Defining and Conceptualizing Descriptive and Inferential Statistics

** Descriptive
Statistics**: A statistical
technique that produces a number or figure that summarizes or

** Inferential
Statistics**: A method that takes
chance factors into account when samples are used to reach conclusions (or make

__Given:__
It is generally impractical to obtain measures (scores) from an entire
population. Thus, true population parameters are almost never known.

__Given__:
Samples are usually used instead of an entire population. Sampling statistics
vary from sample to sample. This variability from sample to sample is
attributable to __chance fluctuations__.

__Given:__
Investigators are almost always (if not always) interested in generalizing from
a smaller sample to a larger population of interest.

__Example:__

1) Say we want to assess
the effects of vitamin C on cognitive ability in adults. Rather than using the
entire __population__ of all adults in the US, we select a random __sample__
of 1000 adults, one-half consume 500mg of vitamin C daily for 4 weeks and the
other one-half do not.

2) Say that the average cognitive ability for adults who do not consume vitamin C is M = 50 (higher numbers indicate better cognitive ability).

3) The average cognitive ability for those adults who consumed vitamin C during the past month is M = 65.

The data indicate a 15-point difference between the two samples. There are two possible interpretations:

1) There is no "real" difference between the two groups (suggesting the mean differences are simply due to chance factors -- i.e., sampling error).

OR

2) The sampling data reflect a "true" difference between the two groups.

__ __

The goal of inferential statistics is to help researchers decide between the two interpretations.

Inferential statistics
begins with actual data (sample data) from the experiment above and ends with a
probability statement (i.e., the probability of obtaining data like those above
if there is __no__ effect of vitamin C on cognitive ability in the
population)

If the probability is very
small (p<.05) that the mean differences were due to chance factors, we can
conclude that vitamin C __does__ affect cognitive ability. That is, the
observed data are __not__ what would be expected by chance alone.

Don't worry. Just try to get the gist of this. For now, just know what is meant by the term inferential statistics and how it differs from descriptive statistics.