Statistics

Statistics is concerned with scientific methods for collecting, organising, summarising, presenting and analysing data.
Stats is the systematic collection, analysis and display of numerical data
The most important aspect is to choose the statistical test that is most appropriate for your date
It is not sufficient just to know the formulas for the various tests, you should also know when (and when not) to apply them.


There are Two Types

  • Descriptive Statistics - Summarising the information as briefly and as accurately as possible.

  • Inferential Statistics - Used to draw informed guesses (inferences) about situations where we only have part of the total information (ie a sample from a population). These are commonly used to analyse the results of an experiment.


We can use statistics to tell us whether samples of numbers appear to have been drawn from one or two populations.



What are Variables ?

The term variable is used to mean anything which is free to change
Sometimes the units are obvious but other times you will have to devise a rating scale specifically for expressing a particular variable in an appropriate kind of unit.
Variables can be divided into 2 different types:
The kind of units you use to quantify the variables will have an important bearing on the statistical tests you can use.


Independent Variables (IV)
These are variables that we manipulate in the experiment.


Dependent Variables (DV)
These are variables that change as a consequence of the changing independent variables.
Most variables can be either dependent or independent within the context of a particular experiment.


All other factors are called Secondary Variables.



Variables - Different Classifications

Variables can be classified into 2 types:

  • Quantitive - Data measuring how much or how many (i.e. an amount or a count)

Discrete Variables - The set of all possible values which consists only on isolated points (eg counting variables)
Continuous Variables - The set of all values consists of intervals (0-9,10-19,20-29 etc). This is data that it does not represent exact values. They have only been measured to a certain degree of accuracy.


  • Qualitative - Data that provides labels or names (eg categories or classes)

Nominal Variables - Variables with no inherent order or ranking sequence
Ordinal Variables - Variables assigned to these variables indicate rank order only - the "distance" between the numbers has no meaning
Interval Variables - Equally spaced variables (eg temperature) these do not have a zero
Ratio Variables - Variables spaced at equal intervals (eg age) these have a zero



Parametric Tests


Non Parametric Tests




Important

Once you have calculated the correlation coefficient and the covariance you can prove whether there is in fact a relationship or not between two variables.


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