the use of statistics in psychology

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the use of statistics in psychology
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statistics

• Essential
• Occasionally misleading

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Two types

• Descriptive mathematical summaries of results
• Inferential statements about large populations
  derived from small samples

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Descriptive statistics

• Measures of the central score
• Mean the average score, found by adding
  all the scores together and then dividing by the
  number of scores
• Vulnerable to skewing by very high scores

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Measures of the central score ii

• Median the middle score after the scores are
  arranged from highest to lowest
• Much less sensitive to skewing

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Central score measures iii

• Mode the most common score
• Usually of limited interest

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Measures of variation

• Enough about the central score, how the scores
  differ, or vary, within a distribution is just as
  important
• The Range the difference between the highest
  and lowest score
• The Standard Deviation a measurement of the
  amount of variation among scores in a normal
  distribution

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examples

• Sample distribution 1,2,3,3,21
• Measures of Central Score
• Mean 6 Median 3 Mode 3
• Variation
• Range 20
• Standard Deviation 7.5

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Inferential statistics

• We found a difference between the experimental
  group and the control group.
• What does that tell us about the population we
  are interested in?
• Could the difference have resulted from chance?

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Inferential statistics ii

• Procedures used to decide whether differences
  really exist between sets of numbers
• Does our experimental group significantly differ
  from the population from which it was drawn?

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significance tests

• Assess the odds that we could have gotten such a
  difference (between the experimental and the
  control group) at random
• We want to prove that the difference would only
  occur 5 of the time by luck
• If we can, then the difference is significant
  our experiment worked.

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Data set 1

• Experimental group
• 3
• 10
• 10
• 10
• 2
• 35
• Mean7 SD4.1

• Control group
• 5
• 7
• 6
• 5
• 7
• 30
• Mean 6 SD 1

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Inferential statistics

• Statements about large populations taken from
  small samples
• How can we be sure that our results really mean
  something?
• That they apply to the entire population and not
  just to the sample?

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data set 2

• Experimental group
• 10
• 6
• 7
• 9
• 8
• 7
• 10
• 8 Mean 8
• 6 SD 1.5
• 9
• 80

• Control group
• 7
• 6
• 5
• 10
• 2
• 4
• 8
• 6 Mean 6
• 5 SD 2.2
• 7
• 60

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In other words

• If the experimental groups free throw shooting
  performance had not been affected by the
  relaxation technique, we would only see such a
  difference between the two groups in 1 out of 500
  occasions.
• We can reasonably claim that the results
  supported our hypothesis.