8 Time to say goodbye

They say that all that has its beginning must have its end. So I guess it’s time to …, OK, but before we part let me give you a word of advice.

Julia is a nice programming language with many applications, including statistics (probably way beyond the level covered in this book). Still, if you are new to (Julia) programming and statistics then most likely you should calibrate your tools first. Before you run some statistical analysis you may want to try it out on an example from a textbook written by an expert (not me though) and see if you get the same (or at least comparable) result on your own. Although this is a sound approach, I suspect you are more prone to visit some statistical blog or internet forum and go with the examples that are contained there. One such option is rseek.org, i.e. a search engine for the R programming language. In that case RCall.jl will be of assistance.

For instance let’s say that I copied the beerVolumes example (see Section 5.2) from some R forum (I didn’t). Now, without leaving Julia I can paste and execute the R’s code (R’s code goes between the quotation marks in RC.R"").

import RCall as RC

RC.R"
beerVolumes <- c(504, 477, 484, 476, 519, 481, 453, 485, 487, 501)
t.test(beerVolumes, mu=500)
"

Note: For that code to work you need to have the R programming language installed on your machine.

        One Sample t-test

data:  beerVolumes
t = -2.3294, df = 9, p-value = 0.04479
alternative hypothesis: true mean is not equal to 500
95 percent confidence interval:
 473.7837 499.6163
sample estimates:
mean of x
    486.7

Then, I can compare it with the output of Ht.OneSampleTTest. That way I can validate it and see if it is a credible Julia’s equivalent of R’s t.test. The above, is also the way to test my understanding of Julia’s function that stems from the docs.

import HypothesisTests as Ht

beerVolumes = [504, 477, 484, 476, 519, 481, 453, 485, 487, 501]
Ht.OneSampleTTest(beerVolumes, 500)

One sample t-test
-----------------
Population details:
    parameter of interest:   Mean
    value under h_0:         500
    point estimate:          486.7
    95% confidence interval: (473.8, 499.6)

Test summary:
    outcome with 95% confidence: reject h_0
    two-sided p-value:           0.0448

Details:
    number of observations:   10
    t-statistic:              -2.329353706113303
    degrees of freedom:       9
    empirical standard error: 5.70973826993069

Once I got both outputs that are similar enough I can be fairly sure I did right. Otherwise I should investigate where the differences come from and possibly make some necessary adjustments.

Now, let me follow a word of advice with a word of warning. The book contains a description of statistics the way I see it, not necessarily the way it really is. Additionally, many times I simplified stuff, e.g. by avoiding mathematics and mathematical formulas that go beyond the level of a primary school (in Poland grades 1-8). Moreover, I also tried to limit the number of Julia’s constructs in the examples. In the end I wrote that book for myself from the past, so if you ever met me then be sure to pass it on me. I would have loved to read it. But then again, back in the day when I was a student there was no Julia, and my English was too poor. Oh, well, just enjoy the book yourself.

Take care.

Bartłomiej Łukaszuk - author