Descriptive and Inferential Statistics

[Example 1]Descriptive and Inferential Statistics

Statistics can be broken into two basic types.

The first is known as descriptive statistics. This is a set of methods to describe data that we have collected.

Ex. Of 350 randomly selected people in the town of Luserna, Italy, 280 people had the last name Nicolussi. An example of descriptive statistics is the following statement :

"80% of these people have the last name Nicolussi."

Ex. On the last 3 Sundays, Henry D. Carsalesman sold 2, 1, and 0 new cars respectively. An example of descriptive statistics is the following statement :

"Henry averaged 1 new car sold for the last 3 Sundays."

These are both descriptive statements because they can actually be verified from the information provided.

The second type of statistics in inferential statistics. This is a set of methods used to make a generalization, estimate, prediction or decision.

Ex. Of 350 randomly selected people in the town of Luserna, Italy, 280 people had the last name Nicolussi. An example of inferential statistics is the following statement :

"80% of all people living in Italy have the last name Nicolussi."

We have no information about all people living in Italy, just about the 350 living in Luserna. We have taken that information and generalized it to talk about all people living in Italy. The easiest way to tell that this statement is not descriptive is by trying to verify it based upon the information provided.

Ex. On the last 3 Sundays, Henry D. Carsalesman sold 2, 1, and 0 new cars respectively. An example of inferential statistics are the following statements :

"Henry never sells more than 2 cars on a Sunday."

Although this statement is true for the last 3 Sundays, we do not know that this is true for all Sundays.

"Henry is selling fewer cars lately because people have caught on to his dirty tricks."

There is nothing in the information given that tells us that this statement is true.

"Henry sold 0 cars last Sunday because he fell asleep in one of the cars on the lot."

Again, this statement is not verifiable based upon the information provided.

The major use of inferential statistics is to use information from a sample to infer something about a population.

[example2]Definition of Descriptive and Inferential Statistics

For the following material, I relied on Statistics, Fifth Edition, by Joseph F. Healey, Wadsworth Publishing Co., 1999. ISBN: 0-534-55260-9. This is not to be construed as an endorsement of the text. It was sent to me for consideration as a statistics text. I like it. It covers rather more than I think we can presently include in our course. But it is clearly written, and includes examples on SPSS. We will further consider it for adoption. You can review it in my office. jeanne

* Descriptive Statistics

Descriptive statistics comprises the kind of analyses we use when we want to describe the population we are studying, and when we have a population that is small enough to permit our including every case.

For example, we might want to describe a physics class and compare it to a class of English literature. We might want to compare the gender composition of the classes, the math attitudes of the two classes, the familial demands and supports of the two classes. Descriptive statistics would allow us to do this.

o The classes are small enough that we can include the whole class in our studies.
o We would have to agree on how to measure gender, math attitude, and familial demands.
o We could then interview the students in the classes, or survey them, or ask them to tell their stories about these issues and code them by content analysis.
o Then we COULD DESCRIBE how these issues affect the members of the classes we studied, and how these variables are related in those classes.
o We COULD NOT CONCLUDE that our results could be generalized to all physics and english literature classes because we have no idea whether the classes in our study were REPRESENTATIVE OF all physics and English literature classes.

* Inferential Statistics

The important keys to the difference between descriptive and inferential statistics are the capitalized words in the description: COULD DESCRIBE, COULD NOT CONCLUDE, AND REPRESENTATIVE OF.

Descriptive statistics can describe the actual sample you study. But to extend your conclusions to a broader population, like all such classes, all workers, all women, you must be use inferential statistics, which means you have to be sure the sample you study is representative of the group you want to generalize to.

This means you can't do a study at the local mall and claim that what you find is valid for all shoppers and malls.

You can't do a study on college sophomores and claim that what you find is valid for the general population.

You can't give a women's movement that includes a majority of a single ethnic group and claim that what you find is valid for women of all ethnic groups.

As you can see, descriptive statistics are useful and serviceable if you don't need to extend your results to whole segments of the population. But the social sciences tend to esteem studies that give us more or less "universal" truths, or at least truths that apply to large segments of the population, like all teenagers, all parents, all women, all perpetrators, all victims, or a fairly large segment of such groups.

Leaving aside the philosophical and methodological soundness of such a search for some kind of general conclusion, different statistical approaches must be used if you aspire to generalize. And the primary difference is that of SAMPLING. You must choose a sample that is REPRESENTATIVE OF THE GROUP TO WHICH YOU PLAN TO GENERALIZE.

Tests of significance are about this problem of generalization. A Chi-Sqaure or a T-Test tells you the probablility that the results you found in the group you studied are representative of the population that group was chosen to represent. Put in other terms that you will hear frequently, Chi-Sqaure or a t-test gives you the probability that the results you found could have occurred by chance when there is really no relationship at all between the variables you studied in the population.

* Summary:

o Descriptive statistics are for describing data on the group you study. Example: Babbie and Halley's survey for describing your own class.
o Inferential statistics are for generalizing your findings to a broader population group. Example: Babbie and Halley's analysis of SPSS data that can be generalized to the population at large.

http://infinity.cos.edu/faculty/woodbury/stats/tutorial/Data_Descr_Infer.htm
http://www.csudh.edu/dearhabermas/stat2f98.htm