Excel and SPSS are visual ways to work with and analyze data. This means they have a (relatively) easy learning curve and are more intuitive to folks. Many folks in particular grew up with Excel as it is probably the most widely-used number crunching software on the planet. The problem with visual systems is that it is hard to repeat analyses. Let’s say you get some data in, you sort it, remove some weird data or rows, do a few calculations, and then make a graph. That’s great and pretty easy to do. But the NEXT time you get that data (maybe next quarter), you have to manually do all those steps again. Did you remember what your criteria were for throwing out the weird values? How exactly did you sort? It’s hard to repeat your analysis.
R and Matlab are for writing scripts so that you can apply the same analysis multiple times reliably. They are both also known for their gorgeous graphical output. Both can do much more complex calculations, statistics and transformations than can be readily done in Excel. R is growing exponentially right now because it is free, open source, and highly used by universities. It tends to shine in acquiring data (i.e. scraping the web or databases), tidying the data (especially with the “tidyverse” addon), and making beautiful (ggplot2) and interactive graphs (Shiny), dashboards (flexdashboard), interactive websites (Shiny), books (bookdown) and blogs (blogdown). Matlab, on the other hand, is used primarily in the engineering and technical fields as a high quality analytical software with excellent graphics and output.
You left off python, which is another tool in this set. It is very similar to R in that it is a scriptable language with great tools and visualization features. It tends to be used mostly by computer programmers/scientists, whereas R tends to be used more in the data analytics/academic/journalism fields, but there is a lot of overlap.
If you want quick and easy: Excel
If you want quick and easy stats: SPSS
If you want an excellent (yet pricey) engineering tool: Matlab
If you want an excellent data analytics toolkit and want to communicate your results with others: R/Rstudio
If you want excellent data analytics toolkit and interact with a lot of computer science folks: Python.
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