One-Way ANOVA

One-Way ANOVA

One-way Analysis of Variance is a statistical technique for assessing if differences exist between two or more "groups". It analyzes comparisons of variance estimates tests to test whether the means of two or more independent groups are equal. Usually, though, comparing the means of two groups can be examined using an independent t-test so One-Way ANOVA is used to test for differences among three groups. The F-test and the t-test are equal and generate the same results when there are only two means to compare. It is one of the reasons that One-Way ANOVA is termed as an expansion of the independent t-test. Only quantitative data can be used for this test.

Statistical Assumptions of One-Way ANOVA

Following are the three assumptions of One-Way ANOVA.

Assumption of Normality: It is assumed that the dependent variable is distributed normally or is nearly distributed normally.

Homogeneity of Variance Assumption: The variance of dependent variable is assumed to be equal for all population.

Independence: It is assumed that the samples are independent.

Independent Variable and Dependent Variable

For the two hypotheses, we have established one dependent and one independent variable each.

Hypothesis:

Dependent Variable = Pregnant as a Result of Rape

Independent Variable = Condition of Health

Hypothesis

The One-Way ANOVA statistic tests the null hypothesis that samples in two or more groups are drawn from the same population.

Our Hypothesis is as follows:

Hypothesis

Null Hypothesis, H0

Alternate Hypothesis, H1

Hypothesis

Condition of health is different in Women who are pregnant due to rape.

Condition of health is not different in Women who are pregnant due to rape.

SPSS Output

Table 1.1: Test of Between-Subject Effects

Tests of Between-Subjects Effects

Dependent Variable: ABORTION IF WOMAN WANTS FOR ANY REASON

Source

Type III Sum of Squares

df

Mean Square

F

Sig.

Partial Eta Squared

Corrected Model

13.413a

1

13.413

62.169

.000

.119

Intercept

688.402

1

688.402

3190.770

.000

.874

ABHLTH

13.413

1

13.413

62.169

.000

.119

Error

99.460

461

.216

Total

1267.000

463

Corrected Total

112.873

462

a. R Squared = .119 (Adjusted R Squared = .117)

The dependent variable is Abortion if women want for any reason. Here Corrected Model, Intercept and independent variable (ABHLTH) have “Sig” values less than 0.05. The Partial ETA Squared is only 0.119.

Table 1.2: Estimated Marginal Means

WOMANS HEALTH SERIOUSLY ENDANGERED

Dependent Variable: ABORTION IF WOMAN WANTS FOR ANY REASON

WOMANS HEALTH SERIOUSLY ENDANGERED

Mean

Std. Error

95% Confidence Interval

Lower Bound

Upper Bound

YES

1.510

.023

1.464

1.556

NO

2.000

.058

1.887

2.113



Table 1.3: Levene's Test of Equality

Levene's Test of Equality of Error Variancesa

Dependent Variable: ABORTION IF WOMAN WANTS FOR ANY REASON

F

df1

df2

Sig.

160119.401

1

461

.000

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

a. Design: Intercept + ABHLTH

Table 2.1: Test of Between-Subjects Effects

Tests of Between-Subjects Effects

Dependent Variable: PREGNANT AS RESULT OF RAPE

Source

Type III Sum of Squares

df

Mean Square

F

Sig.

Partial Eta Squared

Corrected Model

.221a

3

.074

.401

.752

.003

Intercept

283.646

1

283.646

1543.954

.000

.768

HEALTH

.221

3

.074

.401

.752

.003

Error

85.611

466

.184

Total

809.000

470

Corrected Total

85.832

469

a. R Squared = .003 (Adjusted R Squared = -.004)

The dependent variable is “Pregnant as result of rape”. Here the “sig” of Corrected Model and Health is higher than 0.05.

Univariate Analysis of Variance

Between-Subjects Factors

Value Label

N

CONDITION OF HEALTH

1

EXCELLENT

130

2

GOOD

238

3

FAIR

86

4

POOR

16

Descriptive Statistics

Dependent Variable: PREGNANT AS RESULT OF RAPE

CONDITION OF HEALTH

Mean

Std. Deviation

N

EXCELLENT

1.25

.432

130

GOOD

1.23

.420

238

FAIR

1.28

.451

86

POOR

1.19

.403

16

Total

1.24

.428

470

Levene's Test of Equality of Error Variancesa

Dependent Variable: PREGNANT AS RESULT OF RAPE

F

df1

df2

Sig.

1.559

3

466

.199

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

a. Design: Intercept + HEALTH

Tests of Between-Subjects Effects

Dependent Variable: PREGNANT AS RESULT OF RAPE

Source

Type III Sum of Squares

df

Mean ...