Being Descriptive Without Being Mean PSYC 510: Statistics

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

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)

Frequency Counts Major Physics History Chemistry Psychology

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

Central Tendency

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

Getting Mean Score 100 98 97 92 M = 96.75

Getting REALLY Mean Score 100 98 97 92 M = 77.4

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

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

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

Where's the Median? Me = (31 + 34)/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

The Mode: Mr. Popular Major Physics History Chemistry Psychology

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…

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

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.

Getting Bimodal

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

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

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

Questions? Thoughts?