Should I use chi squared to test these observed vs expected ratios?

#1
I'm doing a study about the height:radius ratios of limpets on exposed and sheltered shores (The ratio is calculated by dividing height by radius). There is a theoretical 'optimum' ratio which is 1.06. I have 2 samples: 219 limpets from an exposed shore and 299 limpets from a sheltered shore. I calculated the height:radius ratio of all the limpets sampled.
I want to statistically test if my observed ratios of the limpets are significantly different to the expected ratios of 1.06. I want to do this for the sheltered samples and then exposed samples separately to see if they have different results.

Here are my first 5 data for sheltered limpets...

observed ratios:
1.35
1.64
1.27
1.18
1.63

expected ratios:
1.06
1.06
1.06
1.06
1.06

Should I use chi squared goodness of fit test? I'm not sure because I thought the variables had to be categorical in order to do a chi sqaured test, but isn't ratio a continuous variable? would it be better to use a Mann Whitney U test? I have to use a non-parametric test because the data are not normally distributed. Any help is appreciated, thanks x
 
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#2
You are right. Chi square only works with count data. Your data is calculated, not counts. You need to do a one sample test against the value 1.06.
There are non parametric one sample tests such as the Wilcoxon signed-rank test, but you might find that there is a transformation which will make your data normal. In any event, with such large samples, a one sample t test will give reasonable results.
 

rogojel

TS Contributor
#3
Twi quick remarks to what katxt was telling you:
1. in case of a nonparametric test you will get results concerning the nedian, not the mean.
2. If you transform the data remember to transform the threshold as well (the 1.06) :)

regards