Statistical Methods MCQ's ANOVA

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When would we make use of a Mixed (or split-plot) ANOVA?
When there is more than one factor (independent variable)
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How does a mixed design combine features of both between groups and within subjects designs?
Each level of factor A contains a different group of randomly assigned subjects, and each level of factor B at any given level of factor A contains the same subjects
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What is a One-Way-Mixed-Design?
There is no such thing!
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How does a mixed ANOVA partition the variance for main effects?
Between groups effect, Within subjects effect, interaction effect
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How does a mixed ANOVA partition the variance for error terms?
Between groups error for between groups effect, Within groups error for within groups effect, Within groups error used for interaction
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A mixed ANOVA calculates F-Ratio's for what?
Main effects and the interaction
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The f-score in a Mixed design for main effect A is worked out as:
Fa = MSa/MSs/a
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The f-score in a Mixed design for main effect B is worked out as:
Fb = MSb/MSbxs/a
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The f-score in a Mixed design for the interaction is worked out as:
Fab = MSab/MSbxs/a
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In a mixed design, Homogeneity of variance needs to be tested in which ways?
Overall, Within Subjects and Between Groups
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In a mixed design, how do we check for overall homogeneity of variance?
Box's M
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In a mixed design, how do we check for within subjects homogeneity of variance?
Mauchly's W
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In a mixed design, how do we check for between groups homogeneity of variance?
Levene's test
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How do we test normality in a mixed design?
Box's test of equality and the covariance matrices
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A psychologist, after running a Mixed Design ANOVA on their data, finds a significant main effect for Factors A and B and made no a-priori predictions about this. What must they now do?
Run some post-hoc tests
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A researcher finds a significant interaction between their Factor A and Factor B after running a mixed design ANOVA. What must they now do?
Run a simple main effects analysis.
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What are the key stages to reporting a Mixed Design ANOVA?
1 - Description of design (including variables and levels) 2 - Descriptives table 3 - Report main effects 4 - Report Interactions 5 - Report post-hoc or main effects analysis
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What are the main benefits of a Repeated Measures (Within Subjects) design?
It controls for individual differences between participants, Participants providing scores for each treatment helps prevent fluctuation due to individual participants
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How does a repeated measures ANOVA partition the variance?
Within treatment deviation, and between treatment deviation, residual
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What does between-treatment variance measure in a repeated measures ANOVA?
Effect plus error
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What does within-treatment variance measure in a repeated measures ANOVA?
Error alone
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What is the problem with just using the within treatment variance to measure error in a repeated measures ANOVA?
Some of the within treatment variance is due to individual differences
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What is the 'residual' in a repeated measures ANOVA and what does it measure?
The residual is the effect of participant variability subtracted from the within treatment variance. This acts as a representative measure of experimental error
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What is the 'residual error' in a repeated measures ANOVA?
An interaction between the treatment variable and the subject variable
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How do we calculate the mean square for the main effect in a repeated measures ANOVA?
MSa = SSa/dfa
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How do we calculate the mean square for the participant variables in a repeated measures ANOVA?
MSs = SSs/dfs
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How do we calculate the mean square for the residual in a repeated measures ANOVA?
MSaxs = SSaxs/dfaxs
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What F-ratio's do we calculate for a repeated measures ANOVA?
Main effect and participant variables
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How is the main effect F-ratio calculated in a repeated measures ANOVA?
Fa = MSa/MSaxs
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How is the participant variables ANOVA calculated in a repeated measures ANOVA?
Fs = MSs / MSaxs
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A researcher finds a significant main effect after conducting a repeated measures ANOVA. What does this mean for the results and analysis moving forward?
There is a significant difference between at least one pair of means, post-hoc tests and planned comparisons could be conducted to see where this difference lies
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A psychologist finds that there is a significant main effect of her participant variable in her repeated measures ANOVA. This isn't a problem, unless....
Specific predictions are made about performance, or there is a hidden aptitude treatment problem
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What is an aptitude treatment interaction?
