Psychology 203 2 Chi Square SEMESTER 2

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Psychology 203?2 (Chi Square) SEMESTER 2
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Levels of Measurement

• Categorical (e.g., blue vs green eyes)
• Ordinal (rank, magnitude of differences not
  apparent e.g., attitude scaling)
• Interval (arbitrary zero can do most arithmetic
  operations e.g., IQ)
• Ratio (absolute zero, can do all arithmetic
  operations e.g., Reaction times)

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Statistical Tests and levels of measurement

• ANOVA and t-tests
• interval and ratio data (people also use these
  for attitudes too)
• Correlation
• specific formulae for ranked (Spearman) and
  interval or ratio (Pearson) data
• ?2 (Chi Square)
• Categorical or frequency data

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Non-parametric tests

• Chi square is a non-parametric test
• Hypotheses are not specified in terms of a
  specific parameter
• Sometimes referred to as a distribution-free test
• Such tests do not use or compute means and
  variances
• They are less sensitive and you should use a
  parametric test as a test of choice.

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?2 (Chi Square)

• Like t and F, ?2 tells us how unlikely it is a
  relationship has occurred by chance.
• Like t and F, ?2 does not tell us about the
  magnitude of the relationship
• ?2 tests the relationship between variables by
  assessing the discrepancy between the observed
  data and the expected data given the null
  hypothesis of no relationship.
• Can be used as a test of Goodness of Fit or as a
  test of association (independence)

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?2 as a test of goodness of fit

• Tests how well the obtained sample proportions
  fit the proportions specified by the null
  hypothesis.
• It compares the observed proportions against
  expected proportions
• Typical question might be to what extent are
  students of different socio-economic backgrounds
  accepted into UWA
• If there is no bias (either direct or indirect)
  then the proportions accepted from different
  backgrounds should mirror the proportions from
  the community

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A fictitious example
Expected frequency .25 68 17
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?2 FORMULA
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?2 Distribution

• When the data and the expectation are close Ho is
  true
• You can never have a negative value
• Like F, the distribution of ?2 positively skewed
• Also like F there are a set of distributions
  depending on the degrees of freedom
• Degrees of Freedom determined by the number of
  categories the sum of the expected proportions
  must come to 1 (or 100). So, every category is
  free to vary except 1 in this example.

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?2 Distribution
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?2 Distribution with different DFs
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Some example tables
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?2 Test of Independence

• A question you might ask is there a link
  (association) between sex and smoking?
• Alternatively Do women smoke more than men?
  might also be asked as a specific question.
• From what you know already you might apply a
  correlational approach to the first and a t-test
  to the latter.
• But . Its really the same question are smoking
  (or not) and sex independent?
• This time, unlike the goodness of fit test we
  might not know the expected frequencies.

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?2 for 2x2 tables
EXAMPLE 2
Note independence of categories
N143
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?2 FORMULA
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?2 for 2x2 tables
EXAMPLE
e (8185)/143
e (8158)/143
e (6258)/143
e (6285)/143
e48.15
e32.85
e36.85
e25.15
143
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e48.15
e32.85
e36.85
e25.15
143
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?2 (50-48.15)2/48.15 (31-32.85)2/32.85
(35-36.85)2/36.85 (27-25.15)2 /25.15
?2 .43 with 1 df pgt05
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Test of Significance

• Big differences between the observed and expected
  frequencies make it likely there is an
  association
• Like t or F as ?2 increases the more unusual the
  data become and once a critical value has been
  reached for a given degrees of freedom (df) then
  we say we have a significant effect.
• df (rows-1) (columns-1) The sums of the data
  in the rows must add up to the total number of
  data points for the analysis. The same for the
  columns.
• In a 2x2 table we therefore have 1 degree of
  freedom

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A bigger Contingency table ExampleEffective Use
of CBT
df (Rows 1) (Columns -1)
R1
R2
R3
Total Obs
C1
C2
C3
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?2 and Effect Size

• Like t and F, the ?2 test the test of
  significance (p-value) confounds the size of the
  effect and the sample size.
• The effect size (an association) can be
  calculated from

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And Finally (almost)

• We can calculate confidence intervals around the
  effect size
• Convert reffect into Fisher Zr
• Then calculate
• The confidence limit of Zr is the value in 2
  added and subtracted to the value in 1
• The confidence limit of reffect is determined by
  translating Zr back into reffect using tables

(1/v N-3)1.96
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Cramers V

• When the contingency table is greater than a 2x2
  a minor modification to the formula is needed.

• Where df is the smaller of (R-1) or (C-1)

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Standards for interpreting Cramérs V as proposed
by Cohen (1988).
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The Final Lab Report

• Its a challenge deliberately so
• No references have been given to you. Why?
• This is the way research gets done
• You develop a question
• You seek guidance from researchers who have asked
  a similar question
• What did they find
• What were the issues
• How does what you are doing build on what went
  before
• The video has been set up on the web site and you
  can use it as often as you want.
• Work collaboratively you help someone else
  collect the data they need and theyll help you
  (hopefully). This might be a useful way of
  getting inter-rater reliability.
• BUT if you work collaboratively the extent of
  the collaboration should be limited to deciding
  what the research question is and what the
  dependent measure is
• Literature reviews and the rest of the write up
  must be done independently.

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The Course

• Emphasised statistical decision making and
  experimental design
• The laboratories set the context for the
  measurement and statistical methods

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The Exam

• 2 sections
• 80 Multiple Choice questions
• 10 Short Answer Questions over 2 hours
• Tables provided
• No calculators allowed
• Within each section each question equally
  weighted
• Each component within a question in the short
  answer section has the mark weight indicated
• All material is examinable

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Hints for Study

• Do not get bogged down on context
• Look at what it was that the labs were trying to
  get across (what was the teaching point?)
• You will be asked about material covered in the
  Statplay exercises
• The material in Gravetter and Wallnau will be
  covered specifically the recommended chapters
  listed in the Laboratory Manual
• You may be asked to illustrate or explain a point
  that was contained in certain laboratories

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Statistical Concepts Covered in the Unit During
Semseter 2

• Summary descriptive statistics
• Sampling distributions
• Statistical estimation (confidence intervals
  standard error (sampling distribution of the
  mean, standard error of estimate)

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More Statistical Concepts

• Statistical decision making
• Inferential statistics and hypothesis testing
  (t-tests, ANOVA, ?2)
• Covariation of scores (correlation)
• Regression
• Effect size of an experimental variable
• Interactions between factors
• Research Design

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GOOD LUCK!
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And thats it!