Defining and Conceptualizing Descriptive and Inferential Statistics

Descriptive Statistics A statistical technique that produces a number or figure that summarizes or describes a set of data. The basic idea is that a descriptive statistic summarizes a set of data with one number or graph.

Inferential Statistics A method that takes chance factors into account when samples are used to reach conclusions (or make inferences about) populations.

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

GivenSamples 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.