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What is strict replicability?
The same conditions will yield exactly the same measurement value

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)

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

What is a parameter?
A numerical characteristic of a population that is only constant for specified conditions

What does e denote?
The residual data

How might one find the signal in a noisy data set?
 Add the residuals
 (observation= model prediction+residuals)

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

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

What is the best way to estimate the parameter (µ)?
Use the mean of observations (Ybar)

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)

How might one find the residuals for a data set?
Find the difference between each result and the mean

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=SS_{e}

What is the least squares estimate?
 The estimate of the parameter which minimises the SS of the residuals
 The sample mean (Ybar) is the least squares estimate of the population mean (µ)

What is the population?
The set of all possible observations that might be taken under a specified set of conditions

What is the equation for the null hypothesis?
µ1=µ2=µ

What is the symbol that denotes the null hypothesis?

What is the symbol that denotes the experimental hypothesis?
H_{A}

What is the symbol equation for the experimental hypothesis?
H_{A}: µ_{1}≠µ_{2}

How might one find an estimate of µ
By finding the mean of observed data from all conditions

What is the total sum of squares?
 The sum of squares for all residuals of all conditions
 Referred to as the SS_{total}

How might one quantify the variability accounted for by the full model?
 Find the difference between the SS_{total} and the SS_{e}
 This can be written as:
 SS_{model}=SS_{total}SS_{e}

What is the size of the SS_{model} determined by?
The difference between the means of the different conditions

What does a large SS_{model} 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

How are the SS values usually expressed?
R^{2= }SS_{M}^{}_{odel}/SS_{Total}

