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ANOVA design
- IV manipulated
- DV measured
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ANCOVA design
IV and DV are a mix of manipulated, selected, and measured
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ANOVA analysis
- "analysis of variance"
- categorical IV
- continuous DV
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Regression analysis
- "regression analysis"
- continuous IV
- continuous DV
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ANCOVA analysis
- "analysis of covariance"
- combination of continuous and categorical DV and IV
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simple model
- predicts the same value for everyone
- unconditionally
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complex model
- includes more than the constant in the model
- predicts a different value for everyone
- conditional
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bivariate regression analysis
- DV and IV are continuous
- only a single predictor
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multiple regression analysis
- DV and IV are are continuous
- more than one predictor
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factorial ANOVA analysis
- IV is categorical, DV is continuous
- a categorical variable is linked to another categorical variable
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multivariate ANOVA analysis
- IV is categorical, DV is continuous
- there is more than one DV
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measurement error
error associated with unreliable and invalid measures
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design error
error associated with a poor design and therefore the data is inaccurate and non-representative
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sampling error:
- error associated with non-representative sampling
- always expected to exist because a sample will never truly represent a population
- problematic for analysis if it results from design error
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commission
inclusion of variables to a model that should not be there
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omission
- exclusion of variables to a model that should be there
- usually realized post hoc
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PRE - proportional reduction of error
- [ERROR(C) - ERROR(A)]/ERROR(C)
- estimate of ada squared
- effect size
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SAE - sum of absolute errors
- ∑|Y-ˆY|
- use the median to minimize
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SSE - sum of squared errors
- ∑(Y-ˆY)²
- use the mean to minimize
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MAE - mean of absolute errors
mdn|y-mdn|
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MSE - mean of squared errors
- ∑(y-ˆy)²/[N-(p+1)]
- dividing by the number of parameters that can still be reduced
- b₀ cannot be reduced more
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standard error of estimate
square root of the MSE
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SD - standard deviation
square root of the variance (MSE in simple models)
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variables
get scores from a sample in a certain area (X)
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parameters
how much of the variable predicts y
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unbiased frequency sampling distribution
the mean value of the sampling distribution is close to β₀
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efficient frequency sampling distribution
- the sampling distribution is skinny
- more likely to be close to β₀
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consistent frequency sampling distribution
efficiency of sampling distribution increases as sample size increases
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assumptions regarding error
- normal distribution
- unbiased
- independent
- homeoscedasticity
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homeoscedasticity
error distributions of y are the same across different values of x
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standard error of the mean
the size of the difference between the population mean and expected mean
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central limit theorem
the distribution of errors is normal
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sampling distribution
distribution taken from a population where the null hypothesis, MODEL©, is true
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sample distribution
distribution based on the data
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SSR - sum of squares reduced
SSE(C) - SSE(A)
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SSR (remaining)
- regression analysis: SS(regression)
- ANOVA analysis: SS(between)
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SSE(A)
- regression analysis: SS(residual)
- ANOVA analysis: SS(within)
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SSE(C)
- regression analysis: SS(total)
- ANOVA analysis: SS(total)
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PA
number of parameters in model A
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PC number of parameters in model C
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F
- transformation of PRE to standardized form
- obtained proportion of reduction divided by the amount of known parameter changes, all divided by the remaining unexplained error divided by the number of unknown parameters
- ratio of the amount of explained error to unexplained error
- typically sig if greater than 4 or 5
- equal to t²
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η²
- ada squared
- estimate of PRE
- expected to be 0 when null hypothesis is true
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ἣ²
- unbiased ada squared
- accounts for ada squared always being positive
- critical value which cuts off the most extreme 5%
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Type 1 Error
- wrong conclusion that the null hypothesis is true
- equal to alpha (usually 5%)
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Type 2 Error
- wrong conclusion the null hypothesis is correct, but is actually false in reality
- β is the probability of this type of error
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Power
- the probability of actually detecting an effect that is there
- depends of the effect size (PRE - smaller means harder to detect), the level of alpha (but only ever made more stringent and decrease power), and sample size (N)
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β₁
- how much changer there is on the y-axis for every one unit of change on the x-axis
- slope
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r(xy)
relationship of x and y
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standard error of estimate
- square root of the MSE(A)
- also known as the standard error of prediction
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