Did I actually transform my data points from WGS84 to NAD27?
Not really. Assuming your original coordinates are actually WGS84, you just assigned an erroneous CRS of NAD27(BLM14) the second time you imported the data. Assigning the CRS does not transform the data.
I was hoping to see a difference between the two layers, but I saw
You may have on-the-fly transformations on for your project. If so, your WGS84 points were automatically reprojected (or projected in this case) to NAD27(BLM14). Turn it off (under Project Properties -> CRS) to see the actual differences.
To more clearly see the difference, relative to your Google Maps points (which may be in a different CRS), load the layer, defining it as having a CRS as WGS84 (probably accurate), then right-click on the layer and choose
Save As..., defining your project CRS of NAD27(BLM14) for the resultant file.
Turn off on-the-fly transformations for you project and load the saved NAD27(BLM14) file in. You should see the difference between the projections, i.e. your ~ 50 meters.
You can also use command line utilities to convert your coordinates:
PROJ's cs2cs utility
GDAL's gdaltransform utility
One way to use
gdaltransform is to start a terminal session (OSGeo4W if you are on Windows) and interactively execute:
gdaltransform -s_srs EPSG:<source CRS code> -t_srs EPSG:<target CRS code>
EPSG stands for European Petroleum Survey Group. Reference codes may be found at spatialreference.org.
EPSG:4267 are reference codes for WGS84 and NAD27, respectively:
gdaltransform -s_srs EPSG:4326 -t_srs EPSG:4267
-102.60930001 32.16984002 <-- user input
will return the corresponding coordinate in NAD27,
or, depending upon your platform, you may use
stdout redirection as follows,
gdaltransform -s_srs EPSG:4326 -t_srs EPSG:4267 < input.csv > output.txt
This way, if you construct your lon/lat data as a csv with one coordinate pair per line, like,
then the input redirector, '<', will feed your data in, and the output redirector, '>', will write
output.txt, which will look like,
-102.608865426754 32.1697300184475 0
-102.603066486342 32.1461989948827 0
See also: Proper gdaltransform syntax to transform a list of coordinates?