S3 AQA Sign Test AS

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  • 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)
          • --->
      • 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
          • Accept if Ho is greater than Critical Value
    • 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 -->
      • 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


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