# Ask an Expert: Not sure which statistical test to use

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### Not sure which statistical test to use

My experiment involves animals choosing which environment they would rather live in. So I made 4 different environments, and put animals in the middle and then after a period of time I looked to see where the animals ended up and tallied them. So my data looks something like this:

Environment A: 9

B: 10

C: 3

D: 4

How can I analyze this?

Environment A: 9

B: 10

C: 3

D: 4

How can I analyze this?

### Re: Not sure which statistical test to use

Hello, and welcome to Science Buddies!

At the raw level, you can report simply the ratio (percentage) of animals from your sample that chose each environment. So, 9/26 (34.6%) chose environment A. 10/26 (38.4%) chose B, etc.

However, reporting ratios just for your sample size isn't the best way to report data. You sampled only 26 animals out of a population of 100s, 1000s, or more. How do you know if you choose a separate set of 26 animals that the ratio will be exactly the same? You don't and it likely isn't. So, to account for this uncertainty, it is better to report confidence intervals around your raw results.

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. (Reference: http://www.stat.yale.edu/Courses/1997-98/101/confint.htm). One typically chooses a 90 or 95 % confidence interval, representing the probability the population parameter lies within the reported interval. For example in your case, if the 95% confidence interval states between 25 and 40% of animals choose environment A, if you studied all animals in the population, there is a 95% chance that the true percentage of animals choosing environment A lies between 25 and 40%.

How do you construct these intervals? There are mathematical formulas, online calculators, and instructions on how to do it in excel. Google "confidence intervals for a proportion" and you will find a wealth of information on this topic. Then, I recommend constructing a confidence interval for each of your environments and display on a chart. Do you choose 90 or 95% confidence intervals? There is no single correct answer. Choose one and stick with it for all of your environments.

I hope this helps. Write back with questions. Good luck!

At the raw level, you can report simply the ratio (percentage) of animals from your sample that chose each environment. So, 9/26 (34.6%) chose environment A. 10/26 (38.4%) chose B, etc.

However, reporting ratios just for your sample size isn't the best way to report data. You sampled only 26 animals out of a population of 100s, 1000s, or more. How do you know if you choose a separate set of 26 animals that the ratio will be exactly the same? You don't and it likely isn't. So, to account for this uncertainty, it is better to report confidence intervals around your raw results.

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. (Reference: http://www.stat.yale.edu/Courses/1997-98/101/confint.htm). One typically chooses a 90 or 95 % confidence interval, representing the probability the population parameter lies within the reported interval. For example in your case, if the 95% confidence interval states between 25 and 40% of animals choose environment A, if you studied all animals in the population, there is a 95% chance that the true percentage of animals choosing environment A lies between 25 and 40%.

How do you construct these intervals? There are mathematical formulas, online calculators, and instructions on how to do it in excel. Google "confidence intervals for a proportion" and you will find a wealth of information on this topic. Then, I recommend constructing a confidence interval for each of your environments and display on a chart. Do you choose 90 or 95% confidence intervals? There is no single correct answer. Choose one and stick with it for all of your environments.

I hope this helps. Write back with questions. Good luck!

Deana