Statistics for Linguistics Students

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Statistics for Linguistics Students

• Michaelmas 2004
• Week 7
• Bettina Braun
• www.phon.ox.ac.uk/bettina/teaching.html

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Overview

• Problems from last assignment
• Correlation analyses
• Repeated measures ANOVA
• One-way (one IV)
• Two-way (two IVs)
• Transformations

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Chi-square using SPSS

• Organisation of data

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Chi-square using SPSS

• Where to find it

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Chi-square using SPSS

• How to interpret the output

Table similar to ours
Result sign. interaction (x25.7, df1, p0.017
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More on interactions
MaleFemale
No effect of region, nor gender, no interaction
Effect of region and gender and interaction
North South
No effect of gender, effect of region, no
interaction
North South
Effect of region and gender and interaction
North South
Effect of region and gender no interaction
North South
North South
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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

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Correlation coefficients

• Scatterplots helpful to see whether it is a
  linear relationship

r -1Neg. corr.
r 0no corr.
r 1pos. corr.
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Bivariate correlation

• Do you expect a correlation between the two
  variables?
• Try line-fitting by eye

?
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Pearson correlation

• T-test is used to test if corr. coefficient is
  different from 0 ( gt data must be interval!)
• If not, use Spearmans correlation (non-parametric)

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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!)

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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

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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)

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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
  within-subjects factor
• Note covariates can also be specified for
  between-subjects designs!

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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)

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One-way repeated measures ANOVA in SPSS
1. Define new name and levels for within-subject
factor
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2
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One-way repeated measures ANOVA in SPSS

• Factor-name
• Four levels of the within-subjects variable
• Enter between-subjects and covariates (if
  applicable)

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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
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Post-hoc tests for within-subjects variables

• You can also askfor a comparsonof means

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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
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SPSS output within-subjects contrasts

• Post-hoc test for within-subjects variables

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3 x 3 designs

• 3 x 3 between subjects

Factor B (between) Factor B (between) Factor B (between)
B1 B2 B3
A1 Group1 Group2 Group3
A2 Group4 Group5 Group6
A3 Group7 Group8 Group9
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3 x 3 designs

• 3 x 3 within subjects

Factor B (witin) Factor B (witin) Factor B (witin)
B1 B2 B3
A1 Group1
A2
A3
Group1
Group1
Group1
Group1
Group1
Group1
Group1
Group1
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3 x 3 designs

• 3 x 3 mixed design

Factor B (witin) Factor B (witin) Factor B (witin)
B1 B2 B3
Factor A (between) A1 Group1
Factor A (between) A2
Factor A (between) A3
Group1
Group1
Group2
Group2
Group2
Group3
Group3
Group3
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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)

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What kind of tranformation?