- Created by: frankie_1212
- Created on: 17-06-18 18:50
Variables that are manipulated
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Variables that are measured
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Variables that represent variation in amount
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Variables that are in kind or type
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Characteristics which are intrinsic to the subjects of the experiment
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Potential independent variables which if left uncontrolled could exert a systematic influence on the different treatment conditions
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Completely random design
Subjects are randomly assigned to serve in one of the treatment conditions: Between subjects design
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Randomised block design
Blocks of subjects who are matched closely on some relevant characteristics
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A set of precise hypotheses about the parameters of the different treatment populations
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Assumed nature of the world that gets translated into an experiment
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Statistical hypothesis which will be tested
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The Alternative Hypothesis
The values of the parameter in the different treatment populations are not equal
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Significant level of 0.05
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Type 1 Error:
Reject the null hypothesis when the null hypothesis is actually true: False positive
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Type 2 Error
Accept the null hypothesis when the null hypothesis is actually false: False Negative
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What is ** total?
**within + ** Between
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How do you work out Mean Squares?
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How do you work out between group Df?
DFA = a-1 (Number of groups - 1)
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How do you work out within group Df?
DFa/A = AS-A (Number of pps - number of groups)
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The Between group mean square
MSA = SSA/DFA
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The within group mean squares
MSs/a = ** S/A / DF s/a
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How do you work out the F ratio?
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When is F critical?
F observed has to be bigger than the F critical
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How do you find a critical value?
Degress of freedom for the effect (A) and look along the horizontal axis of the F table, Degrees of freedom for the error term (S/A) and look down the vertical axis of the F table
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What can the omnibus F ratio tell us?
That there is a difference between the means
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What is a planned comparison?
Make predictions about the direction of the effects
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What is a post hoc?
It is a test that is conducted after an experiment
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How is a post hoc conducted?
Calculate the sum of the weighted means
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What is the ** for planned comparison?
Number of subjects * Difference between compared means/ sum of coefficient which we weight the mean 2
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How is the F ratio calculated?
To test the comparison: MSAcomp (Mean square of comparison = SSAcomp/DFcomp=SSAcomp/1
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Per comparison and familywise error
Performing multiple statistical tests on a set of data increases the chance of type 1 error
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A type 1 error involving single tests are known as?
Per comparison errors
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The whole set of type 1 errors is known as?
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What is the relationship between 2 error rates?
Afw = c (aPC)
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Can't affor to ignore the familywise error rate
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What are some post hoc tests?
Scheffe, Tukey HSD, T-tests --> All inccrease the chance of type 2 error
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How to conduct the Scheffe test?
Fscheffe (a-1) F (DFa, DFS/A
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What is a way to work it out?
N x Mean difference 2/2) / Mean squared within MSe
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What is the Tukey test?
D= Q Square root (MSError/N)
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What does the Tukey test work for?
Between group ANOVA with equal Cell sizes
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What is the T-test?
When comparing two means, a modified t-test is available T=(mean 1- mean 2)/Square Root (2MSerror/n)
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What is a T-test also known as?
Bonferroni correction test
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What are the assumptions of the F ratio?
Independence, Random Sampling, Homogeneity of variance and normality
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What is homogeneity of variance meaning?
The different treatment populations have the same variance
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What is normality?
Observations are drawn from noramlly distributed populations
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What is between group design?
Hartley's F max, Bartlett, Cochran's C
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What is within/Mixed design ANOVA
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How do you test the homogeneity of Variance?
Largest Variance/Smallest Variance
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How do you test Normality?
Skew, LilleFors, Shapiro Wilks
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How do you measure out Z scores?
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How do you work out the standard Error of the skew?
SEskew =Square root (6/N)
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What does a Z score have to be?
Greater than 1.96 then sample is significantly different from normal
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What is N?
The number of cases in the sample
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What does a Skew do?
Reduces the probability of making a type 2 error
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What do you do to Moderate, substantial or severe data that has a positive skew?
Square root, Logarithm, reciprocal
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What do you do to moderate, substantial, severe that is negative skew?
square root, logarithm, reciprocal (K-X)
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What is statistical power?
Probability of detecting real effect
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What is the equation for statistical power?
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What is Beta?
The probability of making Type II error
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What does Statistical power depend on?
Alpha level, sample size , effect size
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What is effect size?
Association between Dv and Iv, seperation of means relative to error variance
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What happens when we make alpha less strict
We reduce to risk of type 2 error but increase type 1
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What is sample size?
To small, an effect may be missed, too big and too expensive a study
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What is Eta Squared?
Proportion of total variance that is attributed to an effect
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What is partial eta squared?
Proportion of the effect and error variance that is attributable to the effect
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R2 is the proportion of variance explained by the model
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What is Omega Squared?
Estimate of the dependent variable population variability accounted for by the IV
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What is Cohens F?
One way between groups ANOVA
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What are the 3 null hypothesis for an ANOVA?
The means of the different levels of the first IV will be the same, The means of the different levels of the second IV will be the same, the differences between the means of the different levels of the interaction will be the same
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How is factorial ANOVA variability partitioned?
The effect of A=A-T, the effect of B= B-T, Interaction A x B}Known as residual
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**a + **b +** ab +**sab
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How is interaction mean squares?
MSAB = SSAB/DFAB where dfAB = (a-1)(b-1)
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How is the error mean square?
MSsab = SSsab/dfsab
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What is residual error?
Treatment Variable, subject variable
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What is ANOVA assumptions?
Data from interval or ratio scale, normal distributions, independence, homogeneity of variance, sphericity,
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homogeneity of treatment difference variance
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Mixed or split design
One or more repeated measures, one or more between subject measures
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What is effect of interest?
A between group effect is estimated, a within subject effect is estimated, An interaction effect is estimated
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What is the overall for Homogeneity of Variance?
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What is Within Subjects?
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Between groups homogeneity of variance?
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What are the three basic component of an ANCOVA
Effect, Error, Covariate
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How is the treatment effect estimated?
When covariate scores are available we have information about difference between treatment groups that existed before the experiment was performed
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What does ANCOVA use?
Linear regression to estimate the size of treatment effects given the covariate information
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What can the adjustment for group differences can either what?
Increase or decrease depending on the dependent variables relationship with the covariate
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What is the error variability in ANCOVA?
In between group ANOVA the error variability comes from the subject within group deviation from the mean of the group
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What are the assumptions of an ANCOVA?
Normality of treatment levels, independence of variance estimates, homogeneity of variance, random sampling, linear regression, homogeneity of regression coefficient
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Assumptions of linear Regression
This states that the deviations from the regression equation across the different levels of the independent variable have normal distribution with means of Zero, and heteroscedasity
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What is homogeneity of regression coefficients?
The regression coefficients for each of the groups in the independent variable should the same
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Perform an ANOVA style analysis on several DVs simultaneously
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What is the assumptions of a MANOVA?
Multivariate normality, homogeneity of variance and singularity
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What is the Discriminant function analysis?
Predict membership of groups
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When is it used?
Groups are already known and the researcher is trying to find out what the differences are between the groups
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What is the basic principle used in DFA?
Different functions are calculated that maximise the ability to predict membership of groups, the macimum number of functions calculated either the number of levels of the grouping variable less one, the number of degrees of freedom of the IV
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Variables that are measured