Bivariate Analysis in SPSS_ANOVA

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Bivariate Analysis in SPSS: ANOVA

(Textbook Resources: Chapter 22, pp. 541-546, and Session 1 !

Please use the SPSS data file GSS2004.sav for the following e a!"les.

#. Overview of the ANOVA

Used to determine whether the mean of a given variable is statistically different formore than two different groups within the population

Used for interval or ratio scale data. (At least one of the variables must beinterval/ratio.)

The groups must be independent.

Groups are independent if there is no relationship between the objects or people ineach of the different groups.

This test can also be used to test for statistical differences in proportions ( ) if youhave a variable measured using a nominal scale with only two response categories!

but the variable must be coded using "#$ and "%$. (&ee handout on UnivariateAnalysis for an e'ample of this.)

##. Perfor!ing the ANOVA in SPSS

$ a!"le:

#s there a relationshi" %etween an individual&s level of edu'ation and their feelingsa%out a%ortion( )hat is* are one&s feelings a%out a%ortion a fun'tion of edu'ation(Please use the varia%les ABAN+ and ,$G-$$ for this e a!"le.

n this e'ample which variable is the dependent variable ************

+hat type of measurement scale is used to measure the dependent variable

+hich variable is the independent or grouping variable ************

%


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+hat type of measurement scale is used to measure the independent variable

,ow many groups do we have under the independent variable ************

Are these groups independent

-ven though both variables are nominal/ordinal scale variables we can use the A 0A as a testof proportions. That is! we can focus on the proportion of individuals who say yes. ,owever!the data is not coded correctly so we must fi' this first. 1lease recode A2A 3 so that we canuse a t4test of proportions. 5on6t forget to recode missing values! too! and to specify thecharacteristics of your new variable in the variable view after you have finished recoding.

%. 7or this research problem! what are the null and alternative hypotheses

, #8

, a8

The alternative hypothesis does not imply that all five mean values or proportions arestatistically different from one another but rather that at least one of the five is

statistically different from the others.

9. +hat is the appropriate test to test the null hypothesis *******************

:. ;alculate the test statistic

Analyze Compare Means One-Way ANOVA

< &elect the "5ependent =ist$ (the variable for which the mean will be calculated44must be measured using an interval or ratio scale ornominal scale if a test of proportions)

< &elect "7actor$ (the grouping/independent variable44 may be measured using anominal! ordinal! interval or ratio scale)

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Under the Options tab you can8 Generate descriptive statistics 1erform the =evene test for "homogeneity of variances test$ &pecify the treatment of missing values

Under the Options tab select "5escriptive$.

>. 5o we accept or reject the null hypothesis

?. 2ased on this what can we say +hat can we conclude

urther #nter"retation of the -esults:

+hile the A 0A test allows us to conclude that the five proportions are not statistically thesame! or rather that at least one of the proportions is different from the other four! it does not tellus which specific groups are statistically different from the others. 7or e'ample! is the

proportion of individuals who support abortion and have a high school diploma statisticallydifferent from the proportion of individuals who support abortion but have a college degree

Are all five statistically different from one another The A 0A test alone cannot answer this@uestion.

To get this information you need to use the Post Hoc tab under the A 0A test. Theappropriate 1ost ,oc test! however! depends upon whether or not the variances of the variousgroups are assumed to be e@ual or not.

/ow do you now if the varian'es are e1ual(

ust liBe the t4test for two independent means you use the test for homogeneity of

variances.

Under the Options tab you will find a bo' labeled "statistics$. n this bo' is the option",omogeneity of variance test$.

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The null and alternative hypotheses under this test are8

, #8 9% C 99 C 9: C 9> C 9? , a8 9% 99 9: 9> 9?

where the numbers refer to each of the five groups! respectively.

f the p4value is greater than the significance level then accept the null hypothesis of e@ualvariances.

f the p4value is smaller than the significance level! then reject the null hypothesis that the population variances are e@ual.

Given the results of the test for homogeneity of variances you then go bacB to8

Analyze Compare Means One-Way ANOVA

" &elect the Post Hoc tab.

nder this ta% you will find !any different tests. 3hi'h one should you 'hoose(

The actual choice of the post hoc test does not matter as long as you interpret theresults of the test for homogeneity of variances correctly and picB your test from theappropriate category8 "-@ual variances assumed$ or "-@ual variances not assumed$.

#n this e a!"le should we assu!e e1ual varian'es(

Given this* you 'an sele't any of the tests under e1ual varian'es not assu!ed.

Dun the 1ost ,oc test using Tamhane6s T9.

/ow do you inter"ret the results of the Post /o' test(

The starred values are statistically different at the ? percent significance level.

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Based on this what 'an we say( 3hat 'an we 'on'lude(

$ a!"le:

#s the ha""iness that a "erson feels in their !arriage a fun'tion of their level of edu'ation(

)hat is* are "eo"le !ore or less li ely to %e ha""y in their !arriage de"ending u"on thea!ount of edu'ation that they have( Please use the varia%les /AP A- and $, 5 for thise a!"le.

%. +hich variable in this e'ample is the8

ndependent variable8 ********************

5ependent variable8 *********************

9. +hat is the scale of measurement for the8

ndependent variable8 ********************

5ependent variable8 *********************

:. +hat are the null and alternative hypotheses

>. ;alculate the test statistic. 2e sure to checB "5escriptive$ and ",omogeneity of variancetest$ under Options .

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?. 5o we accept or reject the null hypothesis

E. &hould we assume e@ual variances

F. +hat conclusions can we draw

E

Bivariate Analysis in SPSS_ANOVA

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