Introduction
In this paper we will discover the understanding of basic theories of mathematical statistics and learn how to use measures of central tendency and measures of variation. To do this, we choose two variables from the data set – one variable is continuous and one is nominal. Then we will explore if there any relationships regarding these variables – we perform a hypothesis testing using SPSS 17 Statistical Software. Charts and graphs are also will be used in this paper.
Body
As a continuous variable we choose Total Family Income (INCOME)
As a nominal variable we take Race of Respondent (RACE).
We begin with a descriptive statistics. Use option “Explore” is SPSS to obtain a descriptive statistics for Income by Race:
The syntax is:
GET FILE='D:\ gss04student_corrrected.sav'. >Warning. Command name: GET FILE >SPSS Statistics system file "D:\ gss04student_corrrected.sav" is written in a character encoding (windows-1252) >incompatible with the current LOCALE setting. It may not be readable. >Consider changing LOCALE or setting UNICODE on. (DATA 1721) EXAMINE VARIABLES=INCOME BY RACE /PLOT BOXPLOT HISTOGRAM /COMPARE GROUP /STATISTICS DESCRIPTIVES EXTREME /CINTERVAL 95 /MISSING LISTWISE /NOTOTAL.
After the descriptive part is done, we go the next step – hypothesis testing.
I’m interested in checking the following case: There is a significant difference in income level between the groups formed by race.
The first step is to formulate hypothesis. Since we have 3 groups in Race variable, the hypotheses are:
H0: μ1=μ2=μ3Ha:not all means are equal
The next step is to set the level of significance of our testing. I use the most common level of 5%
α=0.05
The third step is to perform the appropriate test. It’s one-way ANOVA (Fisher’s test). The result of ANOVA is below, via SPSS:
We can see that Fisher’s F is 13.746 and the p-value of the test is less than 0.001 (reported as 0.000).
Since p-value is lesser than alpha level, we can reject the null hypothesis. We have enough evidence to say that there is a significant difference in income level between the groups formed by race (at 5% level of significance).
The syntax is:
ONEWAY INCOME BY RACE /MISSING ANALYSIS.
References
Levesque, R. SPSS Programming and Data Management: A Guide for SPSS and SAS Users, Fourth Edition (2007), SPSS Inc., Chicago Ill. ISBN 1-56827-390-8
SPSS 15.0 Command Syntax Reference 2006, SPSS Inc., Chicago Ill.
Wellman, B. "Doing It Ourselves: The SPSS Manual as Sociology's Most Influential Recent Book." pp. 71–78 in Required Reading: Sociology's Most Influential Books, edited by Dan Clawson. Amherst: University of Massachusetts Press, 1998. ISBN 978-1-55849-153-3