When some treatments are more or less effective for particular individuals depending on their specific abilities
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What is the best way to partition the variance in a Two-Way - Repeated - Measures Design?
Construct an error term for each of the effects of interest ('residuals' for each of the main effects, and the interaction error)
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How would we calculate the F-ratio for I.V one (A) in a Two - Way - Repeated Measures design?
Fa = MSa/MSaxs
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How would be calculate the F-ratio for I.V two (B) in a Two - Way - Repeated measures ANOVA?
Fb = MSb/MSbxs
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If there is a significant main effect with more than two levels of the I.V's of a repeated measures ANOVA, then what can be used to further analyse the data?
Post - Hoc tests
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A psychoanalyst researcher has conducted a two - way repeated measures ANOVA. When considering sphericity, they need to...
Do nothing - sphericity is not an assumption if each I.V has only two levels
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How do we test for sphericity on a repeated measures ANOVA and what should we look for?
We use 'Mauchly's test of sphericity' - if this is NOT significant, then we can presume sphericity.
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A researcher finds that after conducting a repeated measures ANOVA, his Mauchly's test is significant. He needs to correct this violation by checking...
Greenhouse - Geisser or Huynh - Feldt
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A researcher wants to test caffeine consumption and water consumption against memory ability. They split two groups of participants, who partake in three doses of water or caffeine before having their memory tested each time. Describe the design.
A Two - Way - 2x2 - Between -Groups - Design
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A psychologist tests self-efficacy against sports performance on a running track. Each participant listens to a motivational or degrading message before undertaking a 1 mile run each time. Name the type of design.
A One - Way - Repeated - Measures - Design
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A researcher puts p's into each environment condition: statistics lecture, birdsong or rousing speech. They are ascribed 0mg 10mg or 15 mg of anti-depressants and self-reported depression is measured after each environment exposure. Name the design.
A Two - Way - 3x3 - Split -Plot - Design
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The effect of a single variable in an ANOVA is known as the...
Main effect
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The effect of x2 variables considered together is known as what....
An interaction
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If an ANOVA has x2 I.V's, how many Null Hypotheses will there be?
3 - One for each I.V and one for the interaction
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A researcher conducts a two-way between groups design. How many f-ratio's will be calculated?
3 - The main effect of I.V 1, The main effect of I.V 2 and the Interaction between I.V 1 and 2
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When partitioning the variance of a one-way-ANOVA, we calculate what?
The effects of both error and treatment, and the effect of error alone.
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When partitioning the variance of a two-way ANOVA, we calculate what?
The effect of variable A, the effect of variable B, the interaction between the x2 variables
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What is a 'residual' in a Two - Way ANOVA?
The effect of the interaction
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To calculate the mean squares for a two-way ANOVA, f-ratio's must be calculated for what?
The effect of I.V 1, the effect of I.V 2, the interaction and the error term
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Main effect mean squares in two-way ANOVA's for variable 1 are calculated as:
MSa = SSa/dfa
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Main effect mean squares in a two-way ANOVA for variable 2 are calculated as:
MSb = SSb/dfb
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Interaction mean squares for a two-way ANOVA are calculated via:
MSab = SSab/dfab
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The error mean squares for a two way ANOVA is calculated thus:
MSs/ab = SSs/ab/dfs/ab
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In a two - way ANOVA, the f-ratio for the first main effect is calculated as:
MSa/MSs/ab
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In a two - way ANOVA, the f-ratio for the second main effect is calculated as:
MSb/MSs/ab
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A psychologist conducts a two way ANOVA. She needs to work out her interaction f-ratio manually. Which equation should she use?
MSab/MSs/ab
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Outline the basic process of how to work out f-scores for ANOVA's
Partition the variance > Calculate Sum of Squares > Calculate Mean Squares > Calculate F-ratio's
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When writing the results for a two - way ANOVA, it's good practice to go beyond the main effects and look at the differences between different levels of the I.V's. How do we do this?
By looking at simple main effects analysis
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When can we reject the null hypothesis?
When the f-ratio exceeds the f-critical
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What is statistical power?
Our ability to detect an effect when there is one
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What is a type I error?
Not rejecting the Null Hypothesis when we should
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What is a type II error?
Accepting the null Hypothesis when we shouldn't
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Statistical power is expressed as:
