# Accuracy

### Perfect Accuracy

Two plus two is four and this is perfectly accurate but in the majority of situations where statistics are used it is impossible to have perfect accuracy.
For this reason most data is an approximation.
There is very rarely an exact result to be derived from a statistical investigation.
The degree of accuracy required will depend on the type of data.
When you create a summary table of some data, rounding is almost certain to take place and in most cases this is indicated by specifying the degree of approximation.

### Spurious Accuracy

When a number implies a greater accuracy than it really has, this accuracy is referered to spurious accuracy.

### Error

The error is the difference between what is acceptable and what value is taken for the approximation
The error is a way of qualifying the degree of accuracy of the result.
The majority of the data derived from statistical investigation uses approximations and therefore the values are subject to error.

### Rounding

Rounding up or rounding down is not recommended in statistics because this will lead to a biased error.
You should always try and round to the neasrest unit. This way the extra amounts will hopefully balance out the deducted amounts and will lead to a more accurate result.

### Truncation

This is similar to rounding but just removes the extra digits.
Truncating your numbers will produce a downward bias in the final result.

### Significant Figures

Always using a certain number of significant figures will help you to reduce the error.
It will also remove any spurious error.

### Absolute Error

This is the difference between an approximatation (or estimate) and the rue figure.
These are often not very comparable and for this reason we also have the relative error.

### Relative Error

The relative error is the absolute error divided by the estimated value times 100.

### Biased Errors

These are also known as cumulative or systematic errors
If you have a list of values and the errors are all in one direction (ie all positive or negative) then the result will be biased.

### Unbiased Error

Also known as compensating error.
This occurs when an approximation is to the nearest whole number or complete unit.
example peoples ages and the plus and minus cancel each other out.

The majority of the calculations performed in statistics contains approximations and errors are present.
The data has probably been rounded or is only accurate to a certain number of significant figures or contains an element of biased or unbiased error.
Normally the degress of accuracy falld well within the limits of tolerance being used.
It can be useful to know what the limits of error are when you are using statistics.
pg 28-31

### Getting the right Result

For sample results are to be used for decistion making it is very important to access the reliability of these results.
Reaching valid conclusions about a population based on a sample relies on two general laws:
Law of statistical regularity
This states that a large sample selected at random from a large population will be ob average representative of the characteristics of the population.
For this law to work the sample selection must be made at random.
Law of inertia of large numbers
Larger groups of data show a higher degree of stability than smaller ones.

These laws are part of the central limit theorem and are ways of describing the theory of probability.