# determine whether the median of a set of ratios is different from a set value

I have a relatively large set of ratios (n=274). Technically, there is no upper bound, but obviously, the ratios cannot go below 0. Practically, the actual ratios are around 1 (0.8 - 1.2). I am trying to determine whether the median of the distribution is significantly different from 1. I thought about using a single sample t-test, but the ratios are not normally distributed, so I do not think that a t-test is valid? Would (log) normalizing help? Any suggestions would be appreciated!

• Sounds like a problem for the bootstrap! Oct 21 '15 at 5:37

p-value = $P(K\le 100) + P(K\ge 175)$ I'll let you find those binomial probabilities from your favorite statistics package.