# Hypothesis testing in Julia
**URL:** https://discourse.julialang.org/t/hypothesis-testing-in-julia/77784
**Category:** Statistics
**Tags:** question
**Created:** [March 12, 2022, 9:49am UTC](https://discourse.julialang.org/t/hypothesis-testing-in-julia/77784 "2022-03-12T09:49:57Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@mihrits](https://discourse.julialang.org/u/mihrits)
#### Post date: [March 12, 2022, 9:49am UTC](https://discourse.julialang.org/t/hypothesis-testing-in-julia/77784/1 "2022-03-12T09:49:57Z")
I am taking a statistical data science course that is taught using R, and I am trying to replicate all the practical things in Julia. As we are doing quite basic stuff, mostly everything has been quite straightforward and similar to R, but I have been having some problems with hypothesis testing.
The package I am using is [HypothesisTests.jl](https://github.com/JuliaStats/HypothesisTests.jl).
1. I don’t exactly understand the implementation of `ChisqTest` in that package. I get that if I want the goodness-of-fit test I have to provide a vector `x` and `theta0` and that works as expected. But for the contingency table test, it seems to only accept `x` as a matrix and not `x` and `y` (for example `ChisqTest([50,100,50], [50,100,50])`) as it would seem from the docs ([link](https://juliastats.org/HypothesisTests.jl/stable/parametric/#Pearson-chi-squared-test)). The error message shows that the closest candidates are
```julia
ChisqTest(::AbstractVector{T}, ::AbstractVector{T}, ::Tuple{UnitRange{T}, UnitRange{T}})
ChisqTest(::AbstractVector{T}, ::AbstractVector{T}, ::T)
```
I don’t really understand where these come from or what values I should use there. I tried `ChisqTest([50,100,50], [50,100,50], (1:3,1:3))` and `ChisqTest([50,100,50], [50,100,50], 3)`, but both give an error “ArgumentError: at least one entry must be positive”, which confuses me. So I guess the main question here is, what is the argument `y` for? I thought I could use it for a contingency table test with two vectors, but I might be wrong.
1. There is `prop.test` ([link](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/prop.test)) for testing probabilities/proportions in R. RDocumentation doesn’t really explain what is the test behind it. Googling has led me to believe that it is a z-test for proportions, which, if I understand correctly, isn’t available in the `HypothesisTests.jl` package. For a simpler case of comparing two proportions, I tried making a vectors of ones and zeros with correct proportions and then applied a two-sample z-test, but that didn’t yield the same result, so I don’t think that is the correct workaround. The R version gives chisq value for the test and I tried `ChisqTest` with contingency table, which gave a much more similar p-value to the R function, but not the same, and as I’ve understood, that should not be the correct approach. Any suggestions on how to replicate the R’s `prop.test` in Julia would be appreciated.
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### Author:  [@nalimilan](https://discourse.julialang.org/u/nalimilan)
#### Post date: [March 14, 2022, 8:03am UTC](https://discourse.julialang.org/t/hypothesis-testing-in-julia/77784/2 "2022-03-14T08:03:03Z")
1. Regarding the chi-squared test, can you describe what your vectors are? The three-argument `ChisqTest` method expects `x` and `y` to be vectors with one value for each independent observations, and it computes the contingency table from that. The third argument to give the possible values for `x` and `y`. But it only supports ranges (so values must be contiguous), and is undocumented. This would give for example `ChisqTest([50,100,50], [50,100,50], (50:100, 50:100))`. We should probably fix this by not requiring the third argument, feel free to file an issue in GitHub.
If you already have the counts, then you can put them in a matrix, like `ChisqTest([x y])`. AFAICT this is the same in R, isn’t it?
2. `prop.test` in R is a Binomial test with the [Wilson approximation](https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Wilson_score_interval). R also supports the Clopper–Pearson variant via `binom.test`. Both are supported via `BinomialTest` in HypothesisTests, see `?confint` for details about supported variants.
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### Author:  [@mihrits](https://discourse.julialang.org/u/mihrits)
#### Post date: [March 14, 2022, 1:51pm UTC](https://discourse.julialang.org/t/hypothesis-testing-in-julia/77784/3 "2022-03-14T13:51:39Z")
Thank you for the reply!
1. The example I gave was indeed meant to be the counts in vectors. And constructing a matrix from the vectors works. As I saw from the docs that it was possible to use two vectors, I thought I could do so with counts, but apparently misinterpreted the docs. Nevertheless, I now also tried the three-argument method but found that it expects the vectors to be of the same length. It should be possible to compute a contingency table from samples of different sizes, right? This seemed strange, but maybe I am missing something.
2. Thanks for the lead on the Wilson approximation. I forgot to mention that I was thinking of the usage of the `prop.test` for comparing two samples, basically two proportions. I am not sure how to do that with `BinomialTest` if it is possible. After some more googling I found that I could replicate the result from R without the continuity correction when calculating the z-statistic described here: [https://online.stat.psu.edu/stat800/lesson/5/5](https://online.stat.psu.edu/stat800/lesson/5/5). And then finding the two-tailed p-value with it. Is it possible to calculate the hypothesis test for two sample proportions?
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### Author:  [@nalimilan](https://discourse.julialang.org/u/nalimilan)
#### Post date: [March 14, 2022, 7:46pm UTC](https://discourse.julialang.org/t/hypothesis-testing-in-julia/77784/4 "2022-03-14T19:46:39Z")
By definition a contingency table crosses values of variables from a single sample. Maybe you can reformulate your data as a single variable crossed with a variable indicating which sample each value comes from?
Unfortunately we don’t support two sample binomial tests for now, though there’s [a PR open for that](https://github.com/JuliaStats/HypothesisTests.jl/pull/218). If you don’t want to use the code from that PR, you could use Fisher’s exact test instead.
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### Author:  [@mihrits](https://discourse.julialang.org/u/mihrits)
#### Post date: [March 14, 2022, 8:29pm UTC](https://discourse.julialang.org/t/hypothesis-testing-in-julia/77784/5 "2022-03-14T20:29:18Z")
I am not that familiar with the chi-squared test besides some practical examples, so I was just toying around with it. Thank you for the answers!