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Running head: WEEK # 11 – SEX AND CLASS 1
Week # 11 – SEX and CLASS
Cristal Vázquez Dávila
Walden University
Week # 11 – SEX and CLASS
For this week application the Codebook for gss04student spps file.doc, was used to hand-picked the category of variable necessary for the analysis. The gss04student_corrected.sav data file was used to conduct a Chi-Square Test of Independence in SPSS of (SEX) and (CLASS) (Frankfort-Nachmias, Nachmias, & Deward, 2015; Green, S. B., & Salkind, N.J., 2014).
Analysis of Chi- Square Assumption
According to Green and Salkind (2014, p. 331) two assumptions of the data that must be met to ensure the results of the Chi-Square analysis can be generalized to the population. Being the first one that, the observations must be independent. This means that each cell count refers to different individuals or cases. No individuals or cases appear in more than one cell. Also there would be no link between people in each cell. The other assumption, is that the cell counts must be large enough to ensure the statistic’s distribution has the proper shape for this statistic in this case being a Chi- Square distribution. Therefore since all the expected cell counts are greater than 5 we can be relatively confident that this assumption was met (See table 1).
Analysis of Cell differ
In CLASS, we see the Adjusted Residuals for Lower Class of |-1.9| and |1.9| are not equal to or greater than 2. Therefore these cells are not different from expected. Among female or male of Lower Class, approximately equal numbers were male as were female. In Working Class we the Adjusted Residuals are also not equal to or greater than 2 |-1.5| and |1.5|. For that reason these cells are not different from expected. Among female or male of Working Class, approximately equal numbers were male as were female. In Middle Class, we see the Adjusted Residuals of |2.0| and |-2.0| are equal 2. This tells us that more male than expected and fewer female than expected in the Middle Class. More precisely, the Residuals indicate that 19.5 more male and -19.5 fewer female than expected are part of the Middle Class. (See table 1)
Table 1: SUBJECTIVE CLASS IDENTIFICATION (Cross tabulation)
SUBJECTIVE CLASS IDENTIFICATION * RESPONDENTS SEX Crosstabulation
RESPONDENTS SEX
Total
MALE
FEMALE
SUBJECTIVE CLASS IDENTIFICATION
LOWER CLASS
Count
39
64
103
Expected Count
48.5
54.5
103.0
% within SUBJECTIVE CLASS IDENTIFICATION
37.9%
62.1%
100.0%
% within RESPONDENTS SEX
5.5%
8.1%
6.9%
% of Total
2.6%
4.3%
6.9%
Residual
-9.5
9.5
Adjusted Residual
-1.9
1.9
WORKING CLASS
Count
297
365
662
Expected Count
311.5
350.5
662.0
% within SUBJECTIVE CLASS IDENTIFICATION
44.9%
55.1%
100.0%
% within RESPONDENTS SEX
42.2%
46.1%
44.3%
% of Total
19.9%
24.4%
44.3%
Residual
-14.5
14.5
Adjusted Residual
-1.5
1.5
MIDDLE CLASS
Count
340
341
681
Expected Count
320.5
360.5
681.0
% within SUBJECTIVE CLASS IDENTIFICATION
49.9%
50.1%
100.0%
% within RESPONDENTS SEX
48.3%
43.1%
45.5%
% of Total
22.7%
22.8%
45.5%
Residual
19.5
-19.5
Adjusted Residual
2.0
-2.0
UPPER CLASS
Count
28
22
50
Expected Count
23.5
26.5
50.0
% within SUBJECTIVE CLASS IDENTIFICATION
56.0%
44.0%
100.0%
% within RESPONDENTS SEX
4.0%
2.8%
3.3%
% of Total
1.9%
1.5%
3.3%
Residual
4.5
-4.5
Adjusted Residual
1.3
-1.3
Total
Count
704
792
1496
Expected Count
704.0
792.0
1496.0
% within SUBJECTIVE CLASS IDENTIFICATION
47.1%
52.9%
100.0%
% within RESPONDENTS SEX
100.0%
100.0%
100.0%
% of Total
47.1%
52.9%
100.0%
Analysis of results of the Chi-Square Test of Independence
The Chi-Square value was 8.628. The degrees of freedom are 3. The p value is equal to .035. Because the p value is less than a typical alpha level of .05, we can reject the null hypothesis that the variables are independent; the Chi-Square test is significant. CLASS (lower; working, middle, or, upper) was not independent of whether or not participants were male or female (SEX), 2(2, N = 1496) = 8.63, p = .035. (See table 2)
Table 2- Chi-Square Test
Chi-Square Tests
Value
df
Asymp. Sig. (2-sided)
Pearson Chi-Square
8.628a
3
.035
Likelihood Ratio
8.670
3
.034
Linear-by-Linear Association
8.533
1
.003
N of Valid Cases
1496
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 23.53.
Analysis of Effect size
Cramer’s V was = .076. This is considered a small effect. For Cramer’s V and Phi values near .10 are considered small, near .30 are considered medium, and near .50 are considered large. This is typically reported with the Chi-Square results. (See table Symmetric Measures in the Appendix)
The Relationship between SEX and CLASS
A Chi-Square test of Independence was conducted to explore the relationship between the variables SEX (male; female) and CLASS (lower, working, middle, and upper). Participants indicated if they were male or female (1 = Male, 2 = Female) and were categorized as one of eight categories (0 = NAP, 1 = Lower, 2 = Working, 3 = Middle, 4 = Upper, 5= No Class, 8= DK, 9= NA). The Chi-Square test of Independence was appropriate because both variables were categorical.
