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## Revision Notes Stats Notes This is an extract of our Revision Notes Stats document, which we sell as part of our Statistics (2nd year) Notes collection written by the top tier of Durham University students.

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GENERAL

4 questions, 1 each on:
2 way independent ANOVA
Mixed ANOVA
Regression (Stepwise)
Factor Analysis (PCA)
You will have to work out the diff between 2 way and mixed ANOVA  regression and PCA will say
One or Two-Way
Independent ANOVA
Multiple regression
Factor analysis
Repeated Measures
(RM) ANOVA
Mixed ANOVA

Used to study differences in group means (along with interaction effects)
Used to study relationship between variables (whether certain variables predict an outcome variable)
Used to explore whether they is any meaningful pattern in data (no p values)
Used when there are more data points than Ps
And when you have 1 or more IV in a RM design
Used when you have some IV(s) which are of ind design, and some IV(s) which are RM design

Which ANOVA?
What are the IVs? What is the DV?
How many IVs are there?
How many conditions of each IV?
Between subjects, within subjects, or both?

1.1 = small effect size

0.06 = medium effect size

0.14 = large effect size
Case:Variable 25:1, preferably 40:1
Checks for multicollinearity
A tolerance statistic of less than 0.1 is a serious problem
A tolerance statistic of less than 0.2 is a potential problem

Post hoc tests (work similar to t tests)
= tells us the direction of the differences between groups
 If the main effect from the omnibus test is not sig  you do not need to do any post hoc tests
 If the main effect of the omnibus test is sig  we do need to follow up with post hoc tests

Write out all descriptive stats  just copy out SPSS table
ONE-WAY INDEPENDENT ANOVA = when IVs are in groups/conditions
= determines differences between groups when you have more than 2 conditions

SPSS instructions:
Analyse  Compare mean  1-way ANOVA
IV in Factor box
DV in dependent list
Options  select
 Descriptive
 Homogeneity of variance test
 Welch ( test which corrects for unequal variance)
 Means plot
Post Hoc  select
 Scheffe
 Games-Howell
Continue  OK

Step 1
Is the data suitable for a one way independent ANOVA?
More than 2 conditions
One nominal IV (more than 2 groups or categories)
One interval/ratio DV (on a continuous scale)
Step 2
Is the sample suitable for a one way independent ANOVA?
Roughly equal group sizes  largest group size should be no more than twice the smallest group size
At least 30 cases in total
At least 10 cases in each group
(If you fewer cases than this, still run an ANOVA, just mention to be cautious about interpretation. If p values are in the region of .05 to .10, and/or the effect size is large, it is more likely that the result is not significant purely because of a lack of statistical power).
Step 3
Are there equal variances between the groups?
Check the Levene's statistic.
If not significant, groups have equal variance  use the table which reports the standard F statistic.
If significant, it indicates that the groups differ significantly in their variance (ie unequal variance)  use the table with Welch's F statistic.
Step 4
What do the results of the overall ANOVA tell us?
Report: F(df1, df2) = _ , p = _ , η² = _
η² = eta squared (the effect size). In the exam just write 'eta squared'.
Eta squared = (Between groups Ps) / (Total Ps)  x100 to get % Interpret: Was the p value significant? What was the effect size? Is this a small/medium/large effect? 
the p needs to be less than 0.05 to be sig
Step 5
Run post hoc tests (if the main effect of the ANOVA is significant)
If the Levenes test was not significant: Use the Scheffe test
If the Levenes test was significant: Use the Games-Howell test
Report mean scores for the groups
Look at p values from post hoc tests  Interpret these ie if sig or not

