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ANOVA design
 IV manipulated
 DV measured



ANCOVA design
IV and DV are a mix of manipulated, selected, and measured

ANOVA analysis
 "analysis of variance"
 categorical IV
 continuous DV

Regression analysis
 "regression analysis"
 continuous IV
 continuous DV

ANCOVA analysis
 "analysis of covariance"
 combination of continuous and categorical DV and IV

simple model
 predicts the same value for everyone
 unconditionally

complex model
 includes more than the constant in the model
 predicts a different value for everyone
 conditional

bivariate regression analysis
 DV and IV are continuous
 only a single predictor

multiple regression analysis
 DV and IV are are continuous
 more than one predictor

factorial ANOVA analysis
 IV is categorical, DV is continuous
 a categorical variable is linked to another categorical variable

multivariate ANOVA analysis
 IV is categorical, DV is continuous
 there is more than one DV

measurement error
error associated with unreliable and invalid measures

design error
error associated with a poor design and therefore the data is inaccurate and nonrepresentative

sampling error:
 error associated with nonrepresentative sampling
 always expected to exist because a sample will never truly represent a population
 problematic for analysis if it results from design error

commission
inclusion of variables to a model that should not be there

omission
 exclusion of variables to a model that should be there
 usually realized post hoc

PRE  proportional reduction of error
 [ERROR(C)  ERROR(A)]/ERROR(C)
 estimate of ada squared
 effect size

SAE  sum of absolute errors
 ∑YˆY
 use the median to minimize

SSE  sum of squared errors
 ∑(YˆY)²
 use the mean to minimize

MAE  mean of absolute errors
mdnymdn

MSE  mean of squared errors
 ∑(yˆy)²/[N(p+1)]
 dividing by the number of parameters that can still be reduced
 b₀ cannot be reduced more

standard error of estimate
square root of the MSE

SD  standard deviation
square root of the variance (MSE in simple models)

variables
get scores from a sample in a certain area (X)

parameters
how much of the variable predicts y

unbiased frequency sampling distribution
the mean value of the sampling distribution is close to β₀

efficient frequency sampling distribution
 the sampling distribution is skinny
 more likely to be close to β₀

consistent frequency sampling distribution
efficiency of sampling distribution increases as sample size increases

assumptions regarding error
 normal distribution
 unbiased
 independent
 homeoscedasticity

homeoscedasticity
error distributions of y are the same across different values of x

standard error of the mean
the size of the difference between the population mean and expected mean

central limit theorem
the distribution of errors is normal

sampling distribution
distribution taken from a population where the null hypothesis, MODEL©, is true

sample distribution
distribution based on the data

SSR  sum of squares reduced
SSE(C)  SSE(A)

SSR (remaining)
 regression analysis: SS(regression)
 ANOVA analysis: SS(between)

SSE(A)
 regression analysis: SS(residual)
 ANOVA analysis: SS(within)

SSE(C)
 regression analysis: SS(total)
 ANOVA analysis: SS(total)

PA
number of parameters in model A

PC number of parameters in model C

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

η²
 ada squared
 estimate of PRE
 expected to be 0 when null hypothesis is true

ἣ²
 unbiased ada squared
 accounts for ada squared always being positive
 critical value which cuts off the most extreme 5%

Type 1 Error
 wrong conclusion that the null hypothesis is true
 equal to alpha (usually 5%)

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

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)

β₁
 how much changer there is on the yaxis for every one unit of change on the xaxis
 slope

r(xy)
relationship of x and y


standard error of estimate
 square root of the MSE(A)
 also known as the standard error of prediction


