1. Being Descriptive Without Being Mean
PSYC 510: Statistics

2. General Topics: Descriptive Statistics
Levels of Data
Frequency Counts
Measures of Central Tendency: Median, Mean, and Mode
Extreme Scores and Data Transformation
Bimodal Distributions
Practical experience

3. Levels of Data Nominal Ordinal Interval Ratio
Name only (e.g., Ethnicity, Sex, Major)
Ordinal
Serial position, but unequal increments (e.g., 1st and 2nd place, Likert scaling?!?)
Interval
Equal increments, no zero point (e.g., centigrade)
Usually the minimal level of data for most parametric inferential statistics
Ratio
Equal increments with a theoretical zero point (e.g., reaction time, age, distance, Kelvin)

4. Frequency Counts
Major
Physics
History
Chemistry
Psychology

5. Frequency Counts Major Freqency Physics 2 History 4 Chemistry 3
Psychology
Ideal for nominal level data and is useful for Modes!

6. Central Tendency

7. Central Tendency: Big, Average Meanie
Mean = Average
N = population, n = sample
Sigma (S) = Sum
M (Xbar) = S/n
Basis for many inferential stats (e.g, t test)
Sensitive to extreme scores

8. Getting Mean
Score
100 98 97 92
M = 96.75

9. Getting REALLY Mean
Score
100 98 97 92
M = 77.4

10. Options in Dealing With Extreme Scores
Eliminate outliers
Run a statistic that is not sensitive to extreme scores (nonparametric)
Data transformation
Move from least invasive to most invasive:
Square Root
Log
Inverse

11. Median: Second Best in the Middle of the Road
Exact middle score
Organize data in ascending/descending order
Less sensitive to extreme scores
Basis for many nonparametric tests
Less statistical power

12. Finding a Happy Median Score 92 97 98 100 Median here!92 97 98
100
Median here!
M (prior to extreme score) = 96.75

13. Where's the Median?
Me = ( )/2 = 65/2 = 32.5
Age 12 17 20 30 31 34 36 42 60
Just for fun, calculate the mean…
M = 333/10 = 33.3

14. The Mode: Mr. Popular
Major
Physics
History
Chemistry
Psychology

15. This Might Help… Major Freqency Physics 2 History 4 Chemistry 3
Psychology
The mode is obviously “History,” but let’s make it a wee bit more challenging…

16. What's the Mode Now?
Major
Psychology
History
Chemistry
Physics

17. The Bimodal Distribution
Major
Frequency
Physics 1
History 4
Chemistry 3
Psychology
This doesn’t really hurt anything, but it’s something to be aware of.

18. Getting Bimodal

19. Play with SPSS Here Descriptive: Mean, Median Frequency: Mode
Explore: Skew, Kurtosis
Transform: Square Root, Log, Inverse

20. 9 Mean Median Mode Standard Deviation
Which of the following measures of central tendency is most affected by extreme scores?
Mean
Median
Mode
Standard Deviation 9

21. Consider the following distribution: 6, 10, 9, 13, 12, 11, 10, 9
Consider the following distribution: 6, 10, 9, 13, 12, 11, 10, 9. Which of the following best describes this?
Negatively skewed
Positively skewed
Bimodal
Leptokurtic 7

22. Questions? Thoughts?