The ABC Study Guide, University education in plain English alphabetically indexed. Click here to go to the main index
ABC Statistics

Statistics: Origin and Meaning

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One of the origins of statistics origins is state arithmetic

• "The word Statistics appears to have been first used about the middle of the last [18th] century by Achenwall, a professor at Gottingen, to express a summary view of the physical, moral, and political condition of states". (Hawkins, F. B. 1829 p.1)
  
  
• "The word Statistics is of German origin, and is derived from the word staat, signifying the same as our English word state, or a body of men existing in social union. Statistics, therefore, may be said, in the words of the Prospectus of this society, to be the ascertaining and bringing together of those "facts which are calculated to illustrate the condition and prospects of society;" and the objects of Statistical Science is to consider the results which they produce, with a view to determine those principles upon which the well being of society depends. Journal of the Statistical Society of London May 1838. Vol.1, No.1, Introduction.
  
  "The Science of Statistics differs from Political Economy, because, although it has the same end in view, it does not discuss causes, nor reason upon probable effects; it seeks only to collect, arrange, and compare, that class of facts which alone can form the basis of correct conclusions with respect to social and political government". Journal of the Statistical Society of London May 1838. Vol.1, No.1, Introduction.

Descriptive Statistics

Descriptive statistics allow us to describe groups of many numbers. One way to do this is by reducing them to a few numbers that are typical of the groups, or describe their characteristics. The average is one kind of descriptive statistic. Measures of spread are another kind.

Grouping numbers into frequency distributions and drawing charts to illustrate frequency distributions, are other examples of descriptive statistics.

Inferential Statistics , Statistical Tests or Inductive Statistics

Inferential statistics do not just describe numbers, they infer causes. We use them to draw inferences (informed guesses) about situations where we have only gathered part of the information that exists. The part of the information is called a sample. The whole body of information from which it is taken is called the population. In a basic statistical test we would have two samples and would try to establish if they are significantly different.

Statistical inference is the use of samples to reach conclusions about the population from which those samples have been drawn.

For example, twenty people who have not read this passage would be one sample. The same twenty people after they have read the passage is another sample. The population from which both samples are drawn is all the people who could (in theory) read this passage. If we found that,

1. before reading this passage, many of the twenty people could explain what inferential statistics is.

2. after reading this passage, none of the twenty people could explain what inferential statistics is.

Statistical analysis refers to doing something useful with data (letting its meaning free). The two main ways that data is analysed are:

1. by bringing out the information it contains. This is part of descriptive statistics

2. testing or retesting a hypothesis. Hypothesis testing is part of inferential statistics.

Primary analysis is the original analysis of data in a research study.

Secondary analysis is the re-analyis of data. This could be to answer new questions or to use improved statistical techniques,

meta-analyis is the statistical analysis of a large collection of analysis results to integrate the findings.

Frequency Distribution
A frequency distribution is an arrangement of a group of numbers in a pattern that shows how frequently each occurs. This is done by grouping (classifying) the numbers and arranging them in a table according to size:

For example:

1, 1
2, 2, 2
3, 3, 3, 3
4, 4, 4, 4, 4
5, 5, 5, 5, 5, 5
6, 6, 6, 6, 6
7, 7, 7, 7
8, 8, 8
9, 9

• "This result would arise by chance one in twenty times" ( p=0.05)