Calculating statistical significance on survey results Consider a single survey question: "What is your favourite color"
with 4 possible responses: blue, green, red, yellow
If I've collected 100 responses:

*

*blue 20

*green 40

*red 35

*yellow 5

How do I calculate/test whether these results are statistically significant or if I need to collect more data before I make decisions based on this data?
Edit: My current thinking is to do a one-way chi-squared test to calculate statistical significance. Would this be the right way to go about this?

"Statistical significance" has very little meaning and this is not a place for hypothesis testing.  The answer to the question of whether probabilities of colors are equal to certain set values can already be assumed to be false.  An appropriate approach is interval estimation, e.g., provide "best guess" point estimates (observed proportions) and their compatibility (confidence) intervals.  The Wilson confidence interval is the most exact of the easy to use traditional frequentist approaches.  In R you can get this from the Hmisc package binconf function, and I'll bet that it's implemented in many other systems.
