Big Updates to TOSTER

Aaron R. Caldwell

Welcome to version 0.7.1 (April 2023)

I am happy to announce that today version 0.7.1 of TOSTER is now on CRAN. As always, detailed documentation of the package can be found the website. There is a lot in this update, and I want to use this post to highlight the key features.

Correlations

I finally have gotten around to adding new correlation functions to TOSTER. Overall, this covered by 4 functions.

Approximate approach

I have added the z_cor_test function to TOSTER. Unlike the cor.test function native to R, this function uses Fisher’s z transformation to create confidence intervals and calculate p-values. This is less than ideal for Spearman and Kendall correlations. However, it does function as a “better than nothing” test of equivalence or minimal effects. Additionally, the corsum_test function allows you to perform such tests when only the summary statistics are available. Please use both functions with care since they are only approximate tests.

Bootstrap approach

In order to overcome the downsides of the approximate tests, I also created a bootstrap correlation test. The function, boot_cor_test, operates almost exactly like z_cor_test, but allows for 2 more types of correlations to be tested. The bootstrap test allows for Winsorized and “bend percentage” type correlations. Both of these types of correlations are considered robust correlations (see Rand Wilcox’s work for more detail). When possible, I would highly recommend this function over using z_cor_test.

Compare correlations

You can also compare correlation coefficients between studies using the compare_cor and boot_compare_cor functions. The compare_cor function is useful when only summary statistics are available, while boot_compare_cor can be useful when the raw data is available. These functions are useful when you have a replication study where one of the tests is a correlation coefficient.

Log-transformed t-test

Sometimes it is useful to apply a natural logarithim transformation to outcome measures to help “normalize” the residuals from a normal Gaussian model. The only issue is that of interpretation. Since the raw values are transformed then the differences or mean difference is on the log scale. However, when back-transformed (i.e., exponentiation), the differences are ratio between the two means. So, equivalence or minimal effect can be tested as the ratio (e.g., x/y) rather than the difference between two means (e.g., x-y). I created two functions for this purpose: log_TOST and boot_log_TOST. As always, I recommend using the bootstrapped function over the simple parametric version.

Simple Hypothesis Tests

Some people don’t like the output of the traditional t_TOST and wilcox_TOST functions. Honestly, I don’t blame them because they are rather verbose. At some point someone asked why the functions don’t have output like that of t.test or wilcox.test. I think this is fair point as well.

If you would rather have output that looks like the base output in R you can do so in multiple ways.

1. Convert results using the as_htest function. This will convert results to an htest S3 object.
2. Use the simple_htest function. This essentially combines the functionality of t.test and wilcox.test (choose which underlying test using test argument), but allows the user to specify an alternative argument for either “equivalence” or “minimal.effect” in addition to the 3 base options.

I prefer to use simple_htest over t.test or wilcox.test at this point, but the function does not provide standardized effect sizes so t_TOST and wilcox_TOST may be preferable if you want a “all-in-one” type function.

As an example let’s use simple_htest as an alternative to t.test, but with an equivalence hypothesis.

simple_htest(data = sleep,
             extra ~ group,
             mu = 2, # equivalence bound argument
             alternative = "equ" # set hypothesis as equivalence
             )

    Welch Two Sample t-test

data:  extra by group
t = 0.49465, df = 17.776, p-value = 0.3135
alternative hypothesis: equivalence
null values:
difference in means difference in means 
                 -2                   2 
90 percent confidence interval:
 -3.0533815 -0.1066185
sample estimates:
mean of x mean of y 
     0.75      2.33

Descriptions of Results

Another comment I’ve received is that “TOST” is difficult to interpret. Therefore, I created describe methods for most functions in the package and describe_htest for results derived from an htest object. The descriptions will differ slightly on the function that the results are derived from.

Here is an example from simple_htest:

describe_htest(simple_htest(data = sleep,
             extra ~ group,
             mu = 2, # equivalence bound argument
             alternative = "equ" # set hypothesis as equivalence
             ))

[1] "The Welch Two Sample t-test is not statistically significant (t(17.776) = 0.495, p = 0.313, mean of x = 0.75, mean of y = 2.33, 90% C.I.[-3.05, -0.107]) at a 0.05 alpha-level. The null hypothesis cannot be rejected. At the desired error rate, it cannot be stated that the true difference in means is between -2 and 2."

Here is an example from t_TOST:

describe(t_TOST(data = sleep,
             extra ~ group,
             eqb = 2, # equivalence bound argument
             hypothesis = "EQU" # set hypothesis as equivalence
             ))

[1] "Using the Welch Two Sample t-test, a null hypothesis significance test (NHST), and a equivalence test, via two one-sided tests (TOST), were performed with an alpha-level of 0.05. These tested the null hypotheses that true mean difference is equal to 0 (NHST), and true mean difference is more extreme than -2 and 2 (TOST). Both the equivalence test (p = 0.313), and the NHST (p = 0.079) were not significant (mean difference = -1.58 90% C.I.[-3.05, -0.107]; Hedges's g(av) = -0.796 90% C.I.[-1.52, -0.0489]). Therefore, the results are inconclusive: neither null hypothesis can be rejected."

Concluding Remarks

Well, it has been about a year of work to get to this point, but I am rather happy with the way TOSTER is currently functioning. If you have any questions, concerns, or have suggestions please feel free to reach out. I have a “Contact Me” form on my website, and please feel free to send a message at any time. I would appreciate any feedback on the describe functions in particular!

I hope you all enjoy the new TOSTER!

Cheers everyone,

AC