Psychology 203

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Psychology 203

• Semester 1, 2007
• Week 12
• Lecture 23

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Life beyond the parameters!

• Nonparametric tests I Voyage to Planet
  Chi-Square

Gravetter Wallnau, Chapter 18
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(No Transcript)
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Beam me up, Scotty!
Serious Research Hypothesis You are significantly
less likely to survive a mission to an alien
planet if you are not a main character!
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Number of Missions Survived
Skewed distributions
Sample of 10 episodes
Unequal variances
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Recode data into categories
Missions divided into 2 categories
Nonparametric Test
Number of characters
Chi-square tests use sample frequencies and
proportions to test hypotheses about the
population
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Features of parametric tests

• Testing hypotheses about population parameters
• Mean, ?
• Difference between means, ?1- ?2
• And make assumptions about shape of population
  distribution etc
• Data always a numerical score for each
  individual in sample
• Can do arithmetic on scores e.g. add, multiply
  etc
• Measured on interval or ratio scale

(See Text, Chpt 1, pp18-24)
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Features of Nonparametric tests
Distribution-free

• Hypotheses not in terms of specific population
  parameters
• Few, if any, assumptions about population
  distribution
• Individuals put in categories rather than having
  scores
• i.e. measurement on nominal or ordinal scales
• Not as sensitive (less powerful) as parametric
  tests,
• i.e. less likely to detect an effect

e.g. male or female
e.g. 1st, 2nd, 3rd
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Questions

• How does the number of females studying
  psychology in Australia compare to the number of
  males?
• Which of the three nominated housemates should be
  evicted?
• Did the Federal budget have any effect on
  preferred political party?

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Chi-square Test for Goodness of Fit

• Use to answer questions about the proportions in
  a population
• i.e. what proportion of population is in each
  category
• use proportions in sample to test hypotheses
  about proportions in population
• Chi-square GOFT tests how well sample proportions
  fit population proportions specified by the null
  hypothesis
• Why no significance testing on Big Brother?

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Chi-square Test - Goodness of Fit

• Data frequencies
• The Null hypothesis
• Specifies a proportion (or ) in each category,
  based on well defined rationale
• No preference i.e. population divided equally
  among all categories
• No difference from known population

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Chi-square Test - Goodness of Fit

• The experimental hypothesis
• The population distribution is different to that
  specified by the null hypothesis
• Population is not divided equally among all
  categories
• There is a difference from known population

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Calculating Chi-square

• Calculate the observed frequencies (o)

Our sample, n224
a)
Number of students in each category
Each individual counted only once!
b)
n315
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Calculating Chi-square

• Calculate expected frequencies (e)
• i.e. how the data would look if the null
  hypothesis (H0) were true

a)
n
b)
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Calculating Chi-square The formula
Difference btwn observed expected frequency for
each category
Square it so values positive
Greek letter Chi
Divide by expected frequency to standardize
difference
Add values from all categories
Relatively BIG dif
fo fe 16-124
Relatively small dif
fo-fe 232-2284
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Interpreting Chi-square

• The bigger the difference between expected and
  observed frequencies the bigger the value of ?2
• So large value of ?2 means we reject the null
  hypothesis and small value means we dont
• ?2 distribution critical values

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Chi-square Distribution
Most values close to 0
H0 true
Large values rare freaky
All ?2 values greater than 0
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Degrees of Freedom

• The more categories you have (e.g. star signs
  12) the bigger ?2 tends to get because adding
  values for each category
• So different distributions of ?2 for different
  numbers of categories

n100
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Once know values for 2 categories, 3rd is no
longer free to vary
df C - 1
NB df determined by number of categories not n!
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Which do you like best?
1
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2
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3
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4
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Study of aesthetics

• Do any orientations really look better than
  others?
• State hypotheses set alpha
• H0 No preference for one orientation, so all
  four should be selected equally often
• H1 One, or more, orientation is preferred over
  others
• ? .05

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Study of aesthetics

• Calculate Chi-square statistic
• Observed frequencies
• Calculate expected frequencies

n50
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Study of aesthetics
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Study of aesthetics

• Determine critical value of ?2
• df C - 1 4 - 1 3
• Look up critical value of ?2 for df 3, ? .05

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Study of aesthetics

• Make decision and draw conclusions
• Obtained ?2 8.08, Critical ?27.81
• Obtained ?2 gt Critical ?2
• Reject H0
• Conclude that all four orientations are not
  equally preferred

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Our data
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Blue Poles 11, 1952, Jackson Pollock, National
Gallery of Australia, Canberra
2
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For every parametric test theres a nonparametric
equivalent

• Well, almost
• Chi-square Goodness of Fit test is the
  nonparametric equivalent of which parametric
  test?
• Single sample t-test!
• Both test hypotheses about a single population
• Main difference is the data you collect from each
  participant

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Comparing t ?2
data
interval or ratio
nominal or ordinal
calculate
mean, sd etc
pros
most sensitive, powerful
cons
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So Linda, guru of all that is statistical, is
there a nonparametric equivalent of the
independent samples t-test?
Why yes, Ben! There is! Would you like me to
tell you about it?
Heck yeah!
Ben, sceptical 203 student
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Who gets the most action?
High masculine
Low masculine
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Chi-square test for Independence

• Used to test whether there is a relationship
  between two variables

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Classified as either masculine looking or not
60
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48
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11
n 110
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Chi-square test for Independence

• Two ways of framing the question
• Is there a reliable relationship between
  masculinity and number of sexual partners?
• Do highly masculine men differ significantly from
  less masculine men in the number a sexual
  partners?

correlation
t-test
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Chi-square test for Independence

• Data are frequencies
• The Null hypothesis
• H0 There is no relationship between masculinity
  and number of sexual partners
• H0 The distribution of number of sexual partners
  in masculine men does not differ from that for
  low-masculine men
• These are equivalent

If two variables are independent then there is no
predictable relationship between them and the
distributions do not differ