Pearson correlation p-value

New to Julia
1

Hi! I see that HypothesisTests.CorrelationTest makes a test for nonzero correlation. It prints the results of the test, including the two-sided p-value. How can I access that p-value? The output only has the fields k, n, r, and t, and none of them seems to be the p-value.

BTW it would be great if it was easy to access the p-value (and to degrees of freedom), as these are so often reported in publications.

2

There is function pvalue that accepts the test as its argument.

3

Thanks! I guess the documentation is somewhat incomplete here.

4 
using HypothesisTests

# One-sample t-test: test if mean differs from 0
data = [2.3, 1.8, 3.1, 2.5, 2.9, 1.7, 2.8, 3.0, 2.4, 2.6]
t = OneSampleTTest(data)
pvalue(t)

# Two-sample t-test
x = [2.3, 1.8, 3.1, 2.5, 2.9]
y = [1.2, 0.9, 1.5, 1.1, 1.3]
t2 = EqualVarianceTTest(x, y)
pvalue(t2)

# You can also test against a specific mean
t3 = OneSampleTTest(data, 2.0)  # Hβ‚€: ΞΌ = 2.0
pvalue(t3)

?help is your friend in this case to discover where it’s hidden.

help?> OneSampleTTest
search: OneSampleTTest OneSampleZTest OneSampleADTest TwoSampleTTest TwoSampleZTest ExactOneSampleKSTest KSampleADTest OneSampleHotellingT2Test OneWayANOVATest ApproximateOneSampleKSTest

  OneSampleTTest(xbar::Real, stddev::Real, n::Int, ΞΌ0::Real = 0)

  Perform a one sample t-test of the null hypothesis that n values with mean xbar and sample standard deviation stddev come from a distribution with mean ΞΌ0 against the alternative hypothesis
  that the distribution does not have mean ΞΌ0.

  Implements: pvalue, confint

  ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────

  OneSampleTTest(v::AbstractVector{T<:Real}, ΞΌ0::Real = 0)

  Perform a one sample t-test of the null hypothesis that the data in vector v comes from a distribution with mean ΞΌ0 against the alternative hypothesis that the distribution does not have mean
  ΞΌ0.

  Implements: pvalue, confint

  ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────

  OneSampleTTest(x::AbstractVector{T<:Real}, y::AbstractVector{T<:Real}, ΞΌ0::Real = 0)

  Perform a paired sample t-test of the null hypothesis that the differences between pairs of values in vectors x and y come from a distribution with mean ΞΌ0 against the alternative hypothesis
  that the distribution does not have mean ΞΌ0.

  Implements: pvalue, confint

  β”‚ Note
  β”‚
  β”‚  This test is also known as a t-test for paired or dependent samples, see paired difference test on Wikipedia.

julia>
5

Thanks. For those coming from other languages, where the p-value is the second output to a correlation function, maybe some illustrative examples (or even a cor() with two outputs) might be helpful. :slightly_smiling_face:

1 Like
6 
using Statistics
cor(x, y)

julia> cor(x, y)
0.939231860910616

I’ve found that designers of Julia packages tend to define functions like *nix command line utilitiesβ€”do one thing and do it well. In this case, the designer made a selection of the attributes of the t values, and it’s left to the user to add more. You could do this with a function or @macro or even refactor the package to make different choices. It’s a part of the learning curve in new languages to get used to how it differs from familiar languages and adjust expectations accordingly.

1 Like