One assumption of the Chi-Square test is that the observations are independent (Green &
Salkind, 2014, p. 331). No participants belonged to more than one category. Therefore, this condition was met. A second assumption is that the statistic will have a distribution shaped like a
Chi-Square distribution. Because all expected cell counts were higher than five, this assumption was met as well.
The null hypothesis predicted that SEX and CLASS variables would be independent. The alternative hypothesis was that SEX and CLASS variable would not be independent. The Pearson Chi-Square test was significant, 2(2, N = 1496) =8.63, p = .035, Cramer’s V = .76. The null hypothesis was rejected and it was concluded that the variables were not independent, though the low value for Cramer’s V indicates a small effect size.
Figure 1 shows a clustered bar graph of the number of participants in each variable. In the Lower Class (N = 103) approximately equal numbers of Male (N = 39, 38%) and Female (N = 64, 62%). the Adjusted Residuals for Lower Class of |-1.9| and |1.9| are not equal to or greater than 2.
In Working Class (N= 662) 297 participants (43%) reported being Male and 365 (55%) reported that they were Female. The Adjusted Residuals are also not equal to or greater than 2 |-1.5| and |1.5|. However in Middle Class variable (N= 681) patterns reverses. In this variable Male (N= 340, 48%) and Females (N= 341, 43%), the Adjusted Residuals of |2.0| and |-2.0| are equal 2. This tells us that more male than expected and fewer female than expected in the Middle Class. More precisely, the Residuals indicate that 19.5 more male and -19.5 fewer female than expected are part of the Middle Class. When it comes to Upper Class participants (N= 50); male (N= 28, 56%) and female (N= 22, 44%). Upper class had an adjusted residuals of |-0.50| and |0.50| respectively. Because the absolute values of the adjusted residuals were lower than 2.00.
In summary, these results show a small, but significant relationship between SEX and CLASS. The relationship between Female and Male in Lower and Upper Class is observed. Also there is relatively equal results among Females and Males in Working and Middle Class variables.
References
Frankfort-Nachmias, C., & Nachmias, D. (2008). Research methods in the social sciences (7th ed.). New York: Worth.
Green, S. B., & Salkind, N. J. (2014). Using SPSS for Windows and Macintosh: Analyzing and understanding data (7th ed.). Upper Saddle River, NJ: Pearson.
Appendix SPSS Syntax and Output
GET
FILE=’C:UsersCristalDocumentswaldenRSCH 8200I-4WK11 Zip Filegss04student_corrected.sav’.
DATASET NAME DataSet1 WINDOW=FRONT.
CROSSTABS
/TABLES=CLASS BY SEX
/FORMAT=AVALUE TABLES
/STATISTICS=CHISQ PHI
/CELLS=COUNT EXPECTED ROW COLUMN TOTAL RESID ASRESID
/COUNT ROUND CASE
/BARCHART.
Crosstabs
[DataSet1] C:UsersCristalDocumentswaldenRSCH 8200I-4WK11 Zip Filegss04student_corrected.sav
Case Processing Summary
Cases
Valid
Missing
Total
N
Percent
N
Percent
N
Percent
SUBJECTIVE CLASS IDENTIFICATION * RESPONDENTS SEX
1496
99.7%
4
0.3%
1500
100.0%
SUBJECTIVE CLASS IDENTIFICATION * RESPONDENTS SEX Crosstabulation
RESPONDENTS SEX
Total
MALE
FEMALE
SUBJECTIVE CLASS IDENTIFICATION
LOWER CLASS
Count
39
64
103
Expected Count
48.5
54.5
103.0
% within SUBJECTIVE CLASS IDENTIFICATION
37.9%
62.1%
100.0%
% within RESPONDENTS SEX
5.5%
8.1%
6.9%
% of Total
2.6%
4.3%
6.9%
Residual
-9.5
9.5
Adjusted Residual
-1.9
1.9
WORKING CLASS
Count
297
365
662
Expected Count
311.5
350.5
662.0
% within SUBJECTIVE CLASS IDENTIFICATION
44.9%
55.1%
100.0%
% within RESPONDENTS SEX
42.2%
46.1%
44.3%
% of Total
19.9%
24.4%
44.3%
Residual
-14.5
14.5
Adjusted Residual
-1.5
1.5
MIDDLE CLASS
Count
340
341
681
Expected Count
320.5
360.5
681.0
% within SUBJECTIVE CLASS IDENTIFICATION
49.9%
50.1%
100.0%
% within RESPONDENTS SEX
48.3%
43.1%
45.5%
% of Total
22.7%
22.8%
45.5%
Residual
19.5
-19.5
Adjusted Residual
2.0
-2.0
UPPER CLASS
Count
28
22
50
Expected Count
23.5
26.5
50.0
% within SUBJECTIVE CLASS IDENTIFICATION
56.0%
44.0%
100.0%
% within RESPONDENTS SEX
4.0%
2.8%
3.3%
% of Total
1.9%
1.5%
3.3%
Residual
4.5
-4.5
Adjusted Residual
1.3
-1.3
Total
Count
704
792
1496
Expected Count
704.0
792.0
1496.0
% within SUBJECTIVE CLASS IDENTIFICATION
47.1%
52.9%
100.0%
% within RESPONDENTS SEX
100.0%
100.0%
100.0%
% of Total
47.1%
52.9%
100.0%
Chi-Square Tests
Value
df
Asymp. Sig. (2-sided)
Pearson Chi-Square
8.628a
3
.035
Likelihood Ratio
8.670
3
.034
Linear-by-Linear Association
8.533
1
.003
N of Valid Cases
1496
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 23.53.
Symmetric Measures
Value
Approx. Sig.
Nominal by Nominal
Phi
.076
.035
Cramer’s V
.076
.035
N of Valid Cases
1496
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