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KNR 445 Statistics t-tests Slide 1 Measures of Central Tendency 1.

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Presentation on theme: "KNR 445 Statistics t-tests Slide 1 Measures of Central Tendency 1."— Presentation transcript:

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2 KNR 445 Statistics t-tests Slide 1 Measures of Central Tendency 1

3 Study note – using audio slides  Advantages  Revisiting them  No attention lapses  Nothing missed, everything available for comprehensive study guide come exam times  More class time available for discussion/group work/explanation/SPSS  Disadvantage  Not real time lecture/no immediate interaction w/instructor  Can result in wanting to ask questions, but not being able to  Recommendation:  Print slides before listening, make notes and write questions down as you go  Email question/s if needed in order to make progress  Listen to the slides early in the week so that there’s plenty of time to allow for communication with the instructor KNR 445 CT/Spread & Z-scores Slide 2 1 2 3 4

4 KNR 445 CT/Spread & Z-scores Slide 3 Measure of Central Tendency  What SINGLE summary statistic or parameter best describes the central location of an entire distribution?  Mode: which value occurs most (what is fashionable)  Median: the middle value in the data, once it’s ranked (the 50th percentile)  Mean: mathematical balance point; arithmetic mean; mathematical mean 1 2 3 4 General note on this early stuff

5 KNR 445 CT/Spread & Z-scores Slide 4 Mode  Most frequent occurrence  What if data were  17, 19, 20, 20, 22, 23, 23, 28  Problem: set of numbers can be bimodal, or trimodal, depending on the scores  Not a stable measure 1 2 3

6 KNR 445 CT/Spread & Z-scores Slide 5 Median  Rank numbers, pick middle one  What if data were  17, 19, 20, 23, 23, 28  Solution: add up two middle scores, divide by 2 (=21.5)  Best measure in asymmetrical distribution (ie skewed), not sensitive to extreme scores 1 2

7 KNR 445 CT/Spread & Z-scores Slide 6 Mean  Add up the numbers and divide by the sample size (number of numbers!)  Try this one…  5,3,2,6,9  This is the best measure of the three – after all, it uses more information than any of the others 1 2 3

8 KNR 445 CT/Spread & Z-scores Slide 7 Characteristics of the Mean  Balance point  point around which deviations sum to zero  Deviation is difference between two numbers  For instance, if scores are 5,3,2,6,9  Mean is 5  Sum of deviations: 0+(-2)+(-3)+1+4  = 0  See? 1

9 KNR 445 CT/Spread & Z-scores Slide 8 Characteristics of the Mean  Balance point  Affected by extreme scores  Scores 7, 11, 11, 14, 17  Mean = 12, Mode and Median = 11  Scores 7, 11, 11, 14, 170  Mean = 42.6, Mode & Median = 11 1

10 KNR 445 CT/Spread & Z-scores Slide 9 Characteristics of the Mean  Balance point  Affected by extreme scores  Appropriate for use with interval or ratio scales of measurement 1

11 KNR 445 CT/Spread & Z-scores Slide 10 Characteristics of the Mean  Balance point  Affected by extreme scores  Appropriate for use with interval or ratio scales of measurement  More stable than Median or Mode when multiple samples drawn from the same population  Basis for inferential stats 1

12 KNR 445 CT/Spread & Z-scores Slide 11 Guidelines to choose Measure of Central Tendency  Mean is preferred because it is the basis of inferential statistics  Median may be better for skewed data?  Distribution of wealth in the US  Mode to describe average of nominal data (Percentage - relative frequency) 1

13 KNR 445 CT/Spread & Z-scores Slide 12 Median Mode Mean Scores Normal Distribution 1 2 3 4

14 KNR 445 CT/Spread & Z-scores Slide 13 Positively skewed distribution Scores Median Mode Mean 1 2

15 KNR 445 CT/Spread & Z-scores Slide 14 Negatively skewed distribution Median Mode Mean Scores 1 2

16 End of file…variability next. KNR 445 CT/Spread & Z-scores Slide 15


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