reorganize into univariate and bivariate functions, as well as adding…

… documentation for univariate transformations

docs/user_guide/simple_transformations.rst

@@ -1,11 +1,53 @@
-Simple Transformations
-=====
+==========================
+Univariate Transformations
+==========================
 
-There are currently 4 simple transformations implemented in distrx:
+There are currently 4 univariate transformations implemented in distrx:
     * log
     * logit
     * exp
     * expit
 
 These transformations are implemented using the first order delta method, which works in these
-cases as all of the transformations listed are continuous and differentiable.
+cases as all of the transformations listed are continuous and differentiable. To briefly summarize,
+the delta method transforms the variance by multiplying the original standard error by the first
+order Taylor expansion of the transformation function.
+
+Example: Log Transform
+----------------------
+
+Assume that we have some means and standard errors (SEs) of systolic blood pressure (SBP) from
+several different samples. The data may look something like the following,
+
+.. csv-table::
+   :header: mean, se, n
+   :widths: 10, 10, 10
+   :align: center
+
+   122, 10, 106
+   140, 14, 235
+   113, 8, 462
+   124, 15, 226
+   134, 7, 509
+
+and our goal is to obtain the appropriate SEs for the data after applying the log transform.
+
+The first step is to import the required function from the distrx package.
+
+.. code-block:: python
+
+    from distrx import transform_univariate
+
+Different transformation functions can be chosen through specifying a string parameter of which
+transform you would like to apply to your data. In this case, it is the following.
+
+.. code-block:: python
+
+    mu_tx, sigma_tx = transform_univariate(mu=df["means"],
+                                           sigma=df["se"],
+                                           n=df["n"],
+                                           transform="log")
+
+``mu_tx`` and ``sigma_tx`` are simply the means with the transformation function applied and their
+corresponding standard errors, respectively. ``sigma_tx`` has already been scaled by :math:`\sqrt{n}`
+so the we **should not** scale it by square root of the sample size to obtain a confidence interval.