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the use of statistics in psychology. statistics. Essential Occasionally misleading. Two types. Descriptive – mathematical summaries of results Inferential – statements about large populations derived from small samples. Descriptive statistics. Measures of the central score

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statistics
statistics
  • Essential
  • Occasionally misleading
two types
Two types
  • Descriptive – mathematical summaries of results
  • Inferential – statements about large populations derived from small samples
descriptive statistics
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

measures of the central score ii
Measures of the central score ii
  • Median – the middle score after the scores are arranged from highest to lowest
  • Much less sensitive to skewing
central score measures iii
Central score measures iii
  • Mode – the most common score
  • Usually of limited interest
measures of variation
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
examples
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

inferential statistics
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?
inferential statistics ii
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?
significance tests
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.
data set 1
Experimental group

3

10

10

10

2

35

Mean=7; SD=4.1

Control group

5

7

6

5

7

30

Mean= 6; SD= 1

Data set 1
inferential statistics1
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?
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

data set 2
in other words
In other words…
  • If the experimental group’s 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.