Lecture 6 Dispersion

Lecture 6 Dispersion - Defning Dispersion • Quantitative...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Defning Dispersion • Quantitative data • 1) DiFFerence between highest and lowest scores • 2) The width oF an interval spanning some pre-specifed proportion oF scores • 3) The average amount by which scores deviate around some central point • 4) The magnitude oF dispersion expressed as a percentage oF the value oF the mean 1 Range • Defned as the diFFerence between the largest and smallest scores in the data set R = x (largest score)- x (smallest score) 5 9 5 2 6 7 9 8 3 8 R = 9 - 2 = 7 2 Range: Pros and Cons • Pros: • Easy to compute and intuitive • Cons: • Uses information from only 2 scores • Overly sensitive to extreme scores • Not mathematically tractable • Tends to increase with sample size 3 Interquartile Range • A truncated range statistic spanning the middle 50% of scores in a distribution • Median - cuts off the lower 50% of the distribution from the upper 50% • First quartile - cuts off the lower 25% of the distribution from the upper 75% • Third quartile - cuts off the lower 75% of the distribution from the upper 25% 4 5 Interquartile Range • 1) Order observations from least to greatest • 2) Compute ( n +1)/4 , round to the nearest whole number and count in that many steps from both ends of the ordered data set • 3) Compute IQR = ( Q 3- Q 1 ), where Q 1 is the score corresponding to the 1st Quartile and Q 3 is the score corresponding to the 3rd Quartile . That is the Interquartile Range 6 Interquartile Range 2 3 5 5 6 7 8 8 9 9 ( n+ 1)/4 = (10+1)/4 = 2.75 ~ 3 IQR = Q 3- Q 1 = 8 - 5 = 3 7 Quartile Deviation • Also called Semi-Interquartile Range • 1) Identify Q 1 and Q 3 as in IQR • 2) Compute QD = ( Q 3- Q 1 )/2 2 3 5 5 6 7 8 8 9 9 QD = (Q 3-Q 1 )/2 = (8 - 5)/2 = 1.5 8 Interquartile Range/ Quartile Deviation • Pros: • Not affected by extreme scores or sample size • Interquartile Range commonly used for quantifying what counts as an outlier Mdn ± 2( IQR ) • Magnitude of Quartile Deviation roughly comparable to other common measures of quantitative dispersion 9 Interquartile Range/...
View Full Document

This note was uploaded on 01/21/2009 for the course PSYC 60 taught by Professor Ard during the Winter '08 term at UCSD.

Page1 / 34

Lecture 6 Dispersion - Defning Dispersion • Quantitative...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online