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Statistics
ANOVA
65
Psychology
Undergraduate 2
10/31/2011

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Term

Measure variable

Definition

-Commonly known as dependent variable

 

-Response measure, that value of which is depndent on the independent variables

 

-measure that captures the hypothesized differences

Term

Treatment variable

Definition

-Commonly known as independent variable.

 

-Variable that is manipulated

 

-Quantative, Qualitative, Classification

 

Term
Classification Variables
Definition
- Created by selecting subjects ona dimension to be included in the study

- E.g sex of the subject
Term
Nuisance variables
Definition
-if left uncontrolled could exert a systematic influence on the different treatment groups
Term
Completely Randomized design
Definition
-subjects are randomly assigned to serve in one of the treatment groups
Term
Randomised block design
Definition
-Blocks of subjects who are matched on some relevant charcteristic

-Once Blocked, subjects within the blocks are assigned randomly to treatment consditions
Term
Mixed factorial design
Definition
- Randomized factorial design
and
-Block factorial design
Term
Population
Definition
-Defined by a set of membership rules

-Samples are a set from the population
Term
Alternative Hypothesis
Definition
- If parameters observed are too deviant from those specified by null hypothesis

-Usually states that the treatmnent populations are not all equal
Term
μ- Greek letter mu
Definition
- This represnts the popluation mean

-1st defining parameter of distrubution
Term
σ,Greek letter sigma
Definition
-Represents the population standard deviation

-2nd parameter of distrubution
Term
Shared area of two distrubutions is small..
Definition
Then there is a large probability that the populations are different

-If the shared area is large then there is only a very small probability of the populations being different.

-Impossible for the shared area to be zero
Term
Assumptions of parametric statistical tests
Definition
-ALl populations have normal distrubution

-Normal distrubutions have the same standard deviation (variance)

-Data from ratio or interval scale
Term
Individual differences error
Definition
-Come about because the nature of the individual subjects
Term
Measurement error
Definition
-Arises because of problmes with accurately collecting data
Term
Within Group variability
Definition
-Estimate of variability due to particular treatmment condition
Term
Between group variability
Definition
-Estimate of variance due to differences between groups
Term
Treatment effect
Definition
-Systematic source of variability
Term
Null Hypothesis false
Definition
Treatment effects+ Experimental error
-------------------------------------
Experimental error
Term
Null hypothesis true
Definition
Experimental error
-----------------
Experimental error
Term
Total deviation
Definition
_
(AS25- T)
Term
Between groups deviation
Definition
_ _
(A2- T)
Term
WIthin groups deviation
Definition
_ _
(AS25- A)
Term
WIthin groups deviation
Definition
_ _
(AS25- A)
Term
Partitioning
Definition
-Subdividing of the total deviation, in to between groups and within groups
Term
Variance, Defined by
Definition
Sum of squared deviations from the mean
-------------------------------------
Degrees of freedom
Term
Degrees of freedom
Definition
-approximately equal to the number of numbers in a set

-number of scores with independent info which enter in to the calculation of SS, number that are free to vary with some knowledge
Term
F-ratio
Definition
Differences among treatment means
---------------------------------
differences among subjects treated a like
Term
Omnibus F-ratio
Definition
For an overal difference between means

If significant requires further analysis
Term
Pair wise comparrisons
Definition
Planned comparrisons, express the difference between the means as the sum of weighted means

Degrees of freedom always 1
Term
Linear Trend Analysis
Definition
- Used for quantitative data

-Use a weighted coeficent method of deciding whether or not the data describes a linear trend
Term
Power
Definition
1-β

Probability of not making a type 2 error
Term
Power determined by..
Definition
-sample size

-effect size

-Alpha level
Term
ALpha and power
Definition
By making alpha less strict we can increase power, However we also increase type 1 error chance
Term
Power and effect size
Definition
-As the seperation between two means increase so does power

-As variability about a mean decrease, power increases
Term
Eta squared
Definition
-Proportion of the total variance that is attributed to an effect

-Partial ''squared is proporption of the effect + error variance

-Mesure of association
Term
R-squared
Definition
-Proportion of variance explained by the model

-Mesure of association
Term
Omega- squared
Definition
-an estimate of the dependent variable populationvariability accounted to the independent variable

-Mesure of association
Term
d
Definition
-Where there are only two groups it is the standardised difference between the groups

-Measure of differences
Term
f
Definition
-Where there are 3 or more groups it acts as an averadged standardized difference

-small effect: 0.10, Medium effect: 0.25, Large effect: 0.40

-Measure of difference
Term
Factorial design
Definition
-two independent variables

-one way, two way or three way
Term
3x2x4
Definition
3 Independent variables

-One with 3 levels, one with 2 levels, one with 4 levels
Term
Mixed or Split plot design
Definition
Independent variables are a mix of between groups and within group variables
Term
Interaction
Definition
Effect of the two independent variables together
Term
Analysing two way between group variables
Definition
- State null hypothesis

-Partitio the variability

-Calculating mean squares

-Calculate the F ratios
Term
Levene’s test
Definition
-Homogenity of variance

-Between groups test
Term
Mauchlys W
Definition
- Homogenity of variance

-Within Groups test
Term
Box's M
Definition
-HOmogenity of vairance

-Overall test, on mixed plot designs
Term
ANCOVA
Definition
-Used to gain statistical control of error when experimental control of error is not possible

-adjusts treatment effects with respect to the covariates
Term
Co-variates
Definition
-Mainly collected before the experiment

-When not possible can be collected after
Term
Partioning and ANCOVA
Definition
variance here has 3 basic components

-Effect

-Error

-Covariate
Term
Partioning and ANCOVA
Definition
variance here has 3 basic components

-Effect

-Error

-Covariate
Term
Assumptions of ANCOVA
Definition
-Homogenity of regression coefficents

-assumption of linear regression. Cant use for curvelinear
Term
Homoscedasticity
Definition
Similar distrubutions of scores according to the line of best fit
Term
Heterosedacisity
Definition
Distrubution of scores according to line of best fit are not similar
Term
Homogenity of regression coefficents
Definition
- Regression of coefficents for each of the groups in the IV are the same

- asses this by looking at the interaction between IV and covariable
Term
Limitations of ANCOVA
Definition
- Only works best with a small number of covariables

-COvariates must be independent of treatmment
Term
MANOVA
Definition
Multivariate Analysis of Variance
Term
Multivariate analysis
Definition
A new DV is created that attempts to maximise the differences between treatment groups
Term
Advantages of MANOVA
Definition
-Increses chance of finding an effect

-Protects from type 1 errors

--can be more powerful
Term
Box'x M test
Definition
-Homogenity of variacne-covariance

-Very sensitive so use a P value of 0.001
Term
Wilks Lambada
Definition
if significant shows there is a multi variate effect

- if significant then need univariat tests
Term
DFA
Definition
- fins a set of variable which predict group membership

-Discriminat functions analysis
Term
Discriminate Functions Analysis
Definition
-Treats IV as the DV and reverse

-See if we can predict whos in which group
Term
Number of functions for DFA
Definition
- number of levels of the grouping variable - 1
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