Stats 8

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Author:
camturnbull
ID:
287109
Filename:
Stats 8
Updated:
2014-10-26 12:52:16
Tags:
Psychology Stats
Folders:
Psychology,Statistics
Description:
BSc Stats
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  1. What is strict replicability?
    The same conditions will yield exactly the same measurement value
  2. What is the formula for strict replicability?
    • Y(cap)=constant 
    • The cap indicates 'the predicted value of'
    • Conventionally, the constant is denoted by the symbol µ (mu)
  3. How might one describe the signal component of data?
    • Y(cap)=µ
    • U is a parameter of the model
    • This does not account for variability in the data, however
  4. What is a parameter?
    A numerical characteristic of a population that is only constant for specified conditions
  5. What does e denote?
    The residual data
  6. How might one find the signal in a noisy data set?
    • Add the residuals 
    • (observation= model prediction+residuals)
  7. What is the double challenge facing statistical data analysis?
    • Each measurement yields a different value so even if we know the value of µ, predictions will always be imperfect
    • The value of µ is not known
  8. What are the four steps to fitting a model to data?
    • 1: That data are used to estimate any unknown parameters 
    • 2: The estimates are used to obtain a fit between model and data 
    • 3: Using this fitted model, the residuals are calculated 
    • 4: The residuals are used to calculate the 'goodness of fit' of the model
  9. What is the best way to estimate the parameter (µ)?
    Use the mean of observations (Y-bar)
  10. How might one go about finding a fit for the model?
    • Substitute the estimated value of the unknown parameter into the model 
    • Y=Y(bar)+e
    • (observation=model fit+residuals)
  11. How might one find the residuals for a data set?
    Find the difference between each result and the mean
  12. How do we test goodness of fit?
    • Use the sum of squares (SS)
    • SS are the same for observations and residuals as the residuals are simply the original scores minus a constraint (the mean). This linear transformation does not affect the SS
    • When referring to residuals, the SS=SSe
  13. What is the least squares estimate?
    • The estimate of the parameter which minimises the SS of the residuals 
    • The sample mean (Y-bar) is the least squares estimate of the population mean (µ)
  14. What is the population?
    The set of all possible observations that might be taken under a specified set of conditions
  15. What is the equation for the null hypothesis?
    µ1=µ2=µ
  16. What is the symbol that denotes the null hypothesis?
    • HO
  17. What is the symbol that denotes the experimental hypothesis?
    HA
  18. What is the symbol equation for the experimental hypothesis?
    HA: µ1≠µ2
  19. How might one find an estimate of µ
    By finding the mean of observed data from all conditions
  20. What is the total sum of squares?
    • The sum of squares for all residuals of all conditions
    • Referred to as the SStotal
  21. How might one quantify the variability accounted for by the full model?
    • Find the difference between the SStotal and the SSe 
    • This can be written as:
    • SSmodel=SStotal-SSe
  22. What is the size of the SSmodel determined by?
    The difference between the means of the different conditions
  23. What does a large SSmodel mean?
    • There is a large difference between total SS and the SS for residuals.
    • There is a large difference between the means 
    • The null models are inadequate and the full model is required
  24. How are the SS values usually expressed?
    R2= SSModel/SSTotal

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