Descriptive vs. Inferential Statistics: What’s the Difference?

When it comes to statistic analysis, there are two classifications: descriptive statistics and inferential statistics.  In a nutshell, descriptive statistics intend to describe a big hunk of data with summary charts and tables, but do not attempt to draw conclusions about the population from which the sample was taken.  You are simply summarizing the data you have with pretty charts and graphs–kind of like telling someone the key points of a book (executive summary) as opposed to just handing them a thick book (raw data).

Conversely, with inferential statistics, you are testing a hypothesis and drawing conclusions about a population, based on your sample.  In this case, you are going to run into fancy sounding concepts like ANOVA, T-Test, Chi-Squared, confidence interval, regression, etc., but we’ll save those for another day.

To understand the simple difference between descriptive and inferential statistics, all you need to remember is that descriptive statistics summarize your current dataset and inferential statistics aim to draw conclusions about an additional population outside of your dataset.

Perhaps these concepts are most easily explained with some examples…

Descriptive Statistics

Let’s say you’ve administered a survey to 35 people about their favorite ice cream flavors.  You’ve got a bunch of data plugged into your spreadsheet and now it is time to share the results with someone.  You could hand over the spreadsheet and say “here’s what I learned” (not very informative), or you could summarize the data with some charts and graphs that describe the data and communicate some conclusions (e.g. 37% of people said that vanilla is their favorite flavor*).  This would sure be easier for someone to interpret than a big spreadsheet.  There are hundreds of ways to visualize data, including data tables, pie charts, line charts, etc.  That’s the gist of descriptive statistics.  Note that the analysis is limited to your data and that you are not extrapolating any conclusions about a full population.

*All data above is completely fictional.  I’m not sure how many people actually prefer vanilla.  Everyone knows cookies and cream is the best anyway. 

Descriptive statistic reports generally include summary data tables (kind of like the age table above), graphics (like the charts above), and text to explain what the charts and tables are showing.  For example, I might supplement the data above with the conclusion “vanilla is the most common favorite ice cream among those surveyed.”  Just because descriptive statistics don’t draw conclusions about a population doesn’t mean they are not valuable.  There are thousands of expensive research reports that do nothing more than descriptive statistics.

Descriptive statistics usually involve measures of central tendency (mean, median, mode) and measures of dispersion (variance, standard deviation, etc.).  Here’s a great video that explains the concept of “average” very well.

Inferential Statistics

OK, let’s continue with the the ice cream flavor example.  Let’s say you wanted to know the favorite ice cream flavors of everyone in the world.  Well, there are about 7 billion people in the world, and it would be impossible to ask every single person about their ice cream preferences.  Instead, you would try to sample a representative population of people and then extrapolate your sample results to the entire population.  While this process isn’t perfect and it is very difficult to avoid errors, it allows researchers to make well reasoned inferences about the population in question.  This is the idea behind inferential statistics.

As you can imagine, getting a representative sample is really important.  There are all sorts of sampling strategies, including random sampling.  A true random sample means that everyone in the target population has an equal chance of being selected for the sample.  Imagine how difficult that would be in the case of the entire world population since not everyone in the world is easily accessible by phone, email, etc.  Another key component of proper sampling is the size of the sample.  Obviously, the larger the sample size, the better, but there are trade-offs in time and money when it comes to obtaining a large sample.  There are some nice calculators online that help determine appropriate sample sizes.  That’s enough on market research sampling techniques for now.  Let’s get back on track here…

When it comes to inferential statistics, there are generally two forms: estimation statistics and hypothesis testing.

1. Estimation Statistics

“Estimation statistics” is a fancy way of saying that you are estimating population values based on your sample data.  Let’s think back to our sample ice cream data.  First, let’s assume that we had a true random sample of 35 people on this globe and that our full target population is every human alive (7 billion people).  Let’s say that 37% of people in our sample said that vanilla is their favorite flavor.  Can we safely extrapolate that 37% of all people in the world also think that vanilla is the best?  Is that the true value of the world?  Well, we can’t say with 100% confidence, but–using inferential statistical techniques such as the “confidence interval”–I can provide a range of people that prefer vanilla with some level of confidence.

2. Hypothesis Testing

Hypothesis testing is simply another way of drawing conclusions about a population parameter (“parameter” is simply a number, such as a mean, that includes the full population and not just a sample).

With hypothesis testing, one uses a test such as T-Test, Chi-Square, or ANOVA to test whether a hypothesis about the mean is true or not.  I’ll leave it at that.  Again, the point is that this is an inferential statistic method to reach conclusions about a population, based on a sample set of data.

I hope you now have a solid understand of the differences between descriptive and inferential statistics.  If you have any comments or contributions, please leave them in the comments below.

Sources & Additional Resources

DeCaro, S. A. (2003). A student’s guide to the conceptual side of inferential statistics. Retrieved [December 01, 2011], from http://psychology.sdecnet.com/stathelp.htm

The Math Forum: http://mathforum.org/library/drmath/view/69143.html