Statistics Review

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Statistics Review
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Descriptive Statistics

• Scale of Measurement
• Nominal Categorization
• Ordinal Rank ordering
• Interval Rank ordering and intervals between
  elements are equal
• Ratio Interval scale plus true zero

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Measures of Central Tendency

• Mean
• Median
• Mode

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Measures of Variability

• Range
• Variance Standard Deviation

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Pearson Correlation

• Represents the relationship between two variables
• Mathematical score
• Ranges from 1.0 to -1.0
• Absolute value signifies strength of relationship
• Sign signifies nature of the relationship

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Inferential Statistics

• Help you decide whether the IV had an effect
• t-test
• ANOVA

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Inferential Statistics

• Help you decide whether the IV had an effect
• IVs with small inferential statistics occur
  frequently by chance
• HO ?1 ?2
• IVs with large inferential statistics occur
  rarely by chance
• HA ?1 ? ?2, ?1 lt ?2, or ?1 gt ?2
• Significance level p lt .05

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Significance Testing

• In 100 replications of the experiment, HA could
  occur 5 times by chance
• If we find HA, we want to be able to infer that
  HA is because of our IV

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Significance Testing

• If our experiment is one of those 5 times in 100
  that the results occurred by chance
• Actuality HO is true
• Our Conclusion HA is true
• We make a Type I error (?)
• Accepting the experimental hypothesis when the
  null hypothesis is true
• We control the probability of ? by setting our
  significance level

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Significance Testing

• More extreme significance level requires larger
  inferential test statistic to be significant
• Actuality HA is true
• Our Conclusion HO is true
• We make a Type II error (?)
• Accepting the null hypothesis when the
  experimental hypothesis is true

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Significance Testing
True state of affairs
Experimental hypothesis is true
Your decision
Null hypothesis is true
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Significance Testing
True state of affairs
Experimental hypothesis is true
Your decision
Null hypothesis is true
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Effect Size

• Statistical measure that conveys the magnitude of
  the effect produced by the IV
• ? and ? both depend on sample size effect sizes
  dont
• Cohens d
• r 2
• Makes them ideal for decisions about the
  importance of an effect
• Statistically significant or practically
  significant?

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Statistically significant?Practically
significant?

• Statistical significance
• Difference between groups is due to some
  systematic influence (we assume HA) and not
  chance
• Degree of risk you are willing to take that you
  will reject a null hypothesis when it is actually
  true

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Statistically significant?Practically
significant?

• Practical significance (meaningfulness)
• Is the difference between groups meaningful in
  some way?
• Results must be interpreted in the context of the
  experiment
• Results can be statistically significant without
  being practically significant
• Results can be practically significant without
  reaching statistical significance

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Statistically significant?Practically
significant?