The purpose of this paper is to state the statistical assumptions of the oneway analysis of variance with SPSS, select independent and dependent variables, develop the null and alternative hypotheses, calculate an ANOVA, and include a post hoc test, report on the p value, interpret the confidence interval, and reject or retain the null hypothesis. In addition, syntax and output files will be presented with an analysis of the results.
Statistical Assumptions of this Test
The statistical assumptions of this test are that the observations within each sample must be independent of each other; the populations from which the samples are drawn are normal; and the populations have equal variances (Green & Salkind, 2014).
The independent variable chosen for this assignment was race, which is a variable with three or more levels that include White, Black, and Other Races. The dependent variable is income.
The null hypothesis is:
H0: µ1 = µ2 = µ3; There are no differences in income between groups (different races). Race does not have a significant effect on income.
An alternative hypothesis is:
H0: µ1 ≠: µ2 ≠ µ3; There is a difference among the three groups. Race has an effect on income.
Interpretation of Tests
A oneway analysis of variance was conducted to evaluate the relationship between race and income. The independent variable, race included three levels: White, Black, and Other Races. The dependent variable was the level of income. The ANOVA was significant at the .05 level, F(2, 1338) = 13.75, p = 0. Since p > .05, we cannot reject the null hypothesis, which states that race has no effect on income. In this case, race has an effect on income. The strength of the relationship between income and race as assessed by ɳ2, was weak (.02), with race accounting for 2% of the variance of the dependent variable.
I conducted followup tests to evaluate pairwise differences among the means. Because the variances among the three groups ranged from 4.74 to 8.49, I decided not to assume that the variances were homogeneous and conducted post hoc comparisons with the use of the Dunnett's C test, a test that does not assume equal variances among the three groups. There was a significant difference among the means. Therefore, race significantly affects income. According to the Tukey HSD and Dunnett C Post Hoc tests, there was not a significant difference between the incomes of White and Black participants, although there was a significant difference between the incomes of Whites and other races and between the incomes of Blacks and other races.
SPSS Syntax and Output Files
UNIANOVA INCOME
BY RACE
/METHOD=SSTYPE(3)
/INTERCEPT=INCLUDE
/POSTHOC=RACE(TUKEY QREGW C)
/EMMEANS=TABLES(RACE)
/PRINT=ETASQ HOMOGENEITY DESCRIPTIVE
/CRITERIA=ALPHA(.05)
/DESIGN=RACE.
Univariate
Analysis of Variance

[DataSet1]
C:\Users\Deborah\Desktop\Stats\gss04student_corrrected.sav
BetweenSubjects
Factors



Value
Label

N


RACE OF RESPONDENT

1

WHITE

1052

2

BLACK

194


3

OTHER

95

Descriptive
Statistics


Dependent Variable: TOTAL FAMILY INCOME


RACE OF RESPONDENT

Mean

Std.
Deviation

N


WHITE

11.06

2.177

1052


BLACK

10.12

2.913

194


OTHER

10.74

2.606

95


Total

10.90

2.351

1341


Levene's
Test of Equality of Error Variances^{a}


Dependent Variable: TOTAL FAMILY INCOME


F

df1

df2

Sig.


15.598

2

1338

.000


Tests the null hypothesis that the error variance of the
dependent variable is equal across groups.


a. Design: Intercept + RACE


Tests of
BetweenSubjects Effects


Dependent Variable: TOTAL FAMILY INCOME


Source

Type III
Sum of Squares

df

Mean
Square

F

Sig.

Partial
Eta Squared

Corrected Model

149.163^{a}

2

74.582

13.746

.000

.020

Intercept

61258.850

1

61258.850

11290.745

.000

.894

RACE

149.163

2

74.582

13.746

.000

.020

Error

7259.427

1338

5.426




Total

166844.000

1341





Corrected Total

7408.591

1340





a. R Squared = .020 (Adjusted R Squared = .019)

Estimated
Marginal Means
RACE OF
RESPONDENT


Dependent Variable: TOTAL FAMILY INCOME


RACE OF RESPONDENT

Mean

Std.
Error

95%
Confidence Interval


Lower
Bound

Upper
Bound


WHITE

11.064

.072

10.923

11.205

BLACK

10.119

.167

9.790

10.447

OTHER

10.737

.239

10.268

11.206

Post Hoc
Tests
RACE OF
RESPONDENT
Multiple
Comparisons


Dependent Variable: TOTAL FAMILY INCOME



(I) RACE OF RESPONDENT

(J) RACE OF RESPONDENT

Mean
Difference (IJ)

Std.
Error

Sig.

95%
Confidence Interval



Lower
Bound

Upper
Bound


Tukey HSD

WHITE

BLACK

.95^{*}

.182

.000

.52

1.37

OTHER

.33

.250

.390

.26

.91


BLACK

WHITE

.95^{*}

.182

.000

1.37

.52


OTHER

.62

.292

.086

1.30

.07


OTHER

WHITE

.33

.250

.390

.91

.26


BLACK

.62

.292

.086

.07

1.30


Dunnett C

WHITE

BLACK

.95^{*}

.220


.43

1.46

OTHER

.33

.276


.33

.98


BLACK

WHITE

.95^{*}

.220


1.46

.43


OTHER

.62

.339


1.42

.19


OTHER

WHITE

.33

.276


.98

.33


BLACK

.62

.339


.19

1.42


Based on observed means.
The error term is Mean
Square(Error) = 5.426.


*. The mean difference is significant at the .05 level.

Homogeneous
Subsets
TOTAL
FAMILY INCOME



RACE OF RESPONDENT

N

Subset



1

2


Tukey HSD^{a,b,c}

BLACK

194

10.12


OTHER

95


10.74


WHITE

1052


11.06


Sig.


1.000

.377


RyanEinotGabrielWelsch Range^{c}

BLACK

194

10.12


OTHER

95

10.74

10.74


WHITE

1052


11.06


Sig.


.068

.334


Means for groups in homogeneous subsets are displayed.
Based on observed means.
The error term is Mean
Square(Error) = 5.426.


a. Uses Harmonic Mean Sample Size = 180.380.


b. The group sizes are unequal. The harmonic mean of the group
sizes is used. Type I error levels are not guaranteed.


c. Alpha = .05.

References
Green, S. B., & Salkind, N. J. (2014). Using SPSS for Windows and Macintosh: Analyzing and understanding data (7th ed.). Upper Saddle River, NJ: Pearson Education.




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