# S3 AQA Sign Test AS

- Created by: Brandon
- Created on: 29-05-13 12:54

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- Distribution-free methods for single samples and paired comparisons
- The Sign Test
- Tests which do not require the knowledge or assumption that the data involved is normally distributed are known as distribution-free or non-parametric tests
- The Sign Test involves a + or - sign to each reading and using binomial P=0.5 to determine Critical Region
- i.e. sample of 10 = B(10,0.5)
- --->

- i.e. sample of 10 = B(10,0.5)
- Ho: Pop Mean/median = x
- H1: Pop Mean/median is small/greater/not equal too x
- So --->
- Use largest value of T (+or-)
- i.e. 7+ and 3- use *7* and P(X>/7)= 1-P((X0.05 so Accept HO

- Use largest value of T (+or-)
- Accept if Ho is greater than Critical Value

- So --->

- H1: Pop Mean/median is small/greater/not equal too x

- Wilcoxon Signed-Rank Test
- Only Numerical Data
- Assume symmetrically distributed
- Preferred to the Sign Test
- If T>Crit Value Ho= accept
- Use Smallest T value (T+ and T-)

- Ho = Median/Mean same as H1
- Rank + and - too the Ho and show the absolute difference
- + column and - column then rank everything and total your T- and T+
- Then -->

- + column and - column then rank everything and total your T- and T+

- Rank + and - too the Ho and show the absolute difference
- The Wilcoxon takes the relative magnitudes of the differences into account and is therefore preferred to the sign test provided numerical differences can be obtained
- If you get same value then add it up and divide by n value

- Experimental Design
- Such variability of results is called Experimental Error - this means there are always other factors affecting the results.
- Experimental Error should be minimised by keeping factors which are not being investigated as constant as possible and by careful experiment design.
- Untitled
- One of the simplest experimental designs is to plan paired comparisons to reduce experimental error.
- Experimental Design is used to eliminate BIAS and reduce experimental error in data collection

- The Sign Test

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