Using PROC ANOVA For One-Way Analysis of Variance

Using data from the Gapminder codebook: female employ rate  and urban rate. The data output was generated using SAS Studio.


Hypothesis formulation

Based on research review, it appears that while more women have joined the labor force thanks to urbanization, they have encountered several cultural and social obstacles that have negatively impacted their employment rates. It would be interesting to study the correlation between urbanization and the female employment rate in the Gapminder dataset. Hypothesis: Higher urbanization rates lead to lower female employment rates.

Summary of findings:

• The “Class Level Information” table lists the variables that appear in the CLASS statement, their levels, and the number of observations in the data set. There are 6 levels, 213 observations read and 173 observations used.
• The model degrees of freedom (DF) for the one-way analysis of variance are the number of levels minus 1; in this case, 6 - 1=5.
• The Corrected Total degrees of freedom are the total number of observations minus one; in this case 173 – 1 = 172. The sum of Model and Error degrees of freedom equal the Corrected Total.
• The overall F test is significant (F = 6.29; p < 0.0001), indicating that the model as a whole accounts for a significant portion of the variability in the female employ rate.
• The F test for the urbanization rate groups is significant, indicating that some contrast between the means for the different urbanization rate groups is different from zero. The null hypothesis is rejected.
• The Model and Urbanization Rate Groups F tests are identical, since “Urbanizationrategroup”  is the only term in the model.

Further analysis:

• The F test for Urbanization Rate Groups (F = 6.29; p < 0.0001) suggests that there are female employ rate distribution rate differences among the urbanization rate groups, but it does not reveal any information about the nature of the differences. A Mean comparison methods is used to gather further information using Tukey’s multiple comparisons test for pairwise differences between the urbanization rate group means.
• Significant differences in the female employ rate are observed between:
• Urbanization rate group 1 and groups 6, 4, and 5
• Urbanization rate group 2 and groups 6, 4, and 5

Code:

/** USING PROC ANOVA FOR ONE-WAY ANALYSIS OF VARIANCE **/

/** PROC ANOVA is used when the independent variable is categorical and the dependent variable is continuous. 

       Independent variable: UrbanizationRateGroup (categorized in the Binning/Grouping assignment)

Dependent: Female employ rate (continuous variable)

**/

PROC ANOVA  DATA=NEW;

CLASS UrbanizationRateGroup; /** defines the categorical variable **/

MODEL femaleemployrate = UrbanizationRateGroup; /** defines the dependent variable  & effects **/  

RUN;

/** Using the TUKEY procedure to further understand differences in the categorical variable **/

PROC ANOVA  DATA=NEW;

CLASS UrbanizationRateGroup; 

MODEL femaleemployrate = UrbanizationRateGroup; 

    MEANS UrbanizationRateGroup / TUKEY;    / ** studentized range test **/

RUN;

Results:

                                                                Urbanization Rate Vertical Bar Chart

The ANOVA Procedure

Class Level Information
Class	Levels	Values
UrbanizationRateGroup	6	1 2 3 4 5 6

Number of Observations Read	213
Number of Observations Used	173

The ANOVA Procedure

Dependent Variable: femaleemployrate

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	5	5948.15795	1189.63159	6.29	<.0001
Error	167	31599.31337	189.21745
Corrected Total	172	37547.47132

R-Square	Coeff Var	Root MSE	femaleemployrate Mean
0.158417	28.80604	13.75563	47.75260

Source	DF	Anova SS	Mean Square	F Value	Pr > F
UrbanizationRateGrou	5	5948.157954	1189.631591	6.29	<.0001

The ANOVA Procedure

Tukey's Studentized Range (HSD) Test for femaleemployrate

Note:This test controls the Type I experimentwise error rate.

Alpha	0.05
Error Degrees of Freedom	167
Error Mean Square	189.2174
Critical Value of Studentized Range	4.07731

Comparisons significant at the 0.05 level are indicated by ***.
UrbanizationRateGroup Comparison	Difference Between Means	Simultaneous 95% Confidence Limits
1 - 2	13.615	-7.742	34.972
1 - 3	20.462	-0.648	41.572
1 - 6	25.280	4.459	46.102	***
1 - 4	26.208	5.098	47.318	***
1 - 5	27.537	6.845	48.229	***
2 - 1	-13.615	-34.972	7.742
2 - 3	6.847	-3.893	17.586
2 - 6	11.665	1.504	21.826	***
2 - 4	12.593	1.854	23.333	***
2 - 5	13.922	4.030	23.815	***
3 - 1	-20.462	-41.572	0.648
3 - 2	-6.847	-17.586	3.893
3 - 6	4.818	-4.813	14.449
3 - 4	5.747	-4.493	15.987
3 - 5	7.076	-2.272	16.423
6 - 1	-25.280	-46.102	-4.459	***
6 - 2	-11.665	-21.826	-1.504	***
6 - 3	-4.818	-14.449	4.813
6 - 4	0.928	-8.703	10.559
6 - 5	2.257	-6.419	10.934
4 - 1	-26.208	-47.318	-5.098	***
4 - 2	-12.593	-23.333	-1.854	***
4 - 3	-5.747	-15.987	4.493
4 - 6	-0.928	-10.559	8.703
4 - 5	1.329	-8.019	10.677
5 - 1	-27.537	-48.229	-6.845	***
5 - 2	-13.922	-23.815	-4.030	***
5 - 3	-7.076	-16.423	2.272
5 - 6	-2.257	-10.934	6.419
5 - 4	-1.329	-10.677	8.019