Transcript Folie 1 - University of Oxford

Statistics for Linguistics
Students
Michaelmas 2004
Week 7
Bettina Braun
www.phon.ox.ac.uk/~bettina/teaching.html
Overview
• Problems from last assignment
• Correlation analyses
• Repeated measures ANOVA
– One-way (one IV)
– Two-way (two IVs)
• Transformations
Chi-square using SPSS
• Organisation of data:
Chi-square using SPSS
• Where to find it…
Chi-square using SPSS
• How to interpret the output
Table similar
to ours
Result: sign.
interaction
(x2=5.7, df=1,
p=0.017
More on interactions
Male
Female
No effect of region,
nor gender, no
interaction
North
South
No effect of gender,
effect of region, no
interaction
North
North
South
Effect of region and
gender and
interaction
South
Effect of region and
gender no interaction
North
Effect of region and
gender and
interaction
South
North
South
Correlation analyses
• Often found in exploratory research
– You do not test the effect of an independent
variable on the dependent one
– But see what relationships hold between two
or more variables
Correlation coefficients
r = -1
Neg. corr.
r=0
no corr.
r=1
pos. corr.
• Scatterplots helpful to see whether it is a
linear relationship…
Bivariate correlation
• Do you expect a correlation between the
two variables?
• Try “line-fitting” by eye
?
Pearson correlation
• T-test is used to test if corr. coefficient is
different from 0 ( => data must be interval!)
• If not, use Spearmans correlation (nonparametric)
Pearson correlation
• Correlation coefficient
– For interval data
– For linear relationships
• r2 is the proportion of variation of one
variable that is “explained” by the other
• Note: even a highly significant correlation
does not imply a causal relationship (e.g.
There might be another variable
influencing both!)
Repeated measures ANOVA
• Recall:
– In between-subjects designs large individual
differences
– repeated measures (aka within-subjects) has
all participants in all levels of all conditions
• Problems:
– Practice effect (carry-over) effect
Missing data
• You need to have data for every subject in
every condition
• If this is not the case, you cannot include
this subject
• If your design becomes inbalanced by the
exclusion of a subject, you should
randomly exclude a subject from the other
group as well (or run another subject for
the group with the exclusion)
Requirements for repeated
measures ANOVA
• Same as for between-subjects ANOVA
• You can have within- and between-subject
factors (e.g. boys vs. girls, producing /a/
and /i/ and /u/)
• Covariates
– factors that might have an effect on the withinsubjects factor
– Note: covariates can also be specified for
between-subjects designs!
Covariates: example
• You want to study French skills when using 2
different text-books. Students are randomly
assigned to 2 groups. If you have the IQ of these
students, you can decrease the variability within
the groups by using IQ as covariate
• Problem: if the covariate is correlated with
between-groups factor as well, F-value might get
smaller (less significant)!
• You can also assess interaction between
covariates and between-groups factors (e.g. one
textbook might be better suited for smart
students)
One-way repeated measures
ANOVA in SPSS
1. Define new
name and levels
for within-subject
factor
3
2
One-way repeated measures
ANOVA in SPSS
• Factor-name
• Four levels of the
within-subjects
variable
• Enter betweensubjects and
covariates
(if applicable)
Post-hoc tests for within-subjects
variables
• SPSS does not allow you to do post-hoc
tests for within-subjects variables
• Instead do “Contrasts” and define them as
“Repeated”
2
1
Post-hoc tests for within-subjects
variables
• You can also ask
for a comparson
of means
SPSS output: test of Sphericity
• Test for homgeneity of covariances among
scores of within-subjecs factors
• Only calculated if variable has more than 2
levels
If test is significant, you have to reject the
null-hypothesis that the variances are
homogenious
SPSS output: within-subjects
contrasts
• Post-hoc test for within-subjects variables
3 x 3 designs
• 3 x 3 between subjects
Factor B (between)
B1
B2
B3
A1
A2
A3
Group1 Group2
Group4 Group5
Group7 Group8
Group3
Group6
Group9
3 x 3 designs
• 3 x 3 within subjects
A1
A2
A3
Factor B (witin)
B1
B2
B3
Group1
Group1
Group1
Group1
Group1
Group1
Group1
Group1
Group1
3 x 3 designs
• 3 x 3 mixed design
Factor A
(between)
A1
A2
B1
Group1
Group2
A3
Group3
Factor B (witin)
B2
B3
Group1
Group1
Group2
Group3
Group2
Group3
Data transformation
• If you want to caculate an ANOVA but your
interval data is not normally distributed (i.e.
skewed) you can use mathematical
transformations
• The type of transformation depends on the
shape of the sample distribution
• NOTE:
– After transforming data, check the resulting
distribution again for normality!
– Note that your data becomes ordinal by transforming
it!! (but you can do an ANOVA with it)
What kind of tranformation?
Transformation
e.g.
f(x) = x1.5
e.g.
f(x) = log(x)
f(x) = atan(x)