Appendix

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Appendix

• Behavioral Statistics

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Types of Statistics in Psychology

• Descriptive Statistics Summarize numbers so they
  become more meaningful and easier to communicate
  to other people
• Inferential Statistics Used for making
  decisions, for generalizing from small samples,
  and for drawing conclusions

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Graphical Statistics

• Presenting numbers pictorially (usually in a
  graph) so they are easier to visualize
• Subset of descriptive statistics
• Frequency Distribution Table that divides an
  entire range of scores into a series of equal
  classes and then records the number of scores
  that fall into each class
• Histogram Graph of a frequency distribution
  scores are represented by vertical bars
• Frequency Polygon Number of scores in each class
  is represented by points on a line

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Fig. A.1 Frequency histogram of hypnotic
susceptibility scores contained in Table A.2.
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Fig. A.2 Frequency polygon of hypnotic
susceptibility scores contained in Table A.2.
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Measures of Central Tendency

• A number that describes a typical score around
  which the other scores fall
• Mean Add all the scores for each group and then
  divide by the total number of scores one type of
  average
• Sensitive to extremely high or low scores in a
  distribution not always the best measure of
  central tendency

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Measures of Central Tendency (cont.)

• Median Arrange scores from highest to lowest and
  then select the score that falls in the middle
  half the values fall above the median, and half
  fall below it
• Mode Identifies the most frequently occurring
  score in a group
• Easy to obtain but often unreliable
• Main advantage Gives the score actually obtained
  by the most people

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Measures of Variability

• Provide a single number that tell us how spread
  out the scores are
• Range Difference between the highest and lowest
  scores
• Standard Deviation Index of how much a typical
  score differs from the mean of a group of scores

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Standard Scores

• Z Score Indicates how many standard deviations
  above or below the mean a score is
• Normal Curve Bell-shaped curve, with a large
  number of scores in the middle and very few
  extremely high and low scores

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Fig. A.3 The normal curve. The normal curve is an
idealized mathematical model. However, many
measurements in psychology closely approximate a
normal curve. The scales you see here show the
relationship of standard deviations, z-scores,
and other measures to the curve.
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Fig. A.4 Relationship between the standard
deviation and the normal curve.
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Inferential Statistics

• Population Entire set of subjects, objects, or
  events of interest (all married students in the
  United States)
• Impossible or impractical to obtain
• Samples Smaller cross section of a population
• Easier and more practical (and cheaper!) to
  obtain
• More cost effective

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Inferential Statistics (cont.)

• Sample must be representative
• The membership and characteristics of the larger
  population must be reflected accurately
• Members of sample must be chosen randomly
• Each member of the population must have an equal
  chance of being selected for the sample
• Statistical Significance Degree to which an
  event (results of an experiment, results of a
  drug trial) is unlikely to have occurred by
  chance alone

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Correlation

• Consistent, systematic relationship between two
  variables, measures, or events
• Scatter Diagram Best way to visualize
  correlation plots intersection of paired
  measures
• Positive Relationship Increases in one measure
  (X) are matched by increases in the other (Y)
• The more cigarettes you smoke, the more likely
  you are to contract lung cancer

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Correlation (cont.)

• Zero Correlation No relationship exists between
  two variables
• Relationship between hair color and intelligence
  test scores (IQs)
• Negative Relationship (or Correlation) As values
  of one measure increase (X), values in the other
  measure decrease (Y)
• The more alcohol you drink, the lower your
  coordination test scores will be

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Fig. A.5 Scatter diagrams showing various degrees
of relationship for a positive, zero, and
negative correlation. (Adapted from Pagano,
1981.)
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Coefficient of Correlation

• Statistical index ranging from 1.00 to 1.00
  the sign indicates the direction of the
  relationship, and the number, the strength
• Perfect Positive Relationship Correlation of
  1.00
• Perfect Negative Relationship Correlation of
  1.00
• Perfect correlations are rarely found in
  psychology
• It is statistically impossible to have a
  correlation coefficient greater than 1.00 or
  lesser than 1.00
• Percent of Variance Amount of variation in
  scores accounted for by the correlation

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Utility of Correlations

• Correlations help us identify relationships that
  are worth knowing
• Correlations are valuable for making predictions
• If a correlation exists, the two variables are
  related
• Correlation does NOT demonstrate causation!
• Many times a third, or perhaps an extraneous,
  variable could be creating the correlation