My data are not statistically independent, that is why I want to use N*.
So what I've done is modify a function I found here:
http://stackoverflow.com/questions/20425473/calculate-confidence-interval-in-julia
to do what I want:
function t_test(x::Array{Float64,1};
nstar=0, conf_level=0.95)
alpha = (1. - conf_level)
if nstar == 0
nstar=length(x) - 1
end
tstar = quantile(TDist(nstar - 1), 1 - alpha / 2)
SE = std(x) / sqrt(nstar)
lo, hi = mean(x) + [-1, 1] * tstar * SE
end
On Tuesday, November 10, 2015 at 4:48:39 PM UTC+1, j verzani wrote:
>
> If you have the sample data, it is just the length of the data minus 1, so
> does not need to be specified, as it is computed.
>
> On Tuesday, November 10, 2015 at 9:47:43 AM UTC-5, Evan wrote:
>>
>> I want to do the following with some time series data:
>>
>> Calculate 95% confidence interval for mean defined as
>> +/-sigma(x)qt(0.025, N*-1) / sqrt(N*) where sigma(x) is the standard
>> deviation at any point x and qt(0.025, N*-1) is the 2.5 percentage point of
>> the Student-t distribution with N*-1 degrees of freedom.
>>
>> I have been trying to do this with HypothesisTests' ci() and
>> OneSampleTTest() functions, but as far as I can see OneSampleTTest() does
>> not allow me to choose the number of degrees of freedom.
>>
>> julia> t = OneSampleTTest(arr)
>> One sample t-test
>> -----------------
>> Population details:
>> parameter of interest: Mean
>> value under h_0: 0
>> point estimate: 0.3835
>> 95% confidence interval: (0.14217301685460967,0.6248269831453903)
>>
>> Test summary:
>> outcome with 95% confidence: reject h_0
>> two-sided p-value: 0.0057946078675091515 (very significant)
>>
>> Details:
>> number of observations: 10
>> t-statistic: 3.5948622927526235
>> degrees of freedom: 9
>> empirical standard error: 0.10668002520517972
>>
>>
>> julia> t.df
>> 9
>> julia> ci(t, 0.025, tail=:both)
>> (0.09706297518543938,0.6699370248145606)
>>
>>
>> Can anybody point me in the right direction?
>>
>>
>>
>>