1 - b (beta)
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A researcher - counsellor wants to know how many participants to use for her first ever study. What can she use to find this?
Statistical power formulae
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Power is related to effect size. What does ANOVA use to measure effect size?
Eta - squared, R- squared and Omega - Squared
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Eta squared measures what?
The proportion of total variance that is attributable to an effect
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Partial eta-squared measures what?
The proportion of the effect + error variance that is attributable to an effect
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Eta squared is calculated as:
** treatment/ ** total
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Partial eta - squared is calculated as:
** treatment/ ** treatment + ** error
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Omega squared measures what?
The dependent variable population variability accounted for by the I.V
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R- squared measures what?
The proportion of variability explained by the model
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R - squared is calculated by:
** model/** total
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What things should decide which effect size is being aimed for?
Previous research and theoretical importance
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What is the per comparison error rate?
The error rate on one test on a set of data
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What is the family-wise error rate?
The error rate across numerous tests on a set of data
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A researcher wants to control her overall Type I error rate as she's undertaking multiple significance tests. What can she use?
The Bonferroni correction
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The bonferroni correction is calculated as:
alpha / number of comparisons (a/c)
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A researcher has already conducted his experiment, and we are tasked with interpreting his data. Which assumptions do we need to worry about?
Homogeneity of variance and Normality
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Where we have a within groups or mixed design, where do we look for homogeneity of variance?
Box's M
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To test for normality, which three tests/things can we look at?
Skew, Lillefors and Shapiro - Wilks
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To test skew, how do we work this out?
By calculating a Z - Score
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How do we work out a z-score to test skew, and what are we looking for?
z = skew-0/SE Skew SE skew = (square root) 6/N - the Z-Score should come out at less than 1.96
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What source of variability does ANOVA use to test experimental error and treatment effects?
Between groups
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What source of variability does ANOVA use to test experimental error?
Within Subjects
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AS - T denotes
Total sum of squares
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A - T denotes
Between groups sum of squares
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AS - A
Within group sum of squares
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In ANOVA, 'A' denotes
Between groups
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In ANOVA, 'S/A' denotes
Within groups
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Between groups mean square is expressed as:
MSa = SSa/dfa
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Within groups mean square is expressed as:
MSs/a = SSs/a/dfs/a
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The f-ratio is calculated as:
F = MSa/MSs/a
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In terms of F-scores, when can we reject the Null Hypothesis?
When the observed f-score is larger than the critical f
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How do we find the critical f-value in the f-tables?
df for effect (A) horizontal axis, and df for error (s/a) vertical axis
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A psychologist receives the following scores: A df = 2, s/a df =12 f= 7.41 SSa = 105. Use an f table to see if the null can be rejected.
Yes, as critical F = 3.89
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An output shows the following: MSa = 12.6, Ms/a = 17 dfa = 7 dfs/a = 15 F = 1.5
No, as critical F = 2.71
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A researcher finds that her omnibus (reported F) is non-significant. When writing this up...
The analysis can stop there
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When the omnibus F is significant.....
Further analysis is required to see where differences lie/ which are real
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Total deviation is indicated by what?
AS - T (bar)
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Between groups deviation is indicated by what?
A (bar) - T (bar)
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Within subjects deviation is indicated by what?
AS - A (bar)
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Other cards in this set

Card 2

Front

How does a mixed design combine features of both between groups and within subjects designs?

Back

Each level of factor A contains a different group of randomly assigned subjects, and each level of factor B at any given level of factor A contains the same subjects

Card 3

Front

What is a One-Way-Mixed-Design?

Back

Preview of the front of card 3

Card 4

Front

How does a mixed ANOVA partition the variance for main effects?

Back

Preview of the front of card 4

Card 5

Front

How does a mixed ANOVA partition the variance for error terms?

Back

Preview of the front of card 5
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