Statistics Anyone

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Statistics Anyone?

• Matthew Rodger

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Descriptive Statistics
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• Mean (M) is the sum of data points divided by the
  number of points ?X/N
• Mode is the value (or values) of the most
  frequent score(s)
• Median is the central score when all scores are
  arranged ordinally
• Variance
• Standard Deviation

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Standard Deviation (s.d.) and Standard Error
(s.e.)

• Deviation of a score is distance from the mean of
  scores in a sample (X - M)
• Sum of squares is the sum of the squares for all
  score deviations in the sample ?(X M)2
• Variance is the mean squared deviation
• (?(X M)2) / (N-1)
• (N-1) used in place of N when
  estimating population parameters from a sample
• Standard Deviation (s.d.) is the square root of
  the variance v((?(X M)2) / (N-1))
• Standard Error (s.e.) is the Standard Deviation
  divided by the square root of the number of
  scores s.d./vN

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Probability and significance

• Examples
• Adults in the Duple and Triple groups differed
  significantly in the proportion choosing the
  duple test stimulus, as measured by an
  independent samples t-test, t(14) 3.92, p
  .001 (Phillips-Silver Trainor, 2006)
  
• This similarity was revealed because the
  navigation factor exercised no effect (F(1, 7)
  0317, p 0.59) (Segond, et al., 2005)
  
• The first example indicates that the probability
  of observing these results by chance is 0.1
  (below the required 5) and hence statistically
  significant
• In the second example, the probability of finding
  these results by chance is greater than 5 and so
  this factor did not have a significant effect on
  the dependent variable

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Inferential Statistics
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Choosing a statistical test
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Nature of Dependent Variables

• Nominal discrete categories (e.g. gender)
• Ordinal rank order of scores (e.g. position in
  race)
• Interval equal intervals measurements lacking
  real zero point (e.g. temperature in Celsius)
• Ratio equal interval measurement with real zero
  point (e.g. temperature in Kelvin)

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Nature of Independent Variables

• Independent measures each subject contributes a
  score to one level (condition) of the independent
  variable
• Related (dependent) measures subjects
  contribute scores to more than one level
  (condition) of independent variable
• Sample matching is grouping independent samples
  together to use in related measures design

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Parametric/Non-Parametric Data

• Assumptions made for parametric data
• Normal data distribution explained further down
• Homogenity of variance variance should not be
  substantially different between sample groups or
  vary systematically across variables
• Interval data see above
• Independence no interaction between subjects in
  design

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Normal Distribution
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Skewed Distribution
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If Parametric Assumptions are violated, use
corresponding non-parametric test (usually,
corresponding test for ordinal data)
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Thank You