presence of seasonality may be misleading. Try for example this: plot(decompose(ts(rnorm(144),frequency=12))), you will probably conclude that seasonality is strong even though the time series is white noise (no seasonality involved). – javlacalle May 24 '15 at 16:15