**Descriptive statistics**are functions of the data that are intrinsically interesting in describing some feature of the data. Classic descriptive statistics include mean, min, max, standard deviation, median, skew, kurtosis.

**Inferential statistics**are a function of the*sample*data that assists you to draw an inference regarding an hypothesis about a population parameter. Classic inferential statistics include z, t, χ2, F-ratio, etc.There are two major divisions of inferential statistics:

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**confidence interval**gives a range of values for an unknown parameter of the population by measuring a statistical sample. This is expressed in terms of an interval and the degree of confidence that the parameter is within the interval. **Tests of significance**or**hypothesis testing**tests a claim about the population by analyzing a statistical sample. By design there is some uncertainty in this process. This can be expressed in terms of a level of significance.

- A

Example-

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 India, 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.

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