I have data from an annual survey which seeks to assess the needs of consumers on a 1 (least important) to 5 (most important) scale. Thus, I have data that looks like so:
My goal is to assess if the needs of consumers have changed across years and thus I believe the 'correct' approach to assess if needs have changed is to do a one-way ANOVA with year being the factor.
However, another approach is to consider the sample means across years like shown in the table below:
We can then consider a linear regression of RAM vs Years and check if the slope is significantly different from 0. If it is not significantly different from 0 then we can perhaps conclude that the observed variation in customer needs across years is due to random fluctuation and not due to any underlying shifts.
What are the drawbacks of the second approach relative to the first? Are they perhaps addressing different questions? Is the second one a weaker test of changes in customer needs as we lose sample information?