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 #4, Ch 15 - Problem 24, page 402.

Date: April 10, 2004

Use the following algorithm:

1.  Get the data

2.  Manipulate the data

To conduct the Chi-square test:

Having loaded the data
Click Analyze menu and choose Nonparametric and Chi-square

Move the variable "Current Career Interest" into the Test Variable List box;

Click Values;
Insert:
.20
.15
.25
.30
.10 as given in problem 24 on text page 402.

Click OK.

3.  Do something with the data.

Right-click each piece of the output;
For each selected piece, Select copy object;
Paste the copied object into FrontPage  (Before you paste the object, right-click and read the "results coach");
Analyze the results;
Save and send your work.

 

Note:  When the variable you are testing is dichotomous (such as gave blood, did not give blood, is a democrat, isn't a democrat) use the chi-square as a test statistic, or use the binomial distribution.

When the variable you are testing is continuous (such as intelligence, persistance, emotive level, etc.) use the t-test statistic to determine whether outcomes differ from what could have been predicted from chance alone.

 

 

Question:
Suppose that students in grades 7-10 are expected to express career interests in the following areas for the given proportions: fine arts (.20), humanities (.15), social sciences (.25), biological sciences (.30), and physical sciences and mathematics (.10).  Use the SPSS data bank provided with this book to conduct a X2 (chi-square) goodness-of-fit test of the data contained in the data file career.sav for career interests (interest;1= fine arts, 2 = humanities, 3 = social sciences, 4 = biological sciences, 5 = physical sciences and math) among students in grades 7-10.  Given the result of your analysis, do the data fit the expected proportions?

Answer:

NPar Tests

Chi-Square Test

Frequencies

This table lists the number of cases (both observed and expected) in each category of the variable being analyzed.

The expected N corresponds to the user-defined distribution (and is twice the size of the values input for each row of study).

The residual lists the difference between what is expected and what is hypothesized.  Residuals identify categories which vary from the hypothesized distribution.

DF equals the number of categories minus one.

Small significance values (<.05) indicate that the observed distribution does not conform to the hypothesized distribution.

In this example the significance level of .000 IS less than .05.

Therefore the Current Career Interests of students in fine arts, humanities, social sciences, biological sciences, physical sciences and math differ from the hypothesized distribution.

.000 Asymp. Sig. is less than the traditional alpha = .05.

The greatest differences appear to be in Physical Sciences and Math in which the observed performance exceeds the expected performance, and in Humanities in which the reverse occurs, that is, the observed performance is less than the expected performance.  Lesser differences appear in Biological Sciences and in Fine Arts.  Only in Social Science does the observed and expected performance equal one another.

 

 

filename: StatHW3Ch15Prob24page402TomMeyer.doc

Tom Meyer

Thomas Meyer