TWO-WAY INDEPENDENT ANOVA
= when IVs are in groups/conditions = more than 1 IV

SPSS instructions:
Analyse  General Linear Model  Univariate
IV in Factor box
DV in dependent list
Plots  select
 Put first IV in horizontal axis
 Put other IV in separate lines
 Do the same but reverse variables
 OK
Options
 Move all factors from L to RH side into 'display means for' box
From display section  choose
 Descriptive stats
 Estimates of effect size
 Homogeneity tests
Post Hoc
 Select both variables from Factors box  put into Post Hoc Tests for box
 Scheffe
 Continue  OK
Step 1
Is the data suitable for a Two Way independent ANOVA?
More than 1 nominal IV (2 groups or more per IV)
1 interval/ratio DV (on a continuous scale)
Step 2
Report descriptive statistics (means, standard deviations) for each subgroup
Step 3
Is the sample suitable for a Two way independent ANOVA?
Roughly equal group sizes  largest group size should be no more than twice the smallest group size
At least 30 cases in total
At least 10 cases in each group
(If you fewer cases than this, still run an ANOVA, just mention to be cautious about interpretation. If p values are in the region of .05 to .10, and/or the effect size is large, it is more likely that the result is not significant purely because of a lack of statistical power)
Step 4
Are there equal variances between the groups?
Check the Levene's statistic.
If not significant, groups have equal variance  use the table which reports the standard F statistic. If significant, it indicates that the groups differ significantly in their variance (ie unequal variance)  use the table with Welch's F statistic.
Step 5
What do the main effects of the ANOVA tell us?
Report: F(df1, df2) = _ , p = _ , η² = _ for each main effect
η² = partial eta squared (the effect size). In the exam just write 'eta squared'  SPSS calculates this
Interpret: Was the p value significant? What was the effect size? Is this a small/medium/large effect? 
the p needs to be less than 0.05 to be sig
What does the interaction effect tell us?
Report: F(df1, df2) = _ , p = _ , η² = _
Interpret: Was the p value significant? What was the effect size? Is this a small/medium/large effect?
Step 6
The next step will depend on the results of the main effects and interaction effect:
Significant main effects?
 YES: Interpret the direction of the main effects (use the mean scores ignoring the effect of the other IV). If there are more than 2 groups, use the post hoc tests to work out the group differences
 NO: If neither of the main effects is significant then move on to the interaction effect  no need to interpret the direction of the effect if it's not significant in the first place
Significant interaction effect?
 YES: Conduct simple effects analysis using either T tests or One Way ANOVA. Interpret the results.
 NO: Focus on the significant main effects  need to interpret the plot if the interaction is not significant in the first place.

When the interaction is sig  SIMPLE EFFECTS/FOLLOW UP ANALYSIS
Data  Split file
Compare groups  place the IV with 3 conditions in box  OK
 analysis will now be done on each separate group
Running t tests:
Analyse  Compare Mean  Ind t test
Place IV that you HAVE NOT split into Grouping variables box
Place DV in Test Variable box
Define groups  Enter coding from variable view into group 1 and 2
OK
Report Levene's for each
Don't need to report each group if they are all sig/non-sig, just state as such
Step 7
Give a general conclusion/summary regarding the results
REPEATED MEASURES ANOVA Used when there are:
 More than 2 conditions of an IV
 More than 1 IV
SPSS instructions:
Analyse  General Linear Model  Repeated Measures
In RM Design box:
 Replace factor1 with the variable name
 Input number of conditions into Number of Levels
 Select each level of the variable and use right arrow to put them into the Within Subjects variables
Options  Desc Stats
OK

Step 1
Is the data suitable for a RM ANOVA?
DV measured on an interval/ratio scale
More than 1 IV
Normal distribution of scores on the DV
Step 2
Report descriptive statistics (means, standard deviations) for each subgroup
Step 3:
Is the sample suitable for a RM ANOVA?
Minimum of 10 Ps  In a RM design, fewer Ps are usually required
Step 4: Mauchly's Test of Sphericity
Are there equal variances between differences in condition means?
Similar to Levenes
We need at least 3 conditions for this to be an issue
If not significant, differences have equal variance  sphericity is assumed

Step 5: Tests of Within-Subjects Effects table
What does the overall main effect of the ANOVA tell us?
If Mauchly test is non-sig, use the rows labelled Sphericity Assumed
If Mauchly test is sig, use the rows labelled Greenhours-Geisser  this changes the df, thus the assoc
Mean Squares
Report: F(df1, df2) = _ , p = _ , η² = _ for main effect
η² = partial eta squared (the effect size). In the exam just write 'eta squared'  SPSS calculates this
Interpret: Was the p value significant? What was the effect size? Is this a small/medium/large effect?
Step 6: Post hoc tests
Where do the differences lie?  use post hoc tests to determine the specific difference

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