# How can I calculate confidence for a multiplicative (growth) dataset?

I have a dataset of daily price changes, represented as decimals. Perhaps: 0.5, 1.5, 2.0. That's to say it lost 50%, then it gained 50%, then it gained 100%.

I'd like to know how confident I should be that the true mean growth rate is within some margin of the sample mean growth rate.

I've read that I can "Just take logs of the datapoints, then compute arithmetic mean of those results, and then variance, and standard deviation, and compute confidence intervals like you would for arithmetic data, and then once you have the upper and lower bounds of the confidence interval, take exponents".

I think there are answers to this elsewhere in this stack, but I'm not a math major, and get a bit lost with all the exotic Greek symbols, so I'm just wondering if I've understood this correctly, and if I can get this answered using simpler language, and algorithmically. My questions are:

1. Is that above statement to do with taking logs correct?

2. What does "take logs" mean? Does it mean ln(), or log10(), or "It doesn't matter what the base is, so long as you use the same base when taking the exponents of the upper and lower bounds later on?"

3. Assuming it is correct, and the answer is "use ln()", would this be the correct method?

Generate a dataset by taking the ln() of every datapoint of my growth dataset.

Calculate arithmetic mean, variance, and standard deviation of that dataset.

Let N = the sample size, and for 95% confidence, calculate the error like this: Error = (1.96 * σ) / square_root(N)

Let the upper bounds, U = e^(M + Error), and the lower bounds L = e^(M - Error)

I am 95% confident that the true mean growth of this commodity is greater than L, and less than U.

Is that correct?

• So you have a product with daily price changes and you would like to know if the changes are positive and by what amount with a 95 % CI? – user2974951 Jan 9 '19 at 7:58
• I already know in my sample if they're positive, and by what amount. I want to know if my sample has enough data points to be 95% confident that the product has positive price changes in the longer term. – Duncan Marshall Jan 9 '19 at 8:10
• Two options as I see it: 1) either you are asking about power analysis, that is to determine what is the required sample size to claim with a certain probability that the sample estimate is accurate to some degree, or 2) a prediction interval, that is to estimate the statistic in question for future new samples with a certain confidence interval. – user2974951 Jan 9 '19 at 8:17
• It's the first one. – Duncan Marshall Jan 9 '19 at 8:34
• Then you need power analysis for the test you used, what test did you use to determine change? – user2974951 Jan 9 '19 at 8:42