To:  sbaker@odu.edu

From:  Thomas Meyer
tmeyer@ph.vccs.edu
276 656-0283
Patrick Henry Community College

Subject:  Statistics - w/  Dr.Spencer Baker - Homework Assignment #3, Ch 4 - Problem 23, page113.

Date: February 29, 2004

Question:
Use the SPSS program and SPSS data (career.sav) bank to complete the following:

a.    Find the range, standard deviation, variance, skewness, kurtosis, quartiles for the following variables: confidence in doing mathematics (confmath), perception of mother's attitude toward mathematics (mother), perception of father's attitude toward mathematics (father), success at doing mathematics (succesat), perception of current teacher's attitude toward mathematics (teacher), perception of mathematics as a male domain (maledom), perception of the usefulness of mathematics (useful), anxiety about doing mathematics (anxiety), and perception of mathematics as a fun activity (mathfun).

Answer:

Question:


b.    Using the index of skewness and the index of kurtosis, describe the characteristics of the distribution of scores for each variable.

Answer:

 

  Interpretation of Kurtosis
 - A kurtosis of K = 0 is that assigned to a normal bell shaped distribution.
   - A negative number for K indicates  a flat or platykurtic distribution;
   - A positive number for K indicates a leptokurtic or highly peaked distribution.		                        
                     Interpretation of Skewness
    Pearson's index of skewness was computed on the seven scaled variables:

     -  will be positive for positively skewed distributions
        (having a long thin tail to the right)
     - will be negative for negatively skewed distributions
        (having a long thin tail to the left)
     -  Larger numbers indicate more severe skewness.

 

 

See the chart and table of skewness and kurtosis to the right of each frequency table for each of the nine variables below.

 

 

1

 
Skewness -.442
 negatively skewed distributions (having a long thin tail to the left)
Std. Error of Skewness .172
Kurtosis -.161
 playtykurtic (flat)
Std. Error Kurtosis .342
2

 

 
Skewness -1.114
negatively skewed distributions (having a long thin tail to the left)		    
Std. Error of Skewness .172    
Kurtosis 2.878
leptokurtic (peaked)		    
Std. Error Kurtosis .342    
3

 
Skewness -.1252
negatively skewed distributions (having a long thin tail to the left)		    
Std. Error of Skewness .172    
Kurtosis 3.236
leptokurtic (peaked)		    
Std. Error Kurtosis .342    
4

 
Skewness -.445
negatively skewed distributions (having a long thin tail to the left)		    
Std. Error of Skewness .172    
Kurtosis .098
leptokurtic (peaked)		    
Std. Error Kurtosis .342    
5

 
Skewness -.083
negatively skewed distributions (having a long thin tail to the left)		    
Std. Error of Skewness .172    
Kurtosis -.162
playtykurtic (flat)		    
Std. Error Kurtosis .342    
6

 
Skewness -1.635
negatively skewed distributions (having a long thin tail to the left)		    
Std. Error of Skewness .172    
Kurtosis 2.704
leptokurtic (peaked)		    
Std. Error Kurtosis .342    
7

 
Skewness -1.038
negatively skewed distributions (having a long thin tail to the left)		    
Std. Error of Skewness .172    
Kurtosis 1.004
leptokurtic (peaked)		    
Std. Error Kurtosis .342    
8

 
Skewness -.312
 negatively skewed distributions (having a long thin tail to the left)		  
Std. Error of Skewness .172  
Kurtosis -.703
 playtykurtic (flat)		  
Std. Error Kurtosis .342  
9

 
Skewness -.136
 negatively skewed distributions (having a long thin tail to the left)		  
Std. Error of Skewness .172  
Kurtosis -.703
 playtykurtic (flat)		  
Std. Error Kurtosis .342  

 


 


filename: StatHW3Ch4Prob23page113TomMeyer.doc

Tom Meyer

Thomas Meyer