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 #2, Ch 4 - Problem 21, page113.

Date: February 17, 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 Japanese participants only (citizen = 1) 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:

How to do it, step by step:

General Algorithm:
 Step 1:  Get data
Step 2:  Manipulate data
Step 3:  Print out or save data

Step 1 - Get Data
Load the CD containing data;
Load SPSS;
Double-click SPSS;
File - Open - Self.sav; Press Enter

Step 2:  Manipulate data
 2A - Filter the data to include the Japanese only
Data
Select cases
Based on time or case range
Use filtered variable
collect (variable #1 through intsc (variable #7)  arrow over
Based on time or case
Range
 1 to 94 = Japanese
Continue
OK

2B - Get the  range, standard deviation, variance, skewness, kurtosis, and quartiles for each of the variables that follow for Japanese participants only (citizen =1):

1. Collectivism scale score  (collect),
2. Individually-Oriented Achievement Motivation (ioam),
3. Socially-Oriented Achievement Motivation (soam),
4. Individualistic Self-Esteem (indse),
5. Collectivistic Self-Esteem (cses),
6. Independent Self-Construal (indsc),
7. Interdependent Self-Construal (intsc),

Choose Analyze - Descriptive Statistics - Frequencies
Select collect (variable #1) through intsc (variable #7)   and arrow it into the Variables Box
Click Statistics
Click range, standard deviation, variance, skewness, kurtosis, and quartiles
Click Continue
Click OK


 Step 3:  Print out or save data
Right-click the object
Copy the object
Select a location on Frontpage
Paste
Save
Refresh the web.

Here's the 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:

Here's the answer:

 Kurtosis (K)

Symmetric distributions can be perceived as flat (platykurtic, tall and high in the middle (leptokurtic) or somewhat in between and having a bell shape (mesokurtic)>

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.

Larger deviations from zero  indicate more extreme kurtosis.

(text - page 107)

 Skewness (Ps)

Pearson's index of skewness

     -  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
      ( text page 106)

      (also see the illustration on text page 76)


 

1. collect : Kurtosis =  .091   ; Skewness =  -.225 
                  Std. error = .493   ; Std. error =  .249 
leptokurtic (peaked)negatively skewed distributions (having a long thin tail to the left)


 2. ioam : Kurtosis = -.117    ; Skewness =  .027
                  Std. error =.493    ; Std. error = .249 
playtykurtic (flat) positively skewed distributions (having a long thin tail to the right)
 

 

3. soam : Kurtosis =  -.427   ; Skewness =  -.119
                  Std. error = .493   ; Std. error = .249 
playtykurtic (flat) negatively skewed distributions (having a long thin tail to the left)

 

4. indse : Kurtosis =  -.107   ; Skewness =  .275
                  Std. error = .493   ; Std. error =  .249
playtykurtic (flat)   positively skewed distributions (having a long thin tail to the right)

 

5. cses : Kurtosis =  1.119   ; Skewness =  -.775
                  Std. error = .493   ; Std. error =  .249 
leptokurtic (peaked)negatively skewed distributions (having a long thin tail to the left)

 

6. indsc : Kurtosis =  -.105   ; Skewness =  -.033
                  Std. error = .493   ; Std. error =   .249
playtykurtic (flat) negatively skewed distributions (having a long thin tail to the left)

 

7. intsc : Kurtosis =  .206   ; Skewness =  -.492
                  Std. error = .493   ; Std. error =  .249
leptokurtic (peaked)negatively skewed distributions (having a long thin tail to the left)

 

 

 


filename: StatHW2Ch4Prob21page113TomMeyer.doc

Tom Meyer

Thomas Meyer

 

PS  Data for the United States follow below using the same algorithm developed for Japan: