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 22, page113.

Date: February 29, 2004

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

a.    Find the range, standard deviation, variance, skewness, kurtosis, and quartiles for American participants only (citizen - 2) for the following variables:  Collectivism Scale Score (collect), Individually-Oriented Achievement Motivation (ioam) Socially-Oriented Achievement Motivation (soam), Individualistic Self-Esteem (indse), Collectivistic Self-Esteem Scale (cses), Independent Self-Construal (indsc), and Interdependent Self-Construal (intsc).

Answer:

Statistics on USA Respondents

 

 

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.


Table 2B -  Kurtosis and Skewness of United States Variables
 

UNITED STATES RESPONDENTS
Data on the 105 cases from United States of America follow:

Variable Name      Kurtosis                                                         Skewness

1. collect :               Kurtosis =  -.006   ;                                          Skewness =  -.287 
                                 Std. error = .467   ;                                            Std. error =  .236 
                                 playtykurtic (flat)              negatively skewed distributions (having a long thin tail to the left)

 2. ioam :                   Kurtosis =  .074    ;                                           Skewness =  -.508
                                  Std. error =.467    ;                                             Std. error = .236 
                                   leptokurtic (peaked)      negatively skewed distributions (having a long thin tail to the left)
 
3. soam :                  Kurtosis =   .174   ;                                            Skewness =  -.203
                                   Std. error = .467   ;                                             Std. error = .236 
                                   leptokurtic (peaked)      negatively skewed distributions (having a long thin tail to the left)

4. indse :                  Kurtosis =   .204   ;                                             Skewness =  -.830
                                   Std. error = .467   ;                                              Std. error =  .236
                                   leptokurtic (peaked)      negatively skewed distributions (having a long thin tail to the left)

5. cses :                    Kurtosis =  -1.72   ;                                            Skewness =  .633
                                   Std. error = .467   ;                                              Std. error =  .236 
                                    playtykurtic (flat)            positively skewed distributions (having a long thin tail to the right)

6. indsc :                   Kurtosis =  -.233   ;                                             Skewness =  .240
                                    Std. error = .467   ;                                              Std. error =   .236
                                    playtykurtic (flat)            positively skewed distributions (having a long thin tail to the right) 

7. intsc :                     Kurtosis =  .296   ;                                              Skewness =  -.233
                                     Std. error = .467   ;                                             Std. error =  .236
                                     leptokurtic (peaked)    negatively skewed distributions (having a long thin tail to the left)

 

 

 

filename: StatHW3Ch4Prob22page113TomMeyer.doc

Tom Meyer

Thomas Meyer