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<p>Um, not really. First of all, statistics is based upon calculus. If you want to go far enough in statistics to actually get a job in it - even just an applied statistics degree, you need at least a year of college-based calculus and a class in linear algebra.</p>
<p>I work at the intersection of the health sciences and psychology, and your 4-point list (and the last one isn’t even true; the vast majority of our body of knowledge in the social sciences and health sciences is based on non-random samples) covers perhaps the first two weeks of the intro to statistics course you take as a freshman or sophomore psychology major. I do pretty extensive statistical work, but even the most basic of research support positions needs to know far more than that. I’m talking about BA in a social science working at like a market research firm or a testing company or something - they’re going to expect you to at least be able to read and interpret basic inferential statistics like ANOVA, t-test, regression, and certain non-parametric tests, and they’re going to want you to know how to use SPSS (which is a statistical package you use to do the analyses).</p>
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<p>I would divide “stat-heavy” into two fields - social science stats (which don’t require a background in calculus) and mathematical statistics (which does), although there’s some overlap.</p>
<p>Social science stats:
Research psychologist - all fields, but especially quantitative and mathematical psychology
Industrial-organizational psychologists (develop tests to help businesses decide who to hire, and analyzes hiring patterns for productivity)
Certain research sociologists
Market research analyst/sales research
Educational testing and measurement/psychometrics (develops standardized tests for people like ETS, ACT)
Lots and lots of federal social science statistician (CDC, Census Bureau, Bureau of Labor Statistics, Department of Defense, FDA, city and county government…on and on. They hire both social science and mathematical statisticians)
Nursing research
Public Health
Demographers (follow population trends over time)
Sports management (somebody has to track player stats!)
Survey research
Political science</p>
<p>Mathematical stats
Statistician (obviously)
Biostatistician (analyzes data for health studies; they are everywhere: hospitals, federal agencies, universities, private industry)
Bioinformaticists
Epidemiologists
Pharmaceutical research
Financial engineers
Operations research analyst
Economists
Quality assurance/improvement/business analytics
Computational biologist/mathematical biologists
Certain types of physicists
Actuaries/insurance/risk analysis
Metereologists and atmospheric scientists, astronomers
Ecology/environmental sciences
Computer scientists (especially data miners)</p>
<p>Statistics is my passion because it is so useful and multidimensional. Article if you are interested: [For</a> Today’s Graduate, Just One Word: Statistics.](<a href=“http://www.nytimes.com/2009/08/06/technology/06stats.html]For”>http://www.nytimes.com/2009/08/06/technology/06stats.html)</p>
<p>If I could go back in time, I’d double-major in psychology and mathematics and then get my PhD in biostatistics or quantitative psychology. My actual BA is in psychology, I’m currently getting my PhD in public health psychology, but I do plan to add an MS in statistics afterwards (hopefully while I work, and maybe my job will pay for it!). I know enough to be a social science statistician, but I want more - I like statistical modeling and statistical research, and I really like stats consulting and teaching stats.</p>
<p>To answer the question, though, I wouldn’t push a kid into a STEM field (I don’t have any children, and probably won’t have a college-aged kid for at least another 23 years). I do like math and love statistics, and I also love health psychology, but it’s the passion for the field that keeps me going - kept me going in college, and keeps me going now that I am grinding through my PhD. Passion - or at least a healthy liking - of a field is really important, and intrepid and ambitious philosophy and history majors can find jobs too. Even though their unemployment rates are higher, the fact of the matter is that MOST of them are employed somewhere. My emphasis would be on the development of transferable skills and a well-rounded, yet focused, college pursuit.</